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Week/
                                                                                                                                                         Teaching
 Learning        Learning objectives             Learning outcomes                 Suggested activities                 Points to note
                                                                                                                                                      Strategies/ Skills
   Area
                                                                                                                 .

QUADRATIC   1. Understand the concept     1.1 Recognise a quadratic            Use graphing                                                             Noble value :
EQUATIONS
               of quadratic equation          equation and express it in                                                                                Cooperation
                                                                               calculators      or computer
               and its roots.                 general form.
                                                                               software      such    as    the                                              TGA:
                                                                               Geometer’s      Sketchpad and                                             Flashcard
                                                                               spreadsheet    to explore the
                                                                                                                                                         Pedagogy :
                                                                               concept        of     quadratic
                                                                                                                                                     Activity/Cooperativ
   Week                                   1.2 Determine whether a given                                                                                  e Learning
                                                                               equations.
   1&2                                        value is the root of a                                                                                       CCTS:
                                              quadratic equation by                                                                                    Classification.
                                               a) substitution;
                                               b) inspection.

                                                                                                                 Questions for 1.2(b) are given
                                          1.3   Determine roots of quadratic                                     in the form of (x + a)(x + b) =
                                                equations by trial and                                           0; a and b are numerical
                                                improvement method.                                              values.

                                                                                                                 Discuss when
                                                                                                                 (x p)(x q) = 0, hence x – p =           Value :
            2.     Understand the         2.1 Determine the roots of a
                                                                                                                 0 or                                   Cooperation
                   concept of quadratic       quadratic equation by
                                                                                                                 x – q = 0. Include case when               TGA :
                   equations.                 a)   factorisation;
                                                                                                                 p = q.                                 Manila Card
                                              b) completing the square
                                              c) using the formula.                                              Derivation of formula for               Pedagogy :
                                                                                                                 2.1c is not required.                Inquiry Finding,
                                                                                                                                                       Constructisme
                                                                                                                 If x=p and x=q are the roots,
                                                                                                                                                           CCTS:
                                                                                                                 then the quadratic equation is
                                                                                                                                                      Refresh idea and
                                                                                                                 (xp)(xq)=0, that is
                                                                                                                                                        trial & error
                                                                                                                 x2(pq)xpq=0.

                                                                               2
Week/
                                                                                                                                                     Teaching
 Learning   Learning objectives            Learning outcomes                  Suggested activities                  Points to note
                                                                                                                                                  Strategies/ Skills
   Area
                                    2.2 Form a quadratic equation                                          Involve the use of:                      Pedagogy:
                                        from given roots.                                                            −b                    c     Mastery Learning
                                                                                                           I ++=
                                                                                                                      and            =
                                                                                                                                            ,
                                                                                                                     a                     a
                                                                                                           Where Wand       are roots of
                                                                                                           the quadratic equation
                                                                                                           ax2 +bx +c =0

QUADRATIC    1. Understand the      1.1 Recognise quadratic functions     Use computer software or         Discuss the general shape of          Mastery Learning
FUNCTIONS       concept of          1.2 Plot quadratic functions graphs   graphing calculator.             quadratic function.
  Week          quadratic functions     a) based on given tabulated       (ex; GSP, Graphmatica or         Introduce the term of                 Contextual
   3&4          and their graphs            values                        Microsoft Excel to explore       parabola, minimum,
                                       b) by tabulating                   the graphs of quadratic          maximum point and axis of
                                           values based on                functions)                       symmetry for quadratic
                                           given functions                                                 curves.
                                                                          Use example of everyday
                                    1.3 Recognise shapes of graphs        situations to introduce graphs   Discuss cases where a > 0
                                       of quadratic functions             of quadratic functions.          and a < 0 for
                                                                                                           f ( x ) = ax 2 + bx + c
                                    1.4 Relate the position of
                                         quadratic function graphs
                                         with types of roots for
                                        f (x) = 0.


             2. Find maximum and    2.1 Determine the maximum or          Use computer software or         Discuss the general form of           Mastery Learning
             minimum values of           minimum value of quadratic       graphing calculator.             completing the square
             quadratic functions         function by completing the       (ex; GSP, Graphmatica or         f ( x) = a ( x + p) 2 + q             Self-Access Learning
                                         square                           Microsoft Excel to explore
                                                                          the graphs of quadratic
                                                                          functions)




                                                                          3
Week/
                                                                                                                                                      Teaching
 Learning        Learning objectives               Learning outcomes                  Suggested activities              Points to note
                                                                                                                                                   Strategies/ Skills
   Area

               3. Sketch graphs of           3.1 Sketch quadratic functions by    Use graphing calculator or     Emphasis the marking of          Contextual
                  quadratic functions.          determining the maximum or        dynamic geometry software      maximum or minimum point
                                                minimum point and two other       such as the GSP or             and two other points on the
                                                points.                           Graphmatica to reinforce the   graphs drawn or by finding
                                                                                  understanding of graphs of     the axis of symmetry and the
                                                                                  quadratic functions.           intersection with the y – axis
                                                                                                                 Determine other points by
                                                                                                                 finding the intersection with
                                                                                                                 x-axis (if it exists )


               4. Understand and use the     4.1 Determine the ranges of values   Use graphing calculator or     Emphasis on sketching            Contextual
                  concept of quadratic          of x that satisfies quadratic     dynamic geometry software      graphs and use number lines
                  inequalities.                 inequalities                      such as the GSP or             when necessary.
                                                                                  Graphmatica to reinforce the
                                                                                  understanding of graphs of
                                                                                  quadratic inequalities
                                                                                                                                                  Problem solving,
SIMULTANEOUS   Students will be taught to:   Students will be able to :           Use graphing calculator or                                      discovery method,
EQUATIONS                                                                         dynamic geometry software                                       trial and
               1. Solve simultaneous         1.1 Solve simultaneous equations     such as the Geometers          Limit non linear equations up    improvement method.
   Week 5      equations in two                  using the the substitution       Sketchpad to explore the       to second degree only
               unknowns: one linear              method                           concept of simultaneous                                         ICT, relating,
               equation and one non -                                             equations                                                       reasoning,
               linear equation.                                                                                                                   Mathematical
                                             1.2 Solve simultaneous equations     Use examples in real life                                       Communication,
                                                 involving real life situations   situations such as area,                                        Mathematical
                                                                                  perimeter and others.                                           Connections


FUNCTIONS                                                                                                                                         Contextual
                                             1.1 Represent                        Use pictures, role-play and    Discuss the idea of set and
               1. Understanding the
                                                                                  computer software to           introduce set notation.
   Week        concept of relations.              relations using
                                                                                  introduce the concept of
                                                                                  4
Week/
                                                                                                                                Teaching
Learning     Learning objectives          Learning outcomes            Suggested activities         Points to note
                                                                                                                             Strategies/ Skills
  Area
6 , 7 &8                                 a)arrow diagrams          relations.
                                         b) ordered pairs
                                         c) graphs

                                   1.2 Identify domain,
                                       codomain, object,
                                       image and range
                                       of a relation.

                                   1.3 Classify a relation
                                       shown on a
                                       mapped diagram
                                       as: one to one,
                                       many to one, one
                                       to many or many
                                       to many relation.

                                                                                              Represent functions using
           2. Understand           2.1   Recognise                                            arrow diagrams, ordered
              the concept                functions as a special    Use graphing calculators                                 Cooperative
                                                                                              pairs or graphs.
              of functions               relation                  and computer software to                                 learning
                                                                   explore the image of       e.g. f : x → 2x
                                                                   functions.                      f (x) = 2x
                                   2.2 Express functions using
                                                                                              "f : x → 2x" is read as
                                       function notation.
                                                                                              "function f maps x to 2x".
                                   2.3 Determine domain, object,                              f (x) = 2x is read as “2x
                                       image and range of a                                   is the image of x under the
                                       function.                                              function f ”.
                                                                                              Include examples of
                                   2.4 Determine the image of a                               functions that are not
                                       function given the object                              mathematically based.
                                                                   5
Week/
                                                                                                                                              Teaching
Learning         Learning objectives            Learning outcomes                Suggested activities             Points to note
                                                                                                                                           Strategies/ Skills
  Area
                                              and vice versa.

                                                                                                            Examples of functions
                                                                                                            include algebraic (linear
                                                                                                            and quadratic),
                                                                                                            trigonometric and absolute
                                                                                                            value.
                                                                                                            Define and sketch absolute
                                                                                                            value functions.
                        3. Understand     3.1 Determine composition of
                  the                     two functions.                       Use arrow diagrams or        Involve algebraic functions   Mastery learning
                           concept        3.2 Determine the image of           algebraic method to          only.
                                          composite functions given the
                           of composite                                        determine composite
                                          object and vice versa.
                           functions.                                          functions.
                                          3.3 Determine one                                                 Images of composite
                                              of the functions in a                                         functions include a range
                                                                                                            of values. (Limit to linear
                                                                                                            composite functions)

           b)                                 given composite                                               .
                                              function given the
                                              other related
                                              function.
           c)                             4.1 Find the object by inverse       Use sketches of graphs to    Limit to algebraic
                                                                                                                                          Mastery learning
           d) 4. Understand the               mapping given its image          show the relationship        functions.
              concept of inverse              and function.                    between a function and its   Exclude inverse of
              functions.                                                       inverse
                                          4.2 Determine inverse                                             composite functions.
                                              functions using algebra.                                      Emphasise that inverse of a

                                                                           6
Week/
                                                                                                                                   Teaching
Learning        Learning objectives        Learning outcomes               Suggested activities         Points to note
                                                                                                                                Strategies/ Skills
  Area
                                      4.3 Determine and state the                                 function is not necessarily
                                          condition for existence of                              a function.
                                          an inverse function.

   9       e)                                                                  Test 1




                                                                       7
Week/
                                                                                                                                                      Teaching
 Learning       Learning objectives              Learning outcomes                        Suggested activities           Points to note
                                                                                                                                                   Strategies/ Skills
   Area
                                                                                                                                                  Teaching
              1. Understand and use       1.1 Find the value of numbers               •    Use examples of real-   Discuss zero index and         Aids/materials
INDICES AND
LOGARITHMS       the concept of indices       given in the form of:                        life situations to      negative indices.              Scientific calculator,
                 and laws of indices to       a) integer indices.                          introduce the concept                                  Geometer’s
  Week 10        solve problems.              b) fractional indices.                       of indices.                                            Sketchpad, geometric
                                                                                                                                                  set
                                          1.2 Use laws of indices to find             •    Use computer
                                              the value of numbers in                      software such as the                                   CCTS
                                              index form that are                          spreadsheet to                                         Identifying
                                                                                                                                                  relationship
                                              multiplied, divided or                       enhance the
                                              raised to a power.                           understanding of                                       Teaching Strategies
                                                                                           indices.                                               Mastery Learning
                                          1.3   Use laws of indices to                                                                            Multiple intelligent
                                                simplify algebraic                                                                                Contextual learning
                                                expressions.

              2. Understand and use
                                          2.1 Express equation in index               •    Use scientific          xplain definition of
                                              form to logarithm form and                   calculators to          logarithm.
                 the concept of
                                              vice versa.                                  enhance the             N = ax ; loga N = x with a >
                 logarithms and laws
                 of logarithms to solve                                                    understanding of the    0, a ≠ 1.
                                          2.2 Find  logarithm            of   a            concept of logarithm.   Emphasise that:
                 problems
                                              number.                                                              loga 1 = 0; loga a = 1.

                                          2.3 Find logarithm of numbers                                            Emphasise that:
                                              by     using    laws   of                                            a) logarithm of negative
                                              logarithms.                                                             numbers is undefined;
                                                                                                                   b) logarithm of zero is
                                                                                                                      undefined.
                                          2.4 Simplify logarithmic
                                              expressions to the simplest                                          Discuss cases where the
                                              form.                                                                given number is in
                                                                                                                   a) index form
                                                                                                                   b) numerical form.
                                                                                                                   Discuss laws of logarithms
                                                                                  8
Week/
                                                                                                                                    Teaching
Learning     Learning objectives            Learning outcomes              Suggested activities          Points to note
                                                                                                                                 Strategies/ Skills
  Area
Week 11                               3.1 Find the logarithm of a                                 Discuss:                      Vocabulary
           3 Understand and use
                                          number by changing the                                               1
             the change of base of                                                                loga b =
                                          base of the logarithm to a                                         logb a
             logarithms to solve                                                                                                base
                                          suitable base.
             problems.
                                                                                                                                integer indices
                                      3.2 Solve problems involving                                                              fractional indices
                                      the change of base and laws of
                                                                                                                                index form
                                      logarithms.
  13                                  4.1 Solve equations involving                               Equations that involve        raised to a power
           4. Solve equations
                                           indices.                                               indices and logarithms are    law of indices
              involving indices and
                                                                                                  limited to equations with
              logarithms.
                                      4.2 Solve equations involving                               single solution only.
                                          logarithms.                                             Solve equations involving     index form
                                                                                                  indices by:
                                                                                                                                logarithm form
                                                                                                   a) comparison of indices
                                                                                                       and bases;               logarithm
                                                                                                                                undefined
                                                                                                  b)         using logarithms




                                                                       9
Week/
                                                                                                                                                    Teaching
 Learning     Learning objectives              Learning outcomes                   Suggested activities               Points to note
                                                                                                                                                 Strategies/ Skills
   Area
                                                                                                                                                Moral Values
            1. Find distance between    1.1                                    Use examples of real-life       Use the Pythagoras’ Theorem
COORDINAT                                                                                                                                       Cooperative
               two points                                                      situations to find the          to find the formula for
GEOMETRY                                Find the distance between two                                                                           Patriotism
                                                                               distance between two points.    distance between two points.     Respect
                                        points using formula
 Week 14
                                          ( x1 − x2 ) 2 + ( y1 − y2 ) 2                                                                         Teaching Aids/
                                                                                                                                                Material
                                                                                                                                                Chart
                                                                                                                                                Arrow diagram
                                                                                                                                                CCTS
            2. Understand the concept   2.1 Find the midpoint of two                                           Limit to cases where m and n     Analogy
               of division of a line        given points.                                                      are positive.                    Relations
               segment.                                                                                                                         Imagine
                                                                                                               Derivation of the formula
                                        2.2      Find the coordinates of a                                      nx1 + mx2 ny1 + my2           Teaching Strategies
                                                                                                                         ,           is not
                                        point that divides a line according                                     m+n         m+n               Contextual
                                        to a given ratio                                                       required.
                                         m : n.

                                                                                                                                                Moral Values
            3. Find areas of polygons   3.1 Find the area of a triangle        Use dynamic geometry            Limit to numerical values.
  Week                                                                                                                                          Cooperative
                                            based on the area of specific      software such as the            Emphasise the relationship
   15
                                            geometrical shapes.                Geometer’s Sketchpad to         between the sign of the value    Teaching Aids/
                                                                               explore the concept of area     for area obtained with the       Material
                                                                               of polygons.                    order of the vertices used.      Grid Board
                                        3.2 Find the area of a triangle by
                                                                               Use x2 x3 x1
                                                                               1 x1                            Emphasise that when the area
                                            using formula.                                                                                      Teaching Strategies
                                                                               2 y1 y 2 y 3 y 1                of polygon is 0, the given
                                              1 x1 x2 x3 x1                                                                                     Contextual
                                                                                                               points are collinear.
                                              2 y1 y 2 y 3 y1                                                                                   Generate ideas
                                                                               for substitution of
                                                                                                                                                Thinking Skills
                                        3.3 Find the area of a                 coordinates into the formula.
                                            quadrilateral using formula




                                                                              10
Week/
                                                                                                                                                      Teaching
Learning     Learning objectives                 Learning outcomes                   Suggested activities               Points to note
                                                                                                                                                   Strategies/ Skills
  Area
                                                                                                                                                  Moral Values
           4. Understands use the        4.1                                     Use dynamic Geometry                                             Honesty
              concept of equation of a                                           software such as the
                                         Determine the x – intercept and y-                                                                       Accuracy
              straight line.                                                     Geometer’s Sketchpad to
                                         intercept of a line
                                                                                 explore the concept of                                           Teaching Aids/
                                         4.2
                                                                                 equation of a straight lines.                                    Material
                                         Find the gradient of a straight line                                                                     Charts, Graphical
                                         that passes through two points.                                                                          Calculator
                                                                                                                                                  Charts
                                                                                                                                                  Teaching Strategies
                                         4.3 Find the gradient of a staright                                     Answer for learning
                                                                                                                                                  Mastery Learning
                                              line using the x-intercept and                                     outcomes 4.4 (a) and 4.4(b)
                                                                                                                                                  Contextual Approach
                                              y-intercept                                                        must be stated in the simplest
                                                                                                                                                  Mastery Approach
                                                                                                                 form
                                         4.4Find the equation of a straight
                                         line given:                                                             x y
                                                                                                                  + = 1 involve changing
                                               a) gradient and one point                                         a b
                                                                                                                 the equation into gradient
                                               b) two point                                                       y = mx + c and intercept
                                               c) x-intercept and y-intercept                                    form
                                         4.5 Detemine gradient and                                               ax + by + c = 0
                                         intercepts of a straight line given
                                         the equation.                                                                                            Moral Values
                                         4.6 Change the equation of a                                                                             Accuracy
                                         straight line to the general form
                                                                                                                                                  Teaching Aids/
                                         4.7 Find the point of intesection of                                    Solve simultaneous linear        Material
                                         two lines.                                                              equations using the graph        Graph paper
                                                                                                                 method.
                                                                                                                                                  Teaching Strategies
                                                                                                                                                  Self Access Learning




                                                                                11
Week/
                                                                                                                                                     Teaching
Learning     Learning objectives               Learning outcomes                     Suggested activities               Points to note
                                                                                                                                                  Strategies/ Skills
  Area
   16      5.Understand and use the                                              Use example of real-life
                                                                                                                                                 Moral Values
                                         5.1 Determine whether two straight                                       Emphasize that for parallel    Cooperation
              concept of parallel and    lines are parallel when gradients of    situations to explore parallel   lines:                         Gratitude
              perpendicular lines.       both lines are known and vice           end perpendicular lines.
                                                                                                                  m1 = m2                        Careful
                                         versa                                                                                                   Systematic
                                         5.2 Find equation of a straight line                                     Emphasize that for
                                                                                                                  perpendicular lines :          Teaching Aids/
                                         that passes through a fixed point       Use graphic calculator and                                      Material
                                         and parallel to a given line.                                            m1 m2 = −1
                                                                                 dynamic geometry software                                       Exact Systematic
                                         5.3 Determine whether two straight      such as Geometer’s                                              ICT
                                                                                 Sketchpad to explore the                                        Grid Board
                                         lines are perpendicular when
                                                                                 concept of parallel and
                                         gradients of both lines are known       perpendicular lines.
                                                                                                                  Derivation of m1 m 2 = −1 is   Teaching Strategies
                                         and vice versa.                                                                                         Self Access Learning
                                                                                                                  not required.                  Learn How to Study
                                         5.4 Determine the equation of a
                                         straight line that passes through a                                                                     Multiple Intelligent
                                         fixed point and perpendicular to a                                                                      Constructivism
                                                                                                                                                 approach
                                         given line.
                                         5.5 Solve problems involving
                                         equations of straight lines.
                                                                                                                                                 Moral Values
           6. Understand and use the     6.1 Find the equations of locus that    Use examples of real-life                                       Cooperation
              concept of equation of     satisfies the condition if:             situations to explore equation                                  Gratitude
              locus involving distance                                           of locus involving distance
                                         a) The distance of a moving point                                                                       Careful
              between two points.                                                between two points.
                                         from a fixed point is constant;                                                                         Systematic

                                         b) The ratio of the distances of a                                                                      Teaching Aids/
                                         moving point from two fixed             Use graphic calculator and                                      Material
                                         points is constant.                     dynamic geometry software                                       Exact Systematic
                                                                                 such as Geometer’s                                              ICT
                                         6.2 Solve problems involving loci.                                                                      Grid Board
                                                                                 Sketchpad to explore the
                                                                                 concept of loci.

                                                                                12
Week/
                                                                                                                                      Teaching
Learning        Learning objectives        Learning outcomes               Suggested activities              Points to note
                                                                                                                                   Strategies/ Skills
  Area
 17
           1.     Understand and use 1.1 Calculate the mean of         •   Use scientific              Discuss grouped data and   Moral Values
                the concept of           ungrouped data.                   calculators, graphing       ungrouped data.            Cooperation
                measures of central                                        calculators and                                        Gratitude
                tendency to solve    1.2 Determine the mode of             spreadsheets to                                        Careful
                problems.
                                         ungrouped data.                   explore measures of                                    Systematic
                                                                           central tendency.
                                      1.3 Determine the median of                                                                 Teaching Aids/
                                                                       •   Students collect data                                  Material
                                          ungrouped data.
                                                                           from real-life situations                              Exact Systematic
                                                                           to investigate                                         ICT
                                      1.4 Determine the modal class
                                                                           measures of central                                    Grid Board
                                          of grouped data from                                         Involve uniform class
                                                                           tendency.                   intervals only.
                                          frequency distribution                                                                  Teaching Strategies
                                          tables.                                                                                 Self Access Learning
                                                                                                                                  Learn How to Study
                                      1.5 Find the mode from                                                                      Multiple Intelligent
                                          histograms.                                                                             Constructivism
                                                                                                                                  approach

                                      1.6 Calculate the mean of                                        Derivation of the median   Teaching Strategies
                                          grouped data.                                                formula is not required.
                                                                                                                                  Self Access Learning
                                                                                                                                  Learn How to Study
                                      1.7 Calculate the median of
                                                                                                                                  Multiple Intelligent
                                          grouped data from
                                                                                                                                  Constructivism
                                          cumulative frequency                                                                    approach
                                          distribution tables.

                                      1.8 Estimate the median of
                                          grouped data from an
                                          ogive.                                                       Ogive is also known as
                                      1.9 Determine the effects on                                     cumulative frequency
                                          mode, median and mean                                        curve.
                                                                      13
Week/
                                                                                                                                      Teaching
Learning    Learning objectives           Learning outcomes                 Suggested activities         Points to note
                                                                                                                                   Strategies/ Skills
  Area
                                        for a set of data when:
                                         a) each data is changed
                                             uniformly;
                                         b) extreme values exist;                                  Involve grouped and
                                         c) certain data is added                                  ungrouped data
                                             or removed.
                                    1.10 Determine the most
                                         suitable measure of central
                                         tendency for given data.
   18                                                                                                                             Vocabulary
           2. Understand and use    2.1 Find the range of
              the concept of            ungrouped data.
              measures of                                                                                                              measure of
              dispersion to solve   2.2 Find the interquartile range                                                                   central
              problems.                                                                                                                tendency
                                        of ungrouped data.
                                                                                                                                  mean
                                    2.3 Find the range of grouped                                                                 mode
                                        data.
                                                                                                                                  median
                                    2.4 Find the interquartile range                               Determine upper and lower      ungrouped data
                                        of grouped data from the                                   quartiles by using the first
                                        cumulative frequency                                                                      frequency
                                                                                                   principle.
                                        table.                                                                                    distribution table
                                                                                                                                  modal class
                                    2.5 Determine the interquartile                                                               uniform class
                                        range of grouped data                                                                     interval
                                        from an ogive.                                                                            histogram

                                    2.6 Determine the variance of
                                        a)    ungrouped data;
                                        b)    grouped data.


                                                                       14
Week/
                                                                                                                           Teaching
Learning   Learning objectives         Learning outcomes                Suggested activities    Points to note
                                                                                                                        Strategies/ Skills
  Area
                                 2.7 Determine the standard
                                     deviation of:
                                     a) ungrouped data
                                     b)     grouped data.

                                 2.8 Determine the effects on                                  Emphasise that
                                                                                               comparison between
                                     range, interquartile range,
                                                                                               two sets of data using
                                     variance and standard                                     only measures of
                                     deviation for a set of data                               central tendency is
                                     when:                                                     not sufficient.
                                      a) each data is changed
                                         uniformly;
                                      b) extreme values exist;
                                      c) certain data is added
                                         or removed.

                                 2.9 Compare measures of
                                     central tendency and
                                     dispersion between two
                                     sets of data.

                                                 Mid Term Examination Week 19 - 20




                                                                   15
Week/
                                                                                                                                                    Teaching
 Learning     Learning objectives               Learning outcomes                   Suggested activities               Points to note
                                                                                                                                                 Strategies/ Skills
   Area

CIRCULAR    Students will be taught to:   Students will be able to:            Use dynamic geometry             Discuss the definition of one   Moral Values
MEASURES                                                                       software such as Geometer’s      radian.                         Rational, patience
                1. Understand the         Convert measurements in radians      Sketchpad to explore the         “rad” is the abbreviation of
  Week             concept of radian      to degrees and vice versa.           concept of circular measure.     radian.                         Teaching
  21&22                                                                                                         Include measurements in         Aids/materials
                                                                               Or                               radians expressed in terms of   Scientific calculator,
                                                                                                                π                               Geometer’s
                                                                               Use worksheets of Polya's                                        sketchpad, geometric
                                                                               method to explore the                                            set
                                                                               concept of circular measures
                                                                                                                                                CCTS
                                                                                                                                                Compare and contrast

                                                                                                                                                Teaching Strategies
                                                                                                                                                Contextual

                                                                                                                                                Vocabulary
                                                                                                                                                Radian,
                                                                                                                                                Degree

                2. Understand and         Determine                            Use examples of real – life                                      Moral Values
                   use the concept of            a) length of arc              situations to explore circular                                   Diligence, cooperate
                   length of arc of a            b) radius                     measure.
                   circle to solve               c) angle subtended at the                                                                      Teaching
                   problems.                         center of a circle.       Or                                                               Aids/materials
                                                 Based on given                                                                                 Scientific calculator,
                                                 information.                  Use an experiment method to                                      Geometer’s
                                                                               enhance the concept of                                           Sketchpad, geometric
                                          Find the perimeter of segments of    length of an arc of a circle.                                    set
                                          circles
                                                                                                                                                CCTS
                                          Solve problems involving lengths                                                                      Identifying
                                          of arc.                                                                                               relationship

                                                                              16
Week/
                                                                                                                                                    Teaching
 Learning      Learning objectives               Learning outcomes                   Suggested activities              Points to note
                                                                                                                                                 Strategies/ Skills
   Area

CIRCULAR     Students will be taught to:   Students will be able to:            Use Geometer’s Sketchpad to                                     Moral Values
MEASURES                                                                        differentiate between area of                                   Diligence
    23       3. Understand and use the     3.1 Determine :                      a sector and area of                                            cooperation
                 concept of area of            a) area of sector                segments of circles.                                            freedom
                 sector of a circle to         b) radius and
                 solve problems .              c) angle subtended at the        Or                                                              Teaching
                                                   centre of a                                                                                  Aids/materials
                                               based on given                   Use worksheets of Polya's                                       Scientific calculator,
                                               information                      method to explore the                                           Geometer’s
                                                                                concept of area of sector of a                                  Sketchpad, geometric
                                           3.2 Find area of segments of         circle.                                                         set
                                               circles.
                                                                                                                                                CCTS
                                           3.3 Solve problems involving area                                                                    Identifying
                                               of sectors.                                                                                      information
                                                                                                                                                Problem solving

                                                                                                                                                Teaching Strategies
                                                                                                                                                Mastery Learning
                                                                                                                                                Multiple Intelligent

                                                                                                                                                Vocabulary
                                                                                                                                                Area
                                                                                                                                                Sector

             1. Understand and use         Level 1
                the concept of             1.1 Determine value of a            Use graphing calculator or        Idea of limit to a function    Moral value :
DIFFERENTI      gradients of curve             function when its variable      dynamic geometry                  can be illustrated using       accurately
  ATION         and differentiation.           approaches a certain value.     software such as                  graphs.
                                                                               Geometer’s Sketchpad to                                          Pedagogy :
                                           1.2 Find gradient of a chord        explore the concept of                                           Contextual
                                               joining two points on a         differentiation.                  Concepts of first derivative   Vocabulary : limit,
  Week
  24 - 27                                      curve                                                             of a function are explained    tangent,
                                                                               17
Week/
                                                                                                                                         Teaching
Learning    Learning objectives            Learning outcomes                   Suggested activities          Points to note
                                                                                                                                      Strategies/ Skills
  Area
                                                                                                      as a tangent to a curve can    First derivative,
                                     Level 2                                                          be illustrated using graphs.   gradient, induction,
                                     1.3 Find the first derivative of a                                                              curve , fixed point
                                         function y=f(x) as gradient                                  Limit y = axn,
                                         of tangent to its graph                                      a , n are constants
                                                                                                      n = 1,2,3.
                                     1.4 Find the first derivative for
                                                                                                      Notation f’(x) equivalent to
                                         polynomial using first
                                                                                                       dy                          Moral value :
                                         principles.                                                       when y= f(x).
                                                                                                       dx                          rational
                                                                                                      F’(x) read as “f prime x”.   Pedagogy : Mastery
                                     1.5 Deduce the formula for first
                                                                                                                                   Learning
                                         derivative of function
                                         y = axn by induction.
           2. Understand and use     Level 2
              the concept of first   2.1 Determine first derivative of                                Formula y = axn , then         Moral value :
              derivative of          the function y = axn using                                       dy                             rational
                                                                                                         = naxn-1
              polynomial functions   formula.                                                         dx                             Pedagogy : Mastery
              to solve problems.                                                                      a, n are constant and n        Learning
                                     2.2 Determine value of the first                                 integer.
                                         derivative of the function                                   y is a function of x.
                                         y== axn for a given value of
                                         x                                                                   dy                      Pedagogy : Creative
                                                                                                      Find      when y=f(x) +
                                     2.3 Determine first derivative of                                       dx                      thinking
                                         a function involving                                         g(x) or y=f(x) – g(x), f(x)
                                         a. addition or                                               and g(x) is given              ABM : OHP
                                         b. subtraction algebraic
                                             terms.                                                   When y=uv, then
                                     2.4 Determine first derivative of                                dy
                                                                                                         =u
                                                                                                            dv
                                                                                                               +v
                                                                                                                   du
                                                                                                      dx    dx     dx
                                         a product of two                                                      u
                                         polynomials.                                                 When y= v , then
                                     2.5 Determine first derivative of                                                               Vocabulary:
                                         a quotient of two                                                                           product, quotient,
                                                                          18
Week/
                                                                                                                                        Teaching
Learning     Learning objectives           Learning outcomes                  Suggested activities             Points to note
                                                                                                                                     Strategies/ Skills
  Area
                                         polynomials                                                       du     dv                Composite
                                     2.6 Determine first derivative of                                     v   −u                   function, chain rule,
                                                                                                      dy
                                         composite function using                                        = dx 2 dx                  Normal.
                                         chain rule.                                                  dx      v
                                     2.7 Determine gradient of
                                         tangent at a point on a
                                         curve.
                                     2.8 Determine equation of                                        y=f(u) and u=g(x), then
                                         tangent at a point on a                                      dy dy du
                                                                                                        =  X
                                         curve.                                                       dx du dx                      Moral value :
                                     2.9 Determine equation of                                                                      independents,
                                         normal at a point on a curve                                 Limit cases in learning       cooperation
                                                                                                      outcomes 2.7 – 2.9 to rules   Pedagogy:
                                                                                                      Introduced in 2.4 – 2.6.      Mastering learning.
           3. Understand and use  Level 2                                Use graphing calculator or                                 Moral Values :
           the concept of maximum 3.1 Determine coordinates of           dynamic geometry             Emphasis the use of first     Independendant
           and minimum values to turning points of a curve.              software such as             derivative to determine       Cooperation
           solve problems.                                               Graphmatica software to      turning points.
                                  3.2 Determine whether a                explore the concept of
                                  turning points is a maximum or         maximum and minimum          Exclude points of inflexion
                                  minimum point                          values.
                                                                                                      Limit problems to two         CCTS:
                                                                                                      variables only.               Identifying
                                     Level 3                                                                                        relationship
                                     3.3 Solve problems involving                                                                   Teaching Strategies
                                     maximum or minimum values                                                                      :
                                                                                                                                    Mastery Learning
           4. Understand and use     Level 2                             Use graphing calculator      Limit problems to 3           Moral Values :
           the concept of rates of   4.1 Determine rates of change       with computer base ranger    variables only                Cooperation
           change to solve           for related quantities              to explore the concept of
           problems                                                      rates of change.

                                                                         19
Week/
                                                                                                                                 Teaching
Learning    Learning objectives            Learning outcomes                Suggested activities           Points to note
                                                                                                                              Strategies/ Skills
  Area
                                                                                                                             CCTS:
                                                                                                                             Identifying
                                                                                                                             relationship
                                                                                                                             Teaching Strategies
                                                                                                                             :
                                                                                                                             Problem solving
                                                                                                                             Contextual
           5. Understand and use     Level 2                                                       δy ≈ dy                   Moral Values :
           the concept of small      5.1 Determine small changes in                                δx   dx                   Sincere
           changes and               quantities                                                                              Hardworking
           approximations to solve   5.2 Determine approximate                                     Exclude cases involving
           problems                  values using differentiation                                  percentage change

                                                                                                                             CCTS:

                                                                                                                             Teaching Strategies
                                                                                                                             :
                                                                                                                             Mastery Learning
           6. Understand and use     Level 2
           the concept of second     6.1 Determine second                                                                    Moral Values :
           derivative to solve       derivative of function y = f(x)                               Introduce d2y as          Independendant
           problems                  6.2 determine whether a turning                                         dx2             Cooperation
                                     point is maximum or minimum
                                     point of a curve using the                                    d dy        or
                                     second derivative.                                            dx dx                     CCTS:
                                                                                                                             Identifying
                                                                                                              d
                                                                                                   f’’(x) = dx [ f ' ( x)]   relationship
                                                                                                                             Teaching Strategies
                                                                                                                             :
                                                                                                                             Mastery Learning

           SOLUTION OF
                                                                       20
Week/
                                                                                                                               Teaching
Learning    Learning objectives           Learning outcomes              Suggested activities            Points to note
                                                                                                                            Strategies/ Skills
  Area
           TRIANGLES
 Week
           1. Understand and use    1.1 Verify sine rule             Using GSP to verify the                               Sine rule
 28 - 30      the concept of sine                                    sine rule.                                            Acute-angled
              rule to solve                                                                                                triangle
              problems                                                                                                     Obtuse-angled
                                                                                                                           triangle
                                                                                                                           Ambiguous
                                    1.2 Use sine rule to find        Discuss the acute angle       Include obtuse-angled
                                        unknown sides or angles of   triangle and obtuse angle     triangles
                                        a triangle.                  triangle.



                                    1.3 Find unknown sides and       Discuss on ambiguity
                                        angles of a triangle in an   cases where
                                        ambiguous case.                   i)      non-included
                                                                                  angle is given
                                                                          ii)     a<b
                                                                     Questions involving real-
                                                                     life situations
                                    1.4 Solve problems involving
                                        the sine rule.
                                                                     Use GSP to explore the
                                                                     concept of cosine rule


                                                                     Cosine rule
                                                                     c 2 = a 2 + b 2 − 2abkosC

                                                                      -Teams Work
                                                                      -Brainstorming
                                                                     21
Week/
                                                                                                                                Teaching
Learning     Learning objectives          Learning outcomes                Suggested activities           Points to note
                                                                                                                             Strategies/ Skills
  Area

                                    2.1 Verify cosine rule
                                                                      Discuss the acute angle
                                                                      triangle and obtuse angle
                                                                      triangle.
                                                                          - Teams Work
                                    2.2 Use cosine rule to find       Discussion                    Include obtuse-angled
           2. Understand and use unknown sides or
                                                                                                    triangles               Cosine rule
              the concept of cosine   angles of a triangle.
              rule to solve
                                                                      Non-rutin question
              problems              2.3 Solve problems involving
                                    cosine rule
                                                                      Area of triangle =
                                    Level 3                           1
                                    2.4 Solve problems involving        ab sin C
                                                                      2
                                    sine and cosine
                                         rules
                                                                      Related to suitable content

                                                                      -Teams work


                                    Level 2
                                    3.1 Find area of triangle using
                                    formula
                                        1
                                          absin C or its equivalent
                                        2
           3. Understand and use
           the                      Level 3
              formula for area of   3.2 Solve problems involving
             triangles to solve     three-dimensional
                                        objects                                                                             Three-dimensional
                                                                      22
Week/
                                                                                                                                                        Teaching
 Learning        Learning objectives                Learning outcomes                   Suggested activities               Points to note
                                                                                                                                                     Strategies/ Skills
   Area
                 problems                                                                                                                           object


               Students will be taught to:   Students will be able to:            Explain index number.             Index number has no units and   Moral values
  INDEX                                                                               Q                             no % symbol.                      Accurate
 NUMBER        1. Understand and use the     1.1 Calculate index number.           I = 1 × 100
               concept of index number to    1.2 Calculate price index.               Q0                            Q1 and Q0 must be of the same   Teaching aids/
Week 31 & 33   solve problems.               1.3 Find Q0 or Q1 given relevant                                       unit.                           Materials:
                                             information.                                                                                              Newspaper
                                                                                  Q0 = Quantity at base time.
                                                                                  Q1 = Quantity at specific time.                                   Vocabulary:
                                                                                                                                                      Index number,
                                                                                                                                                      Price index,
                                                                                  Use example of real-life
                                                                                                                                                     quantity at base time,
                                                                                  situations to explore index
                                                                                                                                                      quantity at specific
                                                                                  numbers.
                                                                                                                                                              time.

                                                                                                                                                    Pedagogy:
                                                                                                                                                      Contextual


               2. Understand and use the     2.1 Calculate composite index.       Explain weightage and             W can be simplified             Moral Values:
               concept of composite index    2.2 Find index number or weightage   composite index.                  to the smallest number           Accurate
               to solve problems             given relevant information.                                            according to ratio.
                                             2.3 Solve problems involving index
                                             number and composite index            I=
                                                                                        ∑W I i i
                                                                                                                                                    Vocabulary:
                                                                                                                                                    Composite index
                                                                                        ∑W    i                                                     Weightage


                                                                                  Use examples of real-life
                                                                                  situations to explore composite
                                                                                  index.

     34                                      Revision ( Final SBP form 4 2006)

     35                                      Revision ( Final Melaka Form 42006)

                                                                                  23
Week/
                                                                                                              Teaching
Learning   Learning objectives        Learning outcomes            Suggested activities   Points to note
                                                                                                           Strategies/ Skills
  Area
   36                            Revision ( Final SBP 2005)
   37                            Pep PMR / Akhir Tahun

   38                            Final Exam SBP

   39                            Final Exam SBP
   40                            Progression
   41                            Progression
   42                            Progression




                                                              24

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Yearlylessonplanaddmathf42010

  • 1.
  • 2. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area . QUADRATIC 1. Understand the concept 1.1 Recognise a quadratic Use graphing Noble value : EQUATIONS of quadratic equation equation and express it in Cooperation calculators or computer and its roots. general form. software such as the TGA: Geometer’s Sketchpad and Flashcard spreadsheet to explore the Pedagogy : concept of quadratic Activity/Cooperativ Week 1.2 Determine whether a given e Learning equations. 1&2 value is the root of a CCTS: quadratic equation by Classification. a) substitution; b) inspection. Questions for 1.2(b) are given 1.3 Determine roots of quadratic in the form of (x + a)(x + b) = equations by trial and 0; a and b are numerical improvement method. values. Discuss when (x p)(x q) = 0, hence x – p = Value : 2. Understand the 2.1 Determine the roots of a 0 or Cooperation concept of quadratic quadratic equation by x – q = 0. Include case when TGA : equations. a) factorisation; p = q. Manila Card b) completing the square c) using the formula. Derivation of formula for Pedagogy : 2.1c is not required. Inquiry Finding, Constructisme If x=p and x=q are the roots, CCTS: then the quadratic equation is Refresh idea and (xp)(xq)=0, that is trial & error x2(pq)xpq=0. 2
  • 3. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 2.2 Form a quadratic equation Involve the use of: Pedagogy: from given roots. −b c Mastery Learning I ++=   and =  , a a Where Wand are roots of the quadratic equation ax2 +bx +c =0 QUADRATIC 1. Understand the 1.1 Recognise quadratic functions Use computer software or Discuss the general shape of Mastery Learning FUNCTIONS concept of 1.2 Plot quadratic functions graphs graphing calculator. quadratic function. Week quadratic functions a) based on given tabulated (ex; GSP, Graphmatica or Introduce the term of Contextual 3&4 and their graphs values Microsoft Excel to explore parabola, minimum, b) by tabulating the graphs of quadratic maximum point and axis of values based on functions) symmetry for quadratic given functions curves. Use example of everyday 1.3 Recognise shapes of graphs situations to introduce graphs Discuss cases where a > 0 of quadratic functions of quadratic functions. and a < 0 for f ( x ) = ax 2 + bx + c 1.4 Relate the position of quadratic function graphs with types of roots for f (x) = 0. 2. Find maximum and 2.1 Determine the maximum or Use computer software or Discuss the general form of Mastery Learning minimum values of minimum value of quadratic graphing calculator. completing the square quadratic functions function by completing the (ex; GSP, Graphmatica or f ( x) = a ( x + p) 2 + q Self-Access Learning square Microsoft Excel to explore the graphs of quadratic functions) 3
  • 4. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 3. Sketch graphs of 3.1 Sketch quadratic functions by Use graphing calculator or Emphasis the marking of Contextual quadratic functions. determining the maximum or dynamic geometry software maximum or minimum point minimum point and two other such as the GSP or and two other points on the points. Graphmatica to reinforce the graphs drawn or by finding understanding of graphs of the axis of symmetry and the quadratic functions. intersection with the y – axis Determine other points by finding the intersection with x-axis (if it exists ) 4. Understand and use the 4.1 Determine the ranges of values Use graphing calculator or Emphasis on sketching Contextual concept of quadratic of x that satisfies quadratic dynamic geometry software graphs and use number lines inequalities. inequalities such as the GSP or when necessary. Graphmatica to reinforce the understanding of graphs of quadratic inequalities Problem solving, SIMULTANEOUS Students will be taught to: Students will be able to : Use graphing calculator or discovery method, EQUATIONS dynamic geometry software trial and 1. Solve simultaneous 1.1 Solve simultaneous equations such as the Geometers Limit non linear equations up improvement method. Week 5 equations in two using the the substitution Sketchpad to explore the to second degree only unknowns: one linear method concept of simultaneous ICT, relating, equation and one non - equations reasoning, linear equation. Mathematical 1.2 Solve simultaneous equations Use examples in real life Communication, involving real life situations situations such as area, Mathematical perimeter and others. Connections FUNCTIONS Contextual 1.1 Represent Use pictures, role-play and Discuss the idea of set and 1. Understanding the computer software to introduce set notation. Week concept of relations. relations using introduce the concept of 4
  • 5. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 6 , 7 &8 a)arrow diagrams relations. b) ordered pairs c) graphs 1.2 Identify domain, codomain, object, image and range of a relation. 1.3 Classify a relation shown on a mapped diagram as: one to one, many to one, one to many or many to many relation. Represent functions using 2. Understand 2.1 Recognise arrow diagrams, ordered the concept functions as a special Use graphing calculators Cooperative pairs or graphs. of functions relation and computer software to learning explore the image of e.g. f : x → 2x functions. f (x) = 2x 2.2 Express functions using "f : x → 2x" is read as function notation. "function f maps x to 2x". 2.3 Determine domain, object, f (x) = 2x is read as “2x image and range of a is the image of x under the function. function f ”. Include examples of 2.4 Determine the image of a functions that are not function given the object mathematically based. 5
  • 6. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area and vice versa. Examples of functions include algebraic (linear and quadratic), trigonometric and absolute value. Define and sketch absolute value functions. 3. Understand 3.1 Determine composition of the two functions. Use arrow diagrams or Involve algebraic functions Mastery learning concept 3.2 Determine the image of algebraic method to only. composite functions given the of composite determine composite object and vice versa. functions. functions. 3.3 Determine one Images of composite of the functions in a functions include a range of values. (Limit to linear composite functions) b) given composite . function given the other related function. c) 4.1 Find the object by inverse Use sketches of graphs to Limit to algebraic Mastery learning d) 4. Understand the mapping given its image show the relationship functions. concept of inverse and function. between a function and its Exclude inverse of functions. inverse 4.2 Determine inverse composite functions. functions using algebra. Emphasise that inverse of a 6
  • 7. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 4.3 Determine and state the function is not necessarily condition for existence of a function. an inverse function. 9 e) Test 1 7
  • 8. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area Teaching 1. Understand and use 1.1 Find the value of numbers • Use examples of real- Discuss zero index and Aids/materials INDICES AND LOGARITHMS the concept of indices given in the form of: life situations to negative indices. Scientific calculator, and laws of indices to a) integer indices. introduce the concept Geometer’s Week 10 solve problems. b) fractional indices. of indices. Sketchpad, geometric set 1.2 Use laws of indices to find • Use computer the value of numbers in software such as the CCTS index form that are spreadsheet to Identifying relationship multiplied, divided or enhance the raised to a power. understanding of Teaching Strategies indices. Mastery Learning 1.3 Use laws of indices to Multiple intelligent simplify algebraic Contextual learning expressions. 2. Understand and use 2.1 Express equation in index • Use scientific xplain definition of form to logarithm form and calculators to logarithm. the concept of vice versa. enhance the N = ax ; loga N = x with a > logarithms and laws of logarithms to solve understanding of the 0, a ≠ 1. 2.2 Find logarithm of a concept of logarithm. Emphasise that: problems number. loga 1 = 0; loga a = 1. 2.3 Find logarithm of numbers Emphasise that: by using laws of a) logarithm of negative logarithms. numbers is undefined; b) logarithm of zero is undefined. 2.4 Simplify logarithmic expressions to the simplest Discuss cases where the form. given number is in a) index form b) numerical form. Discuss laws of logarithms 8
  • 9. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area Week 11 3.1 Find the logarithm of a Discuss: Vocabulary 3 Understand and use number by changing the 1 the change of base of loga b = base of the logarithm to a logb a logarithms to solve base suitable base. problems. integer indices 3.2 Solve problems involving fractional indices the change of base and laws of index form logarithms. 13 4.1 Solve equations involving Equations that involve raised to a power 4. Solve equations indices. indices and logarithms are law of indices involving indices and limited to equations with logarithms. 4.2 Solve equations involving single solution only. logarithms. Solve equations involving index form indices by: logarithm form a) comparison of indices and bases; logarithm undefined b) using logarithms 9
  • 10. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area Moral Values 1. Find distance between 1.1 Use examples of real-life Use the Pythagoras’ Theorem COORDINAT Cooperative two points situations to find the to find the formula for GEOMETRY Find the distance between two Patriotism distance between two points. distance between two points. Respect points using formula Week 14 ( x1 − x2 ) 2 + ( y1 − y2 ) 2 Teaching Aids/ Material Chart Arrow diagram CCTS 2. Understand the concept 2.1 Find the midpoint of two Limit to cases where m and n Analogy of division of a line given points. are positive. Relations segment. Imagine Derivation of the formula 2.2 Find the coordinates of a  nx1 + mx2 ny1 + my2  Teaching Strategies  ,  is not point that divides a line according  m+n m+n  Contextual to a given ratio required. m : n. Moral Values 3. Find areas of polygons 3.1 Find the area of a triangle Use dynamic geometry Limit to numerical values. Week Cooperative based on the area of specific software such as the Emphasise the relationship 15 geometrical shapes. Geometer’s Sketchpad to between the sign of the value Teaching Aids/ explore the concept of area for area obtained with the Material of polygons. order of the vertices used. Grid Board 3.2 Find the area of a triangle by Use x2 x3 x1 1 x1 Emphasise that when the area using formula. Teaching Strategies 2 y1 y 2 y 3 y 1 of polygon is 0, the given 1 x1 x2 x3 x1 Contextual points are collinear. 2 y1 y 2 y 3 y1 Generate ideas for substitution of Thinking Skills 3.3 Find the area of a coordinates into the formula. quadrilateral using formula 10
  • 11. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area Moral Values 4. Understands use the 4.1 Use dynamic Geometry Honesty concept of equation of a software such as the Determine the x – intercept and y- Accuracy straight line. Geometer’s Sketchpad to intercept of a line explore the concept of Teaching Aids/ 4.2 equation of a straight lines. Material Find the gradient of a straight line Charts, Graphical that passes through two points. Calculator Charts Teaching Strategies 4.3 Find the gradient of a staright Answer for learning Mastery Learning line using the x-intercept and outcomes 4.4 (a) and 4.4(b) Contextual Approach y-intercept must be stated in the simplest Mastery Approach form 4.4Find the equation of a straight line given: x y + = 1 involve changing a) gradient and one point a b the equation into gradient b) two point y = mx + c and intercept c) x-intercept and y-intercept form 4.5 Detemine gradient and ax + by + c = 0 intercepts of a straight line given the equation. Moral Values 4.6 Change the equation of a Accuracy straight line to the general form Teaching Aids/ 4.7 Find the point of intesection of Solve simultaneous linear Material two lines. equations using the graph Graph paper method. Teaching Strategies Self Access Learning 11
  • 12. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 16 5.Understand and use the Use example of real-life Moral Values 5.1 Determine whether two straight Emphasize that for parallel Cooperation concept of parallel and lines are parallel when gradients of situations to explore parallel lines: Gratitude perpendicular lines. both lines are known and vice end perpendicular lines. m1 = m2 Careful versa Systematic 5.2 Find equation of a straight line Emphasize that for perpendicular lines : Teaching Aids/ that passes through a fixed point Use graphic calculator and Material and parallel to a given line. m1 m2 = −1 dynamic geometry software Exact Systematic 5.3 Determine whether two straight such as Geometer’s ICT Sketchpad to explore the Grid Board lines are perpendicular when concept of parallel and gradients of both lines are known perpendicular lines. Derivation of m1 m 2 = −1 is Teaching Strategies and vice versa. Self Access Learning not required. Learn How to Study 5.4 Determine the equation of a straight line that passes through a Multiple Intelligent fixed point and perpendicular to a Constructivism approach given line. 5.5 Solve problems involving equations of straight lines. Moral Values 6. Understand and use the 6.1 Find the equations of locus that Use examples of real-life Cooperation concept of equation of satisfies the condition if: situations to explore equation Gratitude locus involving distance of locus involving distance a) The distance of a moving point Careful between two points. between two points. from a fixed point is constant; Systematic b) The ratio of the distances of a Teaching Aids/ moving point from two fixed Use graphic calculator and Material points is constant. dynamic geometry software Exact Systematic such as Geometer’s ICT 6.2 Solve problems involving loci. Grid Board Sketchpad to explore the concept of loci. 12
  • 13. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 17 1. Understand and use 1.1 Calculate the mean of • Use scientific Discuss grouped data and Moral Values the concept of ungrouped data. calculators, graphing ungrouped data. Cooperation measures of central calculators and Gratitude tendency to solve 1.2 Determine the mode of spreadsheets to Careful problems. ungrouped data. explore measures of Systematic central tendency. 1.3 Determine the median of Teaching Aids/ • Students collect data Material ungrouped data. from real-life situations Exact Systematic to investigate ICT 1.4 Determine the modal class measures of central Grid Board of grouped data from Involve uniform class tendency. intervals only. frequency distribution Teaching Strategies tables. Self Access Learning Learn How to Study 1.5 Find the mode from Multiple Intelligent histograms. Constructivism approach 1.6 Calculate the mean of Derivation of the median Teaching Strategies grouped data. formula is not required. Self Access Learning Learn How to Study 1.7 Calculate the median of Multiple Intelligent grouped data from Constructivism cumulative frequency approach distribution tables. 1.8 Estimate the median of grouped data from an ogive. Ogive is also known as 1.9 Determine the effects on cumulative frequency mode, median and mean curve. 13
  • 14. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area for a set of data when: a) each data is changed uniformly; b) extreme values exist; Involve grouped and c) certain data is added ungrouped data or removed. 1.10 Determine the most suitable measure of central tendency for given data. 18 Vocabulary 2. Understand and use 2.1 Find the range of the concept of ungrouped data. measures of measure of dispersion to solve 2.2 Find the interquartile range central problems. tendency of ungrouped data. mean 2.3 Find the range of grouped mode data. median 2.4 Find the interquartile range Determine upper and lower ungrouped data of grouped data from the quartiles by using the first cumulative frequency frequency principle. table. distribution table modal class 2.5 Determine the interquartile uniform class range of grouped data interval from an ogive. histogram 2.6 Determine the variance of a) ungrouped data; b) grouped data. 14
  • 15. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 2.7 Determine the standard deviation of: a) ungrouped data b) grouped data. 2.8 Determine the effects on Emphasise that comparison between range, interquartile range, two sets of data using variance and standard only measures of deviation for a set of data central tendency is when: not sufficient. a) each data is changed uniformly; b) extreme values exist; c) certain data is added or removed. 2.9 Compare measures of central tendency and dispersion between two sets of data. Mid Term Examination Week 19 - 20 15
  • 16. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area CIRCULAR Students will be taught to: Students will be able to: Use dynamic geometry Discuss the definition of one Moral Values MEASURES software such as Geometer’s radian. Rational, patience 1. Understand the Convert measurements in radians Sketchpad to explore the “rad” is the abbreviation of Week concept of radian to degrees and vice versa. concept of circular measure. radian. Teaching 21&22 Include measurements in Aids/materials Or radians expressed in terms of Scientific calculator, π Geometer’s Use worksheets of Polya's sketchpad, geometric method to explore the set concept of circular measures CCTS Compare and contrast Teaching Strategies Contextual Vocabulary Radian, Degree 2. Understand and Determine Use examples of real – life Moral Values use the concept of a) length of arc situations to explore circular Diligence, cooperate length of arc of a b) radius measure. circle to solve c) angle subtended at the Teaching problems. center of a circle. Or Aids/materials Based on given Scientific calculator, information. Use an experiment method to Geometer’s enhance the concept of Sketchpad, geometric Find the perimeter of segments of length of an arc of a circle. set circles CCTS Solve problems involving lengths Identifying of arc. relationship 16
  • 17. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area CIRCULAR Students will be taught to: Students will be able to: Use Geometer’s Sketchpad to Moral Values MEASURES differentiate between area of Diligence 23 3. Understand and use the 3.1 Determine : a sector and area of cooperation concept of area of a) area of sector segments of circles. freedom sector of a circle to b) radius and solve problems . c) angle subtended at the Or Teaching centre of a Aids/materials based on given Use worksheets of Polya's Scientific calculator, information method to explore the Geometer’s concept of area of sector of a Sketchpad, geometric 3.2 Find area of segments of circle. set circles. CCTS 3.3 Solve problems involving area Identifying of sectors. information Problem solving Teaching Strategies Mastery Learning Multiple Intelligent Vocabulary Area Sector 1. Understand and use Level 1 the concept of 1.1 Determine value of a Use graphing calculator or Idea of limit to a function Moral value : DIFFERENTI gradients of curve function when its variable dynamic geometry can be illustrated using accurately ATION and differentiation. approaches a certain value. software such as graphs. Geometer’s Sketchpad to Pedagogy : 1.2 Find gradient of a chord explore the concept of Contextual joining two points on a differentiation. Concepts of first derivative Vocabulary : limit, Week 24 - 27 curve of a function are explained tangent, 17
  • 18. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area as a tangent to a curve can First derivative, Level 2 be illustrated using graphs. gradient, induction, 1.3 Find the first derivative of a curve , fixed point function y=f(x) as gradient Limit y = axn, of tangent to its graph a , n are constants n = 1,2,3. 1.4 Find the first derivative for Notation f’(x) equivalent to polynomial using first dy Moral value : principles. when y= f(x). dx rational F’(x) read as “f prime x”. Pedagogy : Mastery 1.5 Deduce the formula for first Learning derivative of function y = axn by induction. 2. Understand and use Level 2 the concept of first 2.1 Determine first derivative of Formula y = axn , then Moral value : derivative of the function y = axn using dy rational = naxn-1 polynomial functions formula. dx Pedagogy : Mastery to solve problems. a, n are constant and n Learning 2.2 Determine value of the first integer. derivative of the function y is a function of x. y== axn for a given value of x dy Pedagogy : Creative Find when y=f(x) + 2.3 Determine first derivative of dx thinking a function involving g(x) or y=f(x) – g(x), f(x) a. addition or and g(x) is given ABM : OHP b. subtraction algebraic terms. When y=uv, then 2.4 Determine first derivative of dy =u dv +v du dx dx dx a product of two u polynomials. When y= v , then 2.5 Determine first derivative of Vocabulary: a quotient of two product, quotient, 18
  • 19. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area polynomials du dv Composite 2.6 Determine first derivative of v −u function, chain rule, dy composite function using = dx 2 dx Normal. chain rule. dx v 2.7 Determine gradient of tangent at a point on a curve. 2.8 Determine equation of y=f(u) and u=g(x), then tangent at a point on a dy dy du = X curve. dx du dx Moral value : 2.9 Determine equation of independents, normal at a point on a curve Limit cases in learning cooperation outcomes 2.7 – 2.9 to rules Pedagogy: Introduced in 2.4 – 2.6. Mastering learning. 3. Understand and use Level 2 Use graphing calculator or Moral Values : the concept of maximum 3.1 Determine coordinates of dynamic geometry Emphasis the use of first Independendant and minimum values to turning points of a curve. software such as derivative to determine Cooperation solve problems. Graphmatica software to turning points. 3.2 Determine whether a explore the concept of turning points is a maximum or maximum and minimum Exclude points of inflexion minimum point values. Limit problems to two CCTS: variables only. Identifying Level 3 relationship 3.3 Solve problems involving Teaching Strategies maximum or minimum values : Mastery Learning 4. Understand and use Level 2 Use graphing calculator Limit problems to 3 Moral Values : the concept of rates of 4.1 Determine rates of change with computer base ranger variables only Cooperation change to solve for related quantities to explore the concept of problems rates of change. 19
  • 20. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area CCTS: Identifying relationship Teaching Strategies : Problem solving Contextual 5. Understand and use Level 2 δy ≈ dy Moral Values : the concept of small 5.1 Determine small changes in δx dx Sincere changes and quantities Hardworking approximations to solve 5.2 Determine approximate Exclude cases involving problems values using differentiation percentage change CCTS: Teaching Strategies : Mastery Learning 6. Understand and use Level 2 the concept of second 6.1 Determine second Moral Values : derivative to solve derivative of function y = f(x) Introduce d2y as Independendant problems 6.2 determine whether a turning dx2 Cooperation point is maximum or minimum point of a curve using the d dy or second derivative. dx dx CCTS: Identifying d f’’(x) = dx [ f ' ( x)] relationship Teaching Strategies : Mastery Learning SOLUTION OF 20
  • 21. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area TRIANGLES Week 1. Understand and use 1.1 Verify sine rule Using GSP to verify the Sine rule 28 - 30 the concept of sine sine rule. Acute-angled rule to solve triangle problems Obtuse-angled triangle Ambiguous 1.2 Use sine rule to find Discuss the acute angle Include obtuse-angled unknown sides or angles of triangle and obtuse angle triangles a triangle. triangle. 1.3 Find unknown sides and Discuss on ambiguity angles of a triangle in an cases where ambiguous case. i) non-included angle is given ii) a<b Questions involving real- life situations 1.4 Solve problems involving the sine rule. Use GSP to explore the concept of cosine rule Cosine rule c 2 = a 2 + b 2 − 2abkosC -Teams Work -Brainstorming 21
  • 22. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 2.1 Verify cosine rule Discuss the acute angle triangle and obtuse angle triangle. - Teams Work 2.2 Use cosine rule to find Discussion Include obtuse-angled 2. Understand and use unknown sides or triangles Cosine rule the concept of cosine angles of a triangle. rule to solve Non-rutin question problems 2.3 Solve problems involving cosine rule Area of triangle = Level 3 1 2.4 Solve problems involving ab sin C 2 sine and cosine rules Related to suitable content -Teams work Level 2 3.1 Find area of triangle using formula 1 absin C or its equivalent 2 3. Understand and use the Level 3 formula for area of 3.2 Solve problems involving triangles to solve three-dimensional objects Three-dimensional 22
  • 23. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area problems object Students will be taught to: Students will be able to: Explain index number. Index number has no units and Moral values INDEX Q no % symbol. Accurate NUMBER 1. Understand and use the 1.1 Calculate index number. I = 1 × 100 concept of index number to 1.2 Calculate price index. Q0 Q1 and Q0 must be of the same Teaching aids/ Week 31 & 33 solve problems. 1.3 Find Q0 or Q1 given relevant unit. Materials: information. Newspaper Q0 = Quantity at base time. Q1 = Quantity at specific time. Vocabulary: Index number, Price index, Use example of real-life quantity at base time, situations to explore index quantity at specific numbers. time. Pedagogy: Contextual 2. Understand and use the 2.1 Calculate composite index. Explain weightage and W can be simplified Moral Values: concept of composite index 2.2 Find index number or weightage composite index. to the smallest number Accurate to solve problems given relevant information. according to ratio. 2.3 Solve problems involving index number and composite index I= ∑W I i i Vocabulary: Composite index ∑W i Weightage Use examples of real-life situations to explore composite index. 34 Revision ( Final SBP form 4 2006) 35 Revision ( Final Melaka Form 42006) 23
  • 24. Week/ Teaching Learning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area 36 Revision ( Final SBP 2005) 37 Pep PMR / Akhir Tahun 38 Final Exam SBP 39 Final Exam SBP 40 Progression 41 Progression 42 Progression 24