Ytp Additional Mathematics Form 4
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SMK Dato’ Zulkifli Muhammad, Slim River, Perak
YEARLY TEACHING PLAN ADDITIONAL MATHEMATICS FORM 4 Week 3 Weeks 22/1 – 9/2
2 Weeks 12/2 – 23/2
Syllabus Learning Objective Functions
Suggested Teaching and Learning Activities
Learning Outcomes
(i) Represent a relation using : a) arrow diagrams b) ordered pairs c) graphs (ii) Identify domain, codomain, object, image and range of a relation. (iii) Classify a relation show on a mapped diagram as: one to one, many to one, one to many or many to many relation. 1.2 Understand the concept (i) Recognise functions as a special relation. of functions. (ii) Express functions using function notation. (iii) Determine domain, object, image and range of a function. (iv) Determine image of a function given the objects and vice versa.
•
Use pictures, role-play and computer software to introduce the concept of relations.
•
1.3 Understand the concept (i) Determine composition of two functions. of composite functions (ii) Determine image of composite functions given the object and vice versa. (iii) Determine one of the functions in a given composite function given the other related function. 1.4 Understand the concept (i) Find object by inverse mapping given its image and function. of inverse functions. (ii) Determine inverse function using algebra. (iii) Determine and state the condition for existence of an inverse function.
•
Use graphing calculator and computer software to explore the image of a function. Use arrow diagrams or algebraic method to determine composite functions.
1.1 Understand the concept of relations.
Quadratic Equation 2.1 Understand the concept (i) Recognise quadratic equation and express it in general form. of quadratic equation (ii) Determine whether a given value is the root of a quadratic equation by: and its roots. a) substitution 1
•
Use sketches of graphs to show the relationship between a function and its inverse.
•
Use graphing calculator or computer software such as the Geometer’s Sketchpad and
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
b) Inspection. (iii) Determine roots of a quadratic equation by trial and improvement method. 2.2 Understand the concept (i) Determine the roots of a quadratic equation by: of quadratic equations. a) factorisation b) completing the square c) using the formula. (ii) Form a quadratic equation from given roots. 2.3 Understand and use the (i) Determine types of roots of quadratic equations from the value of conditions for quadratic b 2 − 4ac equation to have (ii) Solve problems involving b 2 − 4ac in quadratic equations to a) two different roots. a) find an unknown value, b) two equal roots. b) derive a relation. c) no roots. 26/2 – 28/2 2 Weeks 5/3 – 23/3
spreadsheet to explore the concept of quadratic equations.
UJIAN RASMI 1 Quadratic Functions 3.1 Understand the concept (i) Recognise quadratic functions. of quadratic functions (ii) Plot quadratic function graphs a) based on given tabulated values; and their graphs. b) by tabulating values based on given functions. (iii) Recognise shapes of graphs of quadratic functions. (iv) Relate the position of quadratic function graphs with types of roots for f(x) = 0. 3.2 Find maximum and (i) Determine the maximum or minimum value of a quadratic function by minimum values of completing the square. quadratic functions.
3.3 Sketch graphs of quadratic functions.
(i)
Sketch quadratic function graphs by determining the maximum or minimum point and two other points.
2
Use graphing calculator or computer software such as the Geometer’s Sketchpad to explore the graphs of quadratic functions. • Use examples of everyday situations to introduce graphs of quadratic functions. • Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to explore the graphs of quadratic functions. •
•
Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to reinforce the understanding of
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
3.4 Understand and use the concept of quadratic inequalities.
10/3 – 18/3 1 Weeks 26/3 – 30/3
10/4 – 12/4 3 Weeks 16/4 – 4/5
(i)
Determine the ranges of values of x that satisfies quadratic inequalities.
•
graphs of quadratic functions. Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of quadratic inequalities.
CUTI PERTENGAHAN PENGGAL 1 Simultaneous Equation 4.1 Solve simultaneous equation in two unknowns one linear equation and one nonlinear equation.
• (i) Solve simultaneous equations using the substitution method. (ii) Solve simultaneous equations involving real-life situations. •
Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of simultaneous equations. Use examples in real-life situations such as area, perimeter and others.
UJIAN RASMI 2 Indices and Logarithms 5.1 Understand and use the concept of indices and laws of indices to solve problems.
5.2 Understand and use the concept of logarithms and laws of logarithms to solve problems. 5.3 Understand and use the change of base of logarithms to solve problems. 5.4 Solve equations
• (i)
(ii) (iii) (i) (ii) (iii) (iv)
Find the values of numbers given in the form of; a) integer indices b) fractional indices Use laws of indices to find the values of numbers in index form that are multiplied divided, or raised to a power. Use laws of indices to simplify algebraic expressions. Express equation in index form to logarithm form and vice versa. Find logarithm of a number. Find logarithm of numbers by using laws of logarithm. Simplify logarithmic expressions to the simplest form.
(i)
Find the logarithm of a number by changing the base of the logarithm to a suitable base. (ii) Solve problems involving the change of base and laws of logarithms. (i)
Solve equations involving indices. 3
•
•
Use examples in real-life situations to introduce the concept of indices. Use computer software such as the spreadsheet to enhance the understanding of indices.
Use scientific calculator to enhance the understanding of the concept of logarithm.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
involving indices and logarithms. 7/5 – 18/5 15/5–5/5
(ii) Solve equations involving logarithms.
REVISION AND PREPARATION FOR MID YEAR EXAMINATIONS PEPERIKSAAN PERTENGAHAN TAHUN CUTI PERTENGAHAN TAHUN
26/5-10/ 6 3 Weeks Coordinate 11/6 – Geometry 6.1 Find distance between 29/6 two points.
(i)
Find distance between two points using formula.
6.2 Understand the concept of division of a line segment. 6.3 Find areas of polygons.
(i) Find midpoint of two given points. (ii) Find coordinates of a point that divides a line according to a given ratio m : n. (i) Find area of a triangle based on the area of specific geometrical shapes. (ii) Find area of a triangle y using formula. (iii) Find area of a quadrilateral using formula.
6.4 Understand and use the concept of equation of a straight line.
(i) (ii) (iii) (iv)
6.5 Understand and use the concept of parallel and perpendicular lines.
Determine the x-intercept and the y-intercept of a line. Find the gradient of a straight line that passes through two points. Find the gradient of a straight line using the x-intercept and y-intercept. Find the equation of a straight line given; a) gradient and one point; b) two points; c) x-intercept and y-intercept. (v) Find the gradient and the intercepts of a straight line given the equation. (vi) Change the equation of a straight line to the general form. (vii) Find the point of intersection of two lines. (i) Determine whether two straight lines are parallel when gradients of both lines are known and vice versa. (ii) Find the equation of a straight line that passes through a fixed point and parallel to a given line. 4
•
Use examples of real-life situations to find the distance between two points.
Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of area of polygons. 1 x1 x 2 x 3 x1 • Use for substitution 2 y1 y 2 y 3 y 4 of coordinates into the formula. a) Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of equation of a straight line. •
•
Use examples of real-life situations to explore parallel and perpendicular lines.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
3 Weeks 2/7 – 20/7
6.6 Understand and use the concept of equation of locus involving distance between two points.
(iii) Determine whether two straight lines are perpendicular when gradients of both lines are known and vice versa. (iv) Determine the equation of a straight line that passes through a fixed point and perpendicular to a given line. (v) Solve problems involving equations of straight lines. (i) Find the equation of locus that satisfies the condition if: a) the distance of a moving point from a fixed point is constant; b) the ratio of the distances of a moving point from two fixed points is constant. (ii) Solve problems involving loci.
Statistics 7.1 Understand and use the concept of measures of central tendency to solve problems.
(i) (ii) (iii) (iv)
7.2 Understand and use the concept of measures of dispersion to solve problems.
•
•
•
Calculate mean of ungrouped data. • Determine mode of ungrouped data. Determine median of ungrouped data. Determine modal class of grouped data from the frequency distribution table. • (v) Find mode from histogram. (vi) Calculate mean of grouped data. (vii) Calculate median of grouped data from the cumulative frequency distribution table. (viii) Estimate median of grouped data from an ogive. (ix) Determine the effects on mode, median and mean for a set of data when: a) each data is changed uniformly, b) extreme values exist, c) certain data is added or removed. (x) Determine the most suitable measure of central tendency for given data. (i) Find the range of ungrouped data. (ii) Find the interquartile range of ungrouped data. (iii) Find the range of grouped data. (iv) Find the interquartile range of grouped data from the cumulative 5
Use graphic calculator and dynamic geometry software such as Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines. Use examples of real-life situations to explore equation of locus involving distance between two points. Use graphic calculator and dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines. Use scientific calculator, graphing calculators and spreadsheets to explore measures of central tendency. Students collect data from real-life situations to investigate measures of central tendency.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
frequency table. (v) Determine the interquartile range of grouped data from an ogive. (vi) Determine the variance of a) ungrouped data; b) grouped data. (vii) Determine standard deviation of a) ungrouped data b) grouped data (viii) Determine the effects 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. (ix) Compare the measures of central tendency and dispersion between two sets of data. 24/7 – 26/7 3 Weeks 30/7 – 17/8
UJIAN RASMI 3 Circular Measures 8.1 Understand the concept of radian.
8.2 Understand and use the concept of length of arc of a circle to solve problems.
8.3 Understand and use the concept of area of sector of a circle to solve problems.
(i)
Convert measurements in radians to degrees and vice versa.
(i)
Determine: a) length of arc b) radius and c) angle subtended at the centre of a circle based on given information. (ii) Find perimeter of segments of circles (iii) Solve problems involving lengths of arcs. (i) Determine: b) area of sector c) radius and d) angle subtended at the centre of a circle based on given information. 6
•
•
Use dynamic geometry software such as Geometer’s Sketchpad to explore the concept of circular measure. Use examples of real-life situations to explore circular measure.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
(ii) (iii) 18/8 – 26/8 4 Weeks 27/8 – 21/9
Find area of segments of circles. Solve problems involving area of sectors.
CUTI PERTENGAHAN PENGGAL 2 Differentiation 9.1 Understand and use the concept of gradients of curve and differentiation
9.2 Understand and use the concept of first derivative of polynomial functions to solve problems.
9.3 Understand and use the concept of maximum and minimum values to solve problems. 9.4 Understand and use the concept of rates of change to solve problems 9.5 Understand and use the concept of small changes and
(i) (ii) (iii) (iv) (v) (i)
Determine value of a function when its variable approaches a certain value. Find gradient of a chord joining two points on a curve. Find the first derivative of a function y = f(x) as gradient of tangent to its graph. Find the first derivative for polynomial using first principles. Deduce the formula for first derivative of function y = f(x) by induction. Determine first derivative of the function y = ax n using formula.
(ii) Determine value of the first derivative of the function y = ax n for a given value of x. (iii) Determine first derivative of a function involving: a) addition, or b) subtraction of algebraic terms. (iv) Determine first derivative of a product of two polynomials. (v) Determine first derivative of a quotient of two polynomials. (vi) Determine first derivative of composite function using chain rule. (vii) Determine gradient of tangent at a point on curve. (viii)Determine equation of tangent at a point on a curve. Determine equation of normal at a point on a curve. (i) Determine coordinates of turning points of a curve. (ii) Determine whether a turning point is a maximum or minimum point. (iii) Solve problems involving maximum or minimum values. (i)
Determine rates of change for related quantities.
(i) Determine small changes in quantities. (ii) Determine approximate values using differentiation. 7
•
Use graphing calculator or dynamic geometry software such as Geometer’s Sketchpad to explore the concept of differentiation.
•
Use graphing calculator or dynamic geometry software to explore the concept of maximum and minimum values. Use graphing calculator with computer base ranger to explore the concept of rates of change.
•
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
2 Weeks 24/9 – 5/10
approximations to solve problems. 9.6 Understand and use the concept of second derivative to solve problems. Solution of Triangles 10.1 Understand and use the concept of sine rule to solve problems.
(i) Determine second derivative of function y = f (x) . (ii) Determine whether a turning point is maximum or minimum point of a curve using the second derivative.
(i) (ii) (iii) (iv)
Verify sine rule. Use sine rule to find unknown sides or a triangle Find unknown sides and angles of a triangle in a ambiguous case. Solve problems involving sine rule.
•
•
10.2 Understand and use the concept of cosine rule to solve problems.
(i) Verify cosine rules. (ii) Use cosine rule to find unknown sides or angles of a triangle. (iii)Solve problem involving cosine rule. (iv) Solving problems involving sine and cosine rules.
•
10.3 Understand and use the formula for area of triangles to solve problems.
1 ab sin C or its equivalent. 2 (ii) Solve problems involving three-dimensional objects.
•
(i) Find area of triangles using formula
•
•
1 Week 8/10 – 12/10
15/10 –
Index Number 11.1 Understand and use the concept of index number to solve problems. 11.2 Understand and use the concept of composite index to solve problems.
(i) Calculate index number. (ii) Calculate price index (iii) Find Qo or Q1 given relevant information. (i) Calculate composite index. (ii) Find index number or weightage given relevant information. (iii) Solve problems involving index number and composite index.
Use dynamic geometry software such as the Geometer’s Sketchpad to explore the sine rule. Use examples of real-life situations to explore the sine rule. Use dynamic geometry software such as the Geometer’s Sketchpad to explore the cosine rule. Use examples of real-life situations to explore the cosine rule Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of area triangles. Use examples of real-life situations to explore area of triangles.
•
Use examples of real-life situations to explore index numbers.
•
Use examples of real-life situations to explore composite index.
REVISION AND PREPARATION FOR THE END OF THE YEAR EXAMINATIONS 8
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
31/10 1/11 – 16/11
END OF THE YEAR EXAMINATION
9
YEARLY TEACHING PLAN ADDITIONAL MATHEMATICS FORM 4 Week 3 Weeks 22/1 – 9/2
2 Weeks 12/2 – 23/2
Syllabus Learning Objective Functions
Suggested Teaching and Learning Activities
Learning Outcomes
(i) Represent a relation using : a) arrow diagrams b) ordered pairs c) graphs (ii) Identify domain, codomain, object, image and range of a relation. (iii) Classify a relation show on a mapped diagram as: one to one, many to one, one to many or many to many relation. 1.2 Understand the concept (i) Recognise functions as a special relation. of functions. (ii) Express functions using function notation. (iii) Determine domain, object, image and range of a function. (iv) Determine image of a function given the objects and vice versa.
•
Use pictures, role-play and computer software to introduce the concept of relations.
•
1.3 Understand the concept (i) Determine composition of two functions. of composite functions (ii) Determine image of composite functions given the object and vice versa. (iii) Determine one of the functions in a given composite function given the other related function. 1.4 Understand the concept (i) Find object by inverse mapping given its image and function. of inverse functions. (ii) Determine inverse function using algebra. (iii) Determine and state the condition for existence of an inverse function.
•
Use graphing calculator and computer software to explore the image of a function. Use arrow diagrams or algebraic method to determine composite functions.
1.1 Understand the concept of relations.
Quadratic Equation 2.1 Understand the concept (i) Recognise quadratic equation and express it in general form. of quadratic equation (ii) Determine whether a given value is the root of a quadratic equation by: and its roots. a) substitution 1
•
Use sketches of graphs to show the relationship between a function and its inverse.
•
Use graphing calculator or computer software such as the Geometer’s Sketchpad and
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
b) Inspection. (iii) Determine roots of a quadratic equation by trial and improvement method. 2.2 Understand the concept (i) Determine the roots of a quadratic equation by: of quadratic equations. a) factorisation b) completing the square c) using the formula. (ii) Form a quadratic equation from given roots. 2.3 Understand and use the (i) Determine types of roots of quadratic equations from the value of conditions for quadratic b 2 − 4ac equation to have (ii) Solve problems involving b 2 − 4ac in quadratic equations to a) two different roots. a) find an unknown value, b) two equal roots. b) derive a relation. c) no roots. 26/2 – 28/2 2 Weeks 5/3 – 23/3
spreadsheet to explore the concept of quadratic equations.
UJIAN RASMI 1 Quadratic Functions 3.1 Understand the concept (i) Recognise quadratic functions. of quadratic functions (ii) Plot quadratic function graphs a) based on given tabulated values; and their graphs. b) by tabulating values based on given functions. (iii) Recognise shapes of graphs of quadratic functions. (iv) Relate the position of quadratic function graphs with types of roots for f(x) = 0. 3.2 Find maximum and (i) Determine the maximum or minimum value of a quadratic function by minimum values of completing the square. quadratic functions.
3.3 Sketch graphs of quadratic functions.
(i)
Sketch quadratic function graphs by determining the maximum or minimum point and two other points.
2
Use graphing calculator or computer software such as the Geometer’s Sketchpad to explore the graphs of quadratic functions. • Use examples of everyday situations to introduce graphs of quadratic functions. • Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to explore the graphs of quadratic functions. •
•
Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to reinforce the understanding of
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
3.4 Understand and use the concept of quadratic inequalities.
10/3 – 18/3 1 Weeks 26/3 – 30/3
10/4 – 12/4 3 Weeks 16/4 – 4/5
(i)
Determine the ranges of values of x that satisfies quadratic inequalities.
•
graphs of quadratic functions. Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of quadratic inequalities.
CUTI PERTENGAHAN PENGGAL 1 Simultaneous Equation 4.1 Solve simultaneous equation in two unknowns one linear equation and one nonlinear equation.
• (i) Solve simultaneous equations using the substitution method. (ii) Solve simultaneous equations involving real-life situations. •
Use graphing calculator or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of simultaneous equations. Use examples in real-life situations such as area, perimeter and others.
UJIAN RASMI 2 Indices and Logarithms 5.1 Understand and use the concept of indices and laws of indices to solve problems.
5.2 Understand and use the concept of logarithms and laws of logarithms to solve problems. 5.3 Understand and use the change of base of logarithms to solve problems. 5.4 Solve equations
• (i)
(ii) (iii) (i) (ii) (iii) (iv)
Find the values of numbers given in the form of; a) integer indices b) fractional indices Use laws of indices to find the values of numbers in index form that are multiplied divided, or raised to a power. Use laws of indices to simplify algebraic expressions. Express equation in index form to logarithm form and vice versa. Find logarithm of a number. Find logarithm of numbers by using laws of logarithm. Simplify logarithmic expressions to the simplest form.
(i)
Find the logarithm of a number by changing the base of the logarithm to a suitable base. (ii) Solve problems involving the change of base and laws of logarithms. (i)
Solve equations involving indices. 3
•
•
Use examples in real-life situations to introduce the concept of indices. Use computer software such as the spreadsheet to enhance the understanding of indices.
Use scientific calculator to enhance the understanding of the concept of logarithm.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
involving indices and logarithms. 7/5 – 18/5 15/5–5/5
(ii) Solve equations involving logarithms.
REVISION AND PREPARATION FOR MID YEAR EXAMINATIONS PEPERIKSAAN PERTENGAHAN TAHUN CUTI PERTENGAHAN TAHUN
26/5-10/ 6 3 Weeks Coordinate 11/6 – Geometry 6.1 Find distance between 29/6 two points.
(i)
Find distance between two points using formula.
6.2 Understand the concept of division of a line segment. 6.3 Find areas of polygons.
(i) Find midpoint of two given points. (ii) Find coordinates of a point that divides a line according to a given ratio m : n. (i) Find area of a triangle based on the area of specific geometrical shapes. (ii) Find area of a triangle y using formula. (iii) Find area of a quadrilateral using formula.
6.4 Understand and use the concept of equation of a straight line.
(i) (ii) (iii) (iv)
6.5 Understand and use the concept of parallel and perpendicular lines.
Determine the x-intercept and the y-intercept of a line. Find the gradient of a straight line that passes through two points. Find the gradient of a straight line using the x-intercept and y-intercept. Find the equation of a straight line given; a) gradient and one point; b) two points; c) x-intercept and y-intercept. (v) Find the gradient and the intercepts of a straight line given the equation. (vi) Change the equation of a straight line to the general form. (vii) Find the point of intersection of two lines. (i) Determine whether two straight lines are parallel when gradients of both lines are known and vice versa. (ii) Find the equation of a straight line that passes through a fixed point and parallel to a given line. 4
•
Use examples of real-life situations to find the distance between two points.
Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of area of polygons. 1 x1 x 2 x 3 x1 • Use for substitution 2 y1 y 2 y 3 y 4 of coordinates into the formula. a) Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of equation of a straight line. •
•
Use examples of real-life situations to explore parallel and perpendicular lines.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
3 Weeks 2/7 – 20/7
6.6 Understand and use the concept of equation of locus involving distance between two points.
(iii) Determine whether two straight lines are perpendicular when gradients of both lines are known and vice versa. (iv) Determine the equation of a straight line that passes through a fixed point and perpendicular to a given line. (v) Solve problems involving equations of straight lines. (i) Find the equation of locus that satisfies the condition if: a) the distance of a moving point from a fixed point is constant; b) the ratio of the distances of a moving point from two fixed points is constant. (ii) Solve problems involving loci.
Statistics 7.1 Understand and use the concept of measures of central tendency to solve problems.
(i) (ii) (iii) (iv)
7.2 Understand and use the concept of measures of dispersion to solve problems.
•
•
•
Calculate mean of ungrouped data. • Determine mode of ungrouped data. Determine median of ungrouped data. Determine modal class of grouped data from the frequency distribution table. • (v) Find mode from histogram. (vi) Calculate mean of grouped data. (vii) Calculate median of grouped data from the cumulative frequency distribution table. (viii) Estimate median of grouped data from an ogive. (ix) Determine the effects on mode, median and mean for a set of data when: a) each data is changed uniformly, b) extreme values exist, c) certain data is added or removed. (x) Determine the most suitable measure of central tendency for given data. (i) Find the range of ungrouped data. (ii) Find the interquartile range of ungrouped data. (iii) Find the range of grouped data. (iv) Find the interquartile range of grouped data from the cumulative 5
Use graphic calculator and dynamic geometry software such as Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines. Use examples of real-life situations to explore equation of locus involving distance between two points. Use graphic calculator and dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines. Use scientific calculator, graphing calculators and spreadsheets to explore measures of central tendency. Students collect data from real-life situations to investigate measures of central tendency.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
frequency table. (v) Determine the interquartile range of grouped data from an ogive. (vi) Determine the variance of a) ungrouped data; b) grouped data. (vii) Determine standard deviation of a) ungrouped data b) grouped data (viii) Determine the effects 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. (ix) Compare the measures of central tendency and dispersion between two sets of data. 24/7 – 26/7 3 Weeks 30/7 – 17/8
UJIAN RASMI 3 Circular Measures 8.1 Understand the concept of radian.
8.2 Understand and use the concept of length of arc of a circle to solve problems.
8.3 Understand and use the concept of area of sector of a circle to solve problems.
(i)
Convert measurements in radians to degrees and vice versa.
(i)
Determine: a) length of arc b) radius and c) angle subtended at the centre of a circle based on given information. (ii) Find perimeter of segments of circles (iii) Solve problems involving lengths of arcs. (i) Determine: b) area of sector c) radius and d) angle subtended at the centre of a circle based on given information. 6
•
•
Use dynamic geometry software such as Geometer’s Sketchpad to explore the concept of circular measure. Use examples of real-life situations to explore circular measure.
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
(ii) (iii) 18/8 – 26/8 4 Weeks 27/8 – 21/9
Find area of segments of circles. Solve problems involving area of sectors.
CUTI PERTENGAHAN PENGGAL 2 Differentiation 9.1 Understand and use the concept of gradients of curve and differentiation
9.2 Understand and use the concept of first derivative of polynomial functions to solve problems.
9.3 Understand and use the concept of maximum and minimum values to solve problems. 9.4 Understand and use the concept of rates of change to solve problems 9.5 Understand and use the concept of small changes and
(i) (ii) (iii) (iv) (v) (i)
Determine value of a function when its variable approaches a certain value. Find gradient of a chord joining two points on a curve. Find the first derivative of a function y = f(x) as gradient of tangent to its graph. Find the first derivative for polynomial using first principles. Deduce the formula for first derivative of function y = f(x) by induction. Determine first derivative of the function y = ax n using formula.
(ii) Determine value of the first derivative of the function y = ax n for a given value of x. (iii) Determine first derivative of a function involving: a) addition, or b) subtraction of algebraic terms. (iv) Determine first derivative of a product of two polynomials. (v) Determine first derivative of a quotient of two polynomials. (vi) Determine first derivative of composite function using chain rule. (vii) Determine gradient of tangent at a point on curve. (viii)Determine equation of tangent at a point on a curve. Determine equation of normal at a point on a curve. (i) Determine coordinates of turning points of a curve. (ii) Determine whether a turning point is a maximum or minimum point. (iii) Solve problems involving maximum or minimum values. (i)
Determine rates of change for related quantities.
(i) Determine small changes in quantities. (ii) Determine approximate values using differentiation. 7
•
Use graphing calculator or dynamic geometry software such as Geometer’s Sketchpad to explore the concept of differentiation.
•
Use graphing calculator or dynamic geometry software to explore the concept of maximum and minimum values. Use graphing calculator with computer base ranger to explore the concept of rates of change.
•
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
2 Weeks 24/9 – 5/10
approximations to solve problems. 9.6 Understand and use the concept of second derivative to solve problems. Solution of Triangles 10.1 Understand and use the concept of sine rule to solve problems.
(i) Determine second derivative of function y = f (x) . (ii) Determine whether a turning point is maximum or minimum point of a curve using the second derivative.
(i) (ii) (iii) (iv)
Verify sine rule. Use sine rule to find unknown sides or a triangle Find unknown sides and angles of a triangle in a ambiguous case. Solve problems involving sine rule.
•
•
10.2 Understand and use the concept of cosine rule to solve problems.
(i) Verify cosine rules. (ii) Use cosine rule to find unknown sides or angles of a triangle. (iii)Solve problem involving cosine rule. (iv) Solving problems involving sine and cosine rules.
•
10.3 Understand and use the formula for area of triangles to solve problems.
1 ab sin C or its equivalent. 2 (ii) Solve problems involving three-dimensional objects.
•
(i) Find area of triangles using formula
•
•
1 Week 8/10 – 12/10
15/10 –
Index Number 11.1 Understand and use the concept of index number to solve problems. 11.2 Understand and use the concept of composite index to solve problems.
(i) Calculate index number. (ii) Calculate price index (iii) Find Qo or Q1 given relevant information. (i) Calculate composite index. (ii) Find index number or weightage given relevant information. (iii) Solve problems involving index number and composite index.
Use dynamic geometry software such as the Geometer’s Sketchpad to explore the sine rule. Use examples of real-life situations to explore the sine rule. Use dynamic geometry software such as the Geometer’s Sketchpad to explore the cosine rule. Use examples of real-life situations to explore the cosine rule Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of area triangles. Use examples of real-life situations to explore area of triangles.
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Use examples of real-life situations to explore index numbers.
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Use examples of real-life situations to explore composite index.
REVISION AND PREPARATION FOR THE END OF THE YEAR EXAMINATIONS 8
SMK Dato’ Zulkifli Muhammad, Slim River, Perak
31/10 1/11 – 16/11
END OF THE YEAR EXAMINATION
9
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