Annual Planning for Additional Mathematics Form 4 2011
ANNUAL PLANNING FOR ADDITIONAL MATHEMATICS FORM 4 / 2011 WEEK TOPICS/LEARNING AREA LEARNING OUTCOMES POINTS TO NOTE3 Jan – • Registration Day 7 Jan • Orientation Week
3 A1 FUNCTIONS Students should be able to :WEEKS(10 Jan – 1.0 Understand the concept of 1.1 Represent a relation using Discuss the idea of set and 28 Jan) relations a) arrow diagram introduce set notation 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 or many to many relation. 2.0 Understand the concept of 2.1 Recognise function as a special Represent functions using functions relation. arrow diagram, ordered 2.2 Express functions using function pairs or graph. notation. Examples of functions 2.3 Determine domain, object, image include algebraic (linear and and range of a function. quadratic), trigonometric 2.4 Determine image of a function and absolute value. given the object and vice versa. Define and sketch absolute value function. 3.0 Understand the concept of 3.1 Determine composition of two Involve algebraic functions composite functions functions. only. 3.2 Determine image of composite Images of composite functions given the object and function include arrange of vice versa. values. 3.3 Determine one of the function in a given composite function given the other related function. 4.0 Understand the concept of inverse 4.1 Find object by inverse mapping Limit to algebraic function. functions given its image and function. Exclude inverse of 4.2 Determine inverse function using composite function. algebra. Emphasise that inverse of a 4.3 Determine and state the function is not necessarily a condition for existence of an function. inverse function.
3 A2 QUADRATIC EQUATIONS Students should be able to:WEEKS (31 1.0 Understand the concept of 1.1 Recognise quadratic equation Questions for 1.2(b) are Jan-11 quadratic equations and its roots and express it in general form. given in the form Feb) 1.2 Determine whether a given value ( x + a)( x + b) = 0 a, b are is the root of a quadratic numerical values. equation by: Involve the use of α and a) substitution β b) inspection 1.3 Determine the roots of a quadratic equation by trial and improvement method. 2.0 Understand the concept of 2.1 Determine the roots of a quadratic equations quadratic equation by a) factorization b) completing the square c) using the formula 2.2 Form a quadratic equation from given roots. 3.0 Understand and use the conditions 3.1 Determine types of roots of b 2 − 4ac > 0 for quadratic equations to have quadratic equations from the b 2 − 4ac = 0 a) two different roots value of b 2 − 4ac . b 2 − 4ac < 0 b) two equal roots 3.2 Solve problems involving c) no roots b − 4ac 2 in quadratic equations to a) find an unknown value b) derive a relation 4 A3 QUADRATIC FUNCTIONS Students should be able to :WEEKS(14 Feb-4 1.0 Understand the concept of 1.1 Recognise quadratic functions. Discuss cases where Mac) quadratic functions and their 1.2 Plot quadratic function graphs a > 0 and a < 0 for graphs a) based on given tabulated f ( x) = ax 2 + bx + c = 0 values b) by tabulating values based on given functions 1.3 Recognise shapes of graphs of quadratic functions. 1.4 Relate the position of quadratic function graphs with types of roots for f(x) = 0.
TEST 1 Will be prepared by: (7 Mac – 11 Mac) PN. SURIANI(21 Mar – 2.0 Find maximum and minimum 2.1 Determine the maximum or Emphasise the marking of 25 Mar) values of quadratic functions minimum value of a quadratic maximum or minimum and function by completing the two other points on the square graphs drawn or finding the axis of symmetry and the(28 Mar 3.0 Sketch graphs of quadratic 3.1 Sketch quadratic function graphs intersection with y-axis.– 1 Apr) functions by determining the maximum or minimum point and two other Emphasise on sketching points graphs and use number lines when necessary(4 Apr – 4.0 Understand and use the concept of 4.1 Determine the ranges of values8 Apr) quadratic inequalities of x that satisfies quadratic inequalities 2 A4 SIMULTANEOUS EQUATIONS Students should be able to:WEEKS (11 Apr 1.0 Solve simultaneous equations in 1.1 Solve simultaneous equations Limit non-linear equations-22 Apr) two unknowns: one linear equation using the substitution method up to second degree only and one non-linear equation 1.2 Solve simultaneous equations involving real-life situations 2 A5 INDICES AND LOGARITHM Students should be able to:WEEKS(25 Apr 1.0 Understand and use the concept 1.1 Find the values of numbers given Discuss zero index and-6 May) of indices and laws of indices to in the form of negative indices solve problems a) integer indices b) fractional indices 1.2 Use laws of indices to find the values of numbers in index form that are multiplied, divided or raised to a power 1.3 Use laws of indices to simplify algebraic expressions
2.0 Understand and use concept of 2.1 Express equation in index form to Explain definition of logarithms and laws of logarithm form and vice versa logarithm logarithms to solve problems 2.2 Find logarithm of a number N = a x ; log a N = x 2.3 Find logarithm of numbers by Emphasise that using laws of logarithms log a 1 = 0 ; log a a = 1 2.4 Simplify logarithmic expressions Discuss cases where the to the simplest form given number is in a) index form b) numerical form Discuss laws of logarithms3.0 Understand and use the change 3.1 Find the logarithm of a number Discuss: of base of logarithms to solve by changing the base of the 1 log a b = problems logarithm to a suitable base log b a 3.2 Solve problems involving the change of base and laws of logarithms4.0 Solve equations involving indices 4.1 Solve equations involving indices. Equations that involve and logarithms 4.2 Solve equations involving indices and logarithms are logarithms. limited to equations with single solution only. Solve equations involving indices by: a) comparison of indices and bases b) using logarithmsMID YEAR EXAM Will be prepared by:(9 MAY – 27 MAY) PN. SURIANI
3 G1 COORDINATE GEOMETRY Students should be able to:WEEKS (13 1.0 Find distance between two points 1.1 Find distance between two Use Pythagoras’ theorem toJune-1 points using formula find the formula for July) distance between two 2.0 Understand the concept of division 2.1 Find midpoint of two given points. of a line segment points. Limit to cases where m and 2.2 Find coordinates of a point that n are positive. divides a line according to a Derivation of the formula given ration m:n nx1 + mx 2 ny1 + my 2 , 3.0 Find areas of polygons 3.1 Find area of triangle based on m+n m+n the area specific geometrical is not required shapes. Limit to numerical values 3.2 Find area of a triangle by using Emphasise the formula. relationship between the 3.3 Find area of a quadrilateral sign of the value for area using formula. obtained with the order of the vertices used 4.0 Understand and use the concept of 4.1 Determine the x-intercept and Derivation of the formula: equation of a straight line the y-intercept of a line. 1 ( x1 y 2 + x 2 y 3 + x3 y1 ) − 4.2 Find the gradient of a straight 2 line that passes through two ( x 2 y1 − x3 y 2 − x1 y 3 ) points. is not required. 4.3 Find the gradient of a straight Emphasise that when area line using the x-intercept and y- of polygon is zero, the intercept. given points are collinear. 4.4 Find the equation of a straight Answers for learning line given: outcomes 4.4(a) and 4.4(b) a) gradient and one point must be stated in the b) two points simplest form. c) x-intercept and y-intercept Involve changing the 4.5 Find the gradient and the equation into gradient and intercepts of a straight line intercept form. given the equation. 4.6 Change the equation of a straight line to the general form. 4.7 Find the point of intersection of two lines. 5.0 Understand and use the concept of 5.1 Determine whether two straight Emphasise that for parallel parallel and perpendicular lines lines are parallel when lines: gradients of both lines are m1 = m2 known and vice versa. Emphasise that for 5.2 Find the equation of a straight perpendicular lines
3 S1 STATISTICS Students should be able to:WEEKS (4 1.0 Understand and use the concept 1.1 Calculate mean of ungrouped Discuss grouped data andJuly-22 of measures of tendency to solve data. ungrouped data. July) problems 1.2 Determine mode of ungrouped data. 1.3 Determine median of ungrouped data. 1.4 Determine modal class of Involve uniform class grouped data from the intervals only. frequency distribution table. 1.5 Find mode from histogram. 1.6 Calculate mean of grouped data. Derivation of the median 1.7 Calculate median of grouped formula is not required. data from the cumulative frequency distribution table. 1.8 Estimate median of grouped Ogive is also known as data from an ogive. cumulative frequency 1.9 Determine the effects on mode, curve. median and mean for a set of data. 1.10 Determine the most suitable Involve grouped and measure of central tendency for ungrouped data. given data. 2.0 Understand and use the concept 2.1 Find the range of ungrouped of measures of dispersion to data. solve problems. 2.2 Find the interquartile range of ungrouped data. 2.3 Find the range of grouped data. 2.4 Find the interquartile range of Determine upper and grouped data from the lower quartiles by using cumulative frequency table. the first principle. 2.5 Determine the interquartile range of grouped data from an ogive. 2.6 Determine the variance of: a) ungrouped data; b) grouped data 2.7 Determine standard deviation of ungrouped data and grouped data. 2.8 Determine the effect on range, interquartile range, variance and standard deviation for a set
of data when: a) each data is changed uniformly b) extreme values exist c) certain data is added or removed 2.9 Compare the measures of Emphasise that central tendency and dispersion comparison between two between two sets of data. sets of data using only measures of central tendency is not sufficient. 4 T1 CIRCULAR MEASURES Students should be able to:WEEKS (25 1.0 Understand the concept of radian. 1.1 Convert measurement in Discuss the definition ofJuly-5 radians to degrees and vice one radian. Aug) versa. ‘rad’ is the abbreviation of radian. 2.0 Understand and use the concept 2.1 Determine: Include measurements in of length of arc of a circle to solve a) length of arc radians expressed in term problems. b) radius and of π. c) angle subtended at the centre of a circle based on given information. 2.2 Find perimeter of segments of circles. 2.3 Solve problems involving lengths of arcs. TEST 2 Will be prepared by: (8 AUG – 12 AUG) PN. SURIANI
(15 Aug – 3.0 Understand and use the concept 3.1 Determine:26 Aug ) of area of sector of a circle to a) area of sector solve problems b) radius and c) angle subtended at the centre of circle based on given information. 3.2 Find area of segments of circles. 3.3 Solve problems involving area of sectors.
3 C1 DIFFERENTIATION Students should be able to:WEEKS(5 Sept 1.0 Understand the concept of radian 1.1 Determine value of a function Idea of limit to a function -23 when its variable approaches a can be illustrated using Sept) certain value. graphs. 1.2 Find gradient of a chord joining Concept of first derivative two points on a curve. of a function is explained 1.3 Find the first derivative of a as a tangent to a curve function y=f(x) as gradient of can be illustrated using tangent to its graph. graphs. 1.4 Find the first derivative for Limit to polynomial using first principles. y = ax n ; a, n are constant, 1.5 Deduce the formula for first n=1,2,3 derivative of function y=f(x) by Notation of f ( x) is induction. dy equaivalent to when dx 2.0 Understand and use the concept 2.1 Determine first derivative of the y = f (x) . f ( x) read of first derivative of polynomial function y = ax n using functions to solve problems as ‘f prime x’. formula. 2.2 Determine value of the first derivative of the function y = ax n for a given value of x. 2.3 Determine first derivative of a function involving: a) addition, or b) subtraction of algebraic terms. 2.4 Determine first derivative of a product of two polynomials. 2.5 Determine first derivative of a quotient of two polynomials. 2.6 Determine the first derivative of composite function using chain rule. 2.7 Determine gradient of tangent Limit cases in learning at a point on a curve. outcomes 2.7 – 2.9 to 2.8 Determine equation of tangent rules introduced in 2.4 – at a point on a curve. 2.6. 2.9 Determine equation of normal at a point on a curve. 3.0 Understand and use the concept 3.1 Determine coordinates of Emphasise the use of first of maximum and minimum values turning points of a curve. derivative to determine to solve problems. 3.2 Determine whether a turning turning points. point is a maximum or minimum Exclude points of inflextion.
2 AST1 SOLUTION OF TRIANGLES Students should be able to:WEEKS(26 Sept 1.0 Understand and use the concept of 1.1 Verify sine rule.- 7 Oct) sine rule to solve problems 1.2 Use sine rule to find unknown Include obtuse-angled sides or angles of triangle. triangles 1.3 Find unknown sides and angles of triangle in ambiguous case. 1.4 Solve problems involving the sine rule. 2.0 Understand and use the concept 2.1 Verify cosine rule. Include obtuse-angled of cosine rule to solve problems 2.2 Use cosine rule to find unknown triangles sides or angles of a triangle. 2.3 Solve problems involving cosine rule. 2.4 Solve problems involving sine and cosine rules. 3.0 Understand and use the formula 3.1 Find area of triangles using for area of triangles to solve 1 formula ab sin C or its problems 2 equivalent. 3.2 Solve problems involving three- dimensional objects. 2 ASS1 INDEX NUMBER Students should be able to:WEEKS (10 1.0 Understand and use the concept 1.1 Calculate index number. Explain index number. Oct-14 of index number to solve 1.2 Calculate price index. Q0 = quantity at base Oct) problems 1.3 Find Q0 orQ1 given relevant time information. Q1 = quantity at specific time 2.0 Understand and use the concept 2.1 Calculate composite index. of composite index to solve 2.2 Find index number or weightage Explain weightage and problems. given relevant information. composite index 2.3 Solve problems involving index number and composite index. • REVISION • FINAL EXAM PPSMI (17 OKT – 4 NOV)