Form 4 Add. Mathematics Yearly Scheme Of Work (2014)

Date

Learning Objectives

Learning Outcomes

2 Jan-24 Jan

27 Jan-21 Feb

24 Feb-11 April

14 Apr-18 April

21 Apr-16 May

16 Jun-18 July

21 July-15 Aug

18 Aug-29 Aug

1 Sept-10 Oct

13 Oct-24 Oct

27 Oct-14 Nov

1 Functions

1.1 Understand the concept of relations

1.2 Understand the concept of functions

1.3 Understand the concept of composite functions

1.4 Understand the concept of inverse functions

2 Quadratic Equations

2.1 Understand the concept of quadratic equation and its roots

2.2 Understand the concept quadratic equations

2.3 Understand and use the conditions for quadratic equations to have (a) two different roots (b) two equal roots (c) no roots.

3 Quadratic Functions

3.1 Understand the concept of quadratic functions and their graphs

3.2 Find the maximum and minimum values of quadratic functions

3.3 Sketch the graphs of quadratic functions

3.4 Understand and use the concept of quadratic inequalities.

4 Simultaneous Equations

4.1 Solve simultaneous equations in two unknowns: one linear and one non-linear equations

5 Indices And Logarithms

5.1 Understand and use the concept of indices and laws of indices

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 involving indices and logarithm

6 Coordinate Geometry

6.1 Find the distance between two points

6.2 Understand the concept of division of a line segment

6.3 Find the areas of polygons

6.4 Understand and use the concept of equation of a straight line

6.5 Understand and use the concept of parallel and perpendicular lines.

6.6 Understand and use the concept of equation of locus involving distance between two points.

7 Statistics

7.1 Understand and use the concept of measures of central tendency to solve problems.

7.2 Understand and use the concept of measures of dispersion to solve problems.

8 Circular Measures

8.1 Understand the concept of radian

8.2 Understand and use the concept of length od arc of a circle to solve problems.

8.3 Understand and use the concept of the area of a sector of a circle to solve problems.

9 Differentiation

9.1 Understand and use the concept of gradients of a 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 approximations to solve problems

9.6 Understand and use the concept of second derivative to solve problems.

10 Solutions of Triangles

10.1 Understand and use the concept of sine rule to solve problems

10.2 Understand and use the concept of cosine rule to solve problems.

10.3 Understand and use the formula for areas of triangles to solve problems.

11 Index Number

11.1 Understand and use the concept of index number to solve problems.

11.2 Understand and use the concept o composite index to solve problems.

1.1.1 Represent a relation using arrow diagram, ordered pairs and graph.

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

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

1.2.1 Recognise function as a special relation.

1.2.2 Express functions using notation.

1.2.3 Determine domain, object, image and range of a function.

1.2.4 Determine image of a function given the object and vice versa.

1.3.1 Determine composition of two functions.

1.3.2 Determine image of composite functions given the object and vice versa.

1.3.3 Determine one of the function in a given composite function given the other related function.

1.4.1 Find object by inverse mapping given its image and function.

1.4.2 Determine inverse function using algebra.

1.4.3 Determine and state the condition for existence of an inverse function.

2.1.1 Recognise quadratic equation and express it in general form.

2.1.2 Determine whether a given value is the root of a quadratic equation by (a) substitution (b) inspection.

2.1.3 Determine roots of a quadratic equation by trial and improvement method.

2.2.1 Determine the roots of a quadratic equation by (a) factorization (b) completing the square (c) using the formula.

2.2.2 Form a quadratic equation from given roots.

2.3.1Determine the types of roots of quadratic equations from the value of b2 4ac.

2.3.2 Solve problems involving b2-4ac in quadratic equations to: (a) find an unknown value(b) derive a relation.

3.1.1 Recognise quadratic functions

3.1.2 Plot graphs of quadratic functions

(a) based on given tabulated values (b) by constructing the tables of values.

3.1.3 Recognise shapes of graphs of quadratic functions

3.1.4 Relate the position of quadratic function graphs with types of roots for f(x)=0

3.2.1 Determine the maximum or minimum value of a of quadratic function by completing the square.

3.3.1 Sketch the graphs of quadratic 18 Aprilfunctions by determining the maximum or minimum point and two other points.

3.4.1 Determine the range of values of x that satisfies quadratic inequalities.

4.1.1Solve simultaneous equations using substitution method.

4.1.2 Solve simultaneous equations involving real-life situations.

5.1.1 Find the values of numbers given in the form of (a) integer indices,(b) fractional indices.

5.1.2 Use laws of indices to find values of numbers in index form that are multiplied, divided or raised to a power.

5.1.3 Use laws of indices to simplify algebraic expressions.

5.2.1 Convert equation in index form to logarithmic form and vice versa.

5.2.2 Find the logarithm of a number.

5.2.3 Find the logarithm of a number by using laws of logarithms.

5.2.4 Simplify logarithmic expressions to the simplest form.

5.3.1 Find the logarithm of a number by changing the base of the logarithm to a suitable base.

5.3.2 Solve problems involving the change of base using laws of logarithms.

5.4.1 Solve equations involving indices.

5.4.2 Solve equations involving logarithms.

6.1.1 Find distance between two points using formula.

6.2.1 Find the midpoint of two given points

6.2.2 Find the coordinates of a point that divides a line according to a given ratio m:n

6.3.1 Find area of a triangle based on area of specific geometrical shapes.

6.3.2 Find area of a triangle using formula.

6.3.3 Find area of a quadrilateral using formula.

6.4.1 Determine the x-intercept and the y-intercept of a line.

6.4.2 Find the gradient of a straight line that passes through two points.

6.4.3 Find the gradient of a straight line using x-intercept and y-intercept.

6.4.4 Find the equation of a straight given (a) gradient and one point (b) two points (c) x-intercept and y-intercept.

6.4.5 Find the gradient and the intercepts of a straight line to the general form

6.4.6 Change the equation of a straight line to the general form

6.4.7 Find the point of intersection of two lines.

6.5.1 Determine whether two straight lines are parallel when gradients of both lines are known and vice versa.

6.5.2 find the equation of a straight line that passes through a fixed point and parallel to a given line

6.5.3 Determine whether two straight lines are perpendicular when gradients of both lines are known and vice versa.

6.5.4 Determine the equation of a straight line that passes through a fixed point and perpendicular to a given line.

6.5.5 Solve problems involving equation of straight lines.

6.6.1 Find the equation of a 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.

6.6.2 Solve problems involving loci.

7.1.1 Calculate mean of ungrouped data.

7.1.2 Determine mode of ungrouped data

7.1.3 Determine median of ungrouped data.

7.1.4 Determine modal class of grouped data from the frequency distribution table.

7.1.5 Find mode from histogram.

7.1.6 Calculate mean of grouped data.

7.1.7 calculate median of grouped data from the cumulative frequency distribution table.

7.1.8 Estimate median of grouped data from ogive

7.1.9 Determine the effect on mode, median and mean for a set of data when (a) every value of the data is changed uniformly (b) extreme values exist (c) certain values are added or removed.

7.1.10 Determine the most suitable measure of central tendency for given data.

7.2.1Find the range of ungrouped data.

7.2.2 Find the interquartile range of ungrouped data.

7.2.3 Find the range of grouped data.

7.2.4 Find the interquartile range of grouped data from cumulative frequency table.

7.2.5 Determine the interquartile range of grouped data from an ogive.

7.2.6 Determine the variance of (a) ungrouped data (b) grouped data.

7.2.7 Determine standard deviation of (a) ungrouped data (b) grouped data.

7.2.8 Determine the effects on range, interquartile range, variance and standard deviation for a set of data (a) every value of the data is changed uniformly (b) Extreme values exist (c) certain values are added or removed.

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

8.1.2 Convert measurements in radians to degrees and vice versa.

8.2.1 Determine (a) length of arc (b) radius (c) angle subtended at the centre of a circle, based on given information.

8.2.2 Find perimeter of segments of a circle.

8.2.3 Solve problems involving lengths of arcs.

8.3.1 Determine (a) area of sector (b) radius (c) angle subtended at the centre of a circle, based on given information

8.3.2 Find area of segments of a circle.

8.3.3 Solve problems involving area of sectors.

9.1.1 Determine value of a function when its variable approaches a certain value.

9.1.2 Find the gradient of chord joining two points on a curve.

9.1.3 Find the first derivative of a function y=f(x) as a gradient tangent to its graph.

9.1.4 Find the first derivative for polynomial using the first principle.

9.1.5 Deduce the formula for the first derivative of function y=f(x) by induction

9.2.1 Determine first derivative of the function y=axn using formula.

9.2.2 Determine value of the first derivative of a function y=axn for a given value of x.

9.2.3 Determine first derivative of a function involving addition and subtraction of algebraic terms.

9.2.4 Determine first derivative of a product of two polynomials

9.2.5 Determine first derivative of a quotient of two polynomials.

9.2.6 Determine first derivative of a composite function using chain rule.

9.2.7 Determine gradient of tangent at a point on a curve.

9.2.8 Determine equation of tangent at a point on a curve.

9.2.9 Determine equation of normal at a point on a curve

9.3.1 Determine coordinates of turning points of a curve.

9.3.2 Determine whether a turning points is a maximum or minimum point.

9.3.3 Solve problems involving maximum or minimum values.

9.4.1 Determine rates of change for related quantities.

9.5.1 Determine small changes in quantities.

9.5.2 Determine approximate values using differentiation.

9.6.1 determine second derivative of function y=f(x)

9.6.2 determine whether a turning point is a maximum or minimum point of a curve using the second derivative.

10.1.1 Verify the sine rule

10.1.2 Use the sine rule to find the unknown sides or angles of a triangle.

10.1.3 Find the unknown sides or angles of a triangle in an ambiguous case.

10.1.4 Solve problems involving the sine rule.

10.2.1 Verify the cosine rule.

10.2.2 Use the cosine rule to find the unknown sides or angles of a triangle

10.2.3 Solve problems involving the cosine rule.

10.2.4 Solve problems involving the sine and cosine rule.

10.3.1 find the area of triangles using the formula absinC or its equivalent.

10.3.2 Solve problems involving

3- dimensional objects.

11.1.1 Calculate index number

11.1.2 Calculate price index

11.1.3 Find Q0 and Q1 given relevant information.

11.2.1 Calculate composite index

11.2.2 find the index number or weightage given relevant information

11.2.3 Solve problem involving index number and composite index