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3. 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. ConnectionsFUNCTIONS 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
4. 4. Week/ TeachingLearning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills Area6 , 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
5. 5. Week/ TeachingLearning 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
6. 6. Week/ TeachingLearning 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
7. 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/materialsINDICES ANDLOGARITHMS 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
8. 8. Week/ TeachingLearning Learning objectives Learning outcomes Suggested activities Points to note Strategies/ Skills AreaWeek 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
9. 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’ TheoremCOORDINAT Cooperative two points situations to find the to find the formula forGEOMETRY 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
10. 10. Week/ TeachingLearning 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
11. 11. Week/ TeachingLearning 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
12. 12. Week/ TeachingLearning 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
13. 13. Week/ TeachingLearning 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
14. 14. Week/ TeachingLearning 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