add maths - form 4 - year-plan

8/14/2019 Add Maths - Form 4 - Year-plan

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WEEK/

DATE

LEARNING

OBJECTIVES

SUGGESTED TEACHING

AND LEARNING

ACTIVITIES

LEARNING OUTCOMES

Students will be

taught to:

Students will be able to:

3 FUNCTIONS

1. Understand the

concept of

relations.

Use pictures, role-

play and computer

software to introduce

the concept of relations.

1.1 Represent relations using

a) arrow diagrams

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.

2. Understand the

concept of

functions.

Use graphing

calculators and

computer software to

explore the image of

functions.

2.1 Recognize functions as a special

relation.

2.2 Express functions using function

notation.

2.3 Determine domain, object, image

and range of a function.

2.4 Determine the image of a

function given the object and vice

versa.

FORM 4 ADDITIONAL MATHEMTICS YEARLY SCHEME OF WORK


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3. Understand the

concept of

composite

functions.

Use arrow

diagrams or algebraic

method to determine

composite functions.

3.1 Determine composition of twofunctions.

3.2 Determine the image ofcomposite functions given the

object and vice versa.

3.3 Determine one of the functionsin a given composite functiongiven the other related function.

4. Understand the

concept of

inverse functions.

Use sketches ofgraphs to show therelationship between afunction and itsinverse.

4.1 Find the object by inversemapping given its image andfunction.

4.2 Determine inverse functionsusing algebra.

ii. 4.3 Determine and statethe condition for existence of aninverse function.

4

QUADRATIC

EQUATIONS

1. Understand the

concept of

quadratic equation

and its roots.

Use graphing

calculators or

computer software

such as the

Geometers

Sketchpad and

spreadsheet to

explore the conceptof quadratic

equations.

1.1 Recognise a quadratic equationand express it in general form.

1.2 Determine whether a given valueis the root of a quadraticequation bya) substitution;

b) inspection.

1.3 Determine roots of quadraticequations by trial andimprovement method.


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2. Understand the

concept of

quadratic

equations.

2.1 Determine the roots of aquadratic equation by

a) factorisation;b) completing the squarec) using the formula.

2.2 Form a quadratic equation fromgiven roots.

3. Understand and

use the conditions

for quadratic

equations to have

a) two different

roots;b) two equal

roots;

c) no roots.

3.1 Determine types of roots ofquadratic equations from thevalue of b2 4ac.

3.2 Solve problems involvingb2 4ac in quadratic equations

to:a) find an unknown value;b) derive a relation.

4

QUADRATIC

FUNCTIONS

1. Understand the

concept of

quadratic functions

and their graphs.

Use graphing

calculators or computersoftware such as

Geometers Sketchpad

to explore the graphs

of quadratic functions.

Use

examples of everyday

situations to introduce

graphs of quadratic

functions.

1.1 Recognise quadratic functions.

1.2 Plot quadratic function graphs

a) based on given tabulatedvalues;

b) by tabulating values basedon given functions.

1.3 Recognise shapes of graphs ofquadratic functions.

1.4 Relate the position of quadratic

function graphs withtypes of roots for f (x)0.


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2. Find the

maximum and

minimum values

of quadratic

functions.

Use

graphing calculators or

dynamic geometry

software such as the

GeometersSketchpad to explore

the graphs of

quadratic functions.

2.1 Determine the maximum orminimum value of a quadraticfunction by completing thesquare.

3. Sketch graphs of

quadratic

functions.

Use


dynamic geometry


Geometers

Sketchpad to reinforce

the understanding of

graphs of quadratic

functions.

3.1 Sketch quadratic function graphsby determining the maximum orminimum point and two other

points.

4. Understand and

use the concept

of quadratic

inequalities.

Use


dynamic geometry


Geometers

Sketchpad to explore

the concept of

quadratic inequalities.

4.1 Determine the ranges of valuesof x that satisfies quadraticinequalities.

1

SIMULTANEOUS

EQUATIONS

1. Solve

simultaneous

equations in two

unknowns: one

linear equation

and one non-

linear equation.

Use


dynamic geometry


Geometers


the concept of

simultaneous

equations.

1.1 Solve simultaneous equationsusing the substitution method.

1.2 Solve simultaneous equationsinvolving real-life situations.


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Use

examples in real-life

situations such as

area, perimeter and

others.

4

INDICES AND

LOGARITHMS

1. Understand and

use the concept of

indices and laws of

indices to solve

problems.

Use examples of

real-life situations to

introduce the concept

of indices.

Use

computer software

such as the

spreadsheet to

enhance the

understanding of

indices.

1.1 Find the value of numbers givenin the form of:a) integer indices.b) fractional indices.

1.2 Use laws of indices to find thevalue of numbers in index formthat are multiplied, divided orraised to a power.

1.3 Use laws of indices to simplifyalgebraic expressions.

2. Understand and

use the concept

of logarithms andlaws of

logarithms to

solve problems.

Use

scientific calculators to

enhance the

understanding of the

concept of logarithm.

2.1 Express equation in index formto logarithm form and vice versa.

2.2 Find logarithm of a number.

2.3 Find logarithm of numbers byusing laws of logarithms.

2.4 Simplify logarithmic expressionsto the simplest form.

3. Understand anduse the change ofbase oflogarithms tosolve problems.

3.1 Find the logarithm of a numberby changing the base of thelogarithm to a suitable base.

3.2 Solve problems involving thechange of base and laws oflogarithms.


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4. Solve equationsinvolving indicesand logarithms.

4.1 Solve equations involvingindices.

4.2 Solve equations involvinglogarithms.

4

COORDINATE

GEOMETRY

1. Find distance

between two

points.

Use

examples of

real-lifesituations to

find the

distance

between two

points.

1.1 Find the distance between twopoints using formula.

2. Understand the

concept of division

of a line segment.

2.1 Find the midpoint of two givenpoints.

2.2 Find the coordinates of a pointthat divides a line according to agiven ratio m : n.

3. Find areas of

polygons.

Use

dynamic geometry


Geometers


the concept of area of

polygons.

Use

for

substitution of

coordinates into the

formula.

3.1 Find the area of a triangle basedon the area of specificgeometrical shapes.

3.2 Find the area of a triangle by

using formula.

3.3 Find the area of a quadrilateral

1321

1321

2

1

yyyy

xxxx


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using formula.

4. Understand and

use the concept

of equation of astraight line.

Use

dynamic geometry

software such as theGeometers


the concept of

equation of a straight

line.

4.1 Determine the x-intercept and they-intercept of a line.

4.2 Find the gradient of a straightline that passes through two

points.

4.3 Find the gradient of a straightline using the x-intercept and y-intercept.

4.4 Find the equation of a straightline given:

a) gradient and one point;

b) two points;

c) x-intercept and y-intercept.

4.5 Find the gradient and theintercepts of a straight line given

the equation.

4.6 Change the equation of a straightline to the general form.

4.7 Find the point of intersection oftwo lines.


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5. Understand anduse the concept ofparallel andperpendicular -lines.

Use

examples of real-life

situations to explore

parallel and

perpendicular lines.

Use

graphic calculator and

dynamic geometry

software such as

Geometers


the concept of parallel

and perpendicular -

lines.

5.1 Determine whether two straightlines are parallel when thegradients of both lines are knownand vice versa.

5.2 Find the equation of a straightline that passes through a fixed

point and parallel to a given line.

5.3 Determine whether two straightlines are perpendicular when thegradients of both lines are knownand vice versa.

5.4 Determine the equation of astraight line that passes through

a fixed point and perpendicular toa given line.

5.5 Solve problems involvingequations of straight lines.

6. Understand anduse the conceptof equation oflocus involvingdistance betweentwo points.

Use



equation of locusinvolving distance

between two points.

Use

graphic calculators

and dynamic geometry


Geometers


the concept of parallel

and perpendicular -

lines.

6.1 Find the equation of locus thatsatisfies the condition if:

a) the distance of a moving

point from a fixed point isconstant;

b) the ratio of the distances of amoving point from two fixed

points is constant.

6.2 Solve problems involving loci.


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4

STATISTICS

1. Understand anduse the conceptof measures ofcentral tendency

to solveproblems.

Use

scientific calculators,

graphing calculators

and spreadsheets toexplore measures of

central tendency.

Student

s collect data from


investigate measures

of central tendency.

1.1 Calculate the mean of ungroupeddata.

1.2 Determine the mode ofungrouped data.

1.3 Determine the median ofungrouped data.

1.4 Determine the modal class ofgrouped data from frequencydistribution tables.

1.5 Find the mode from histograms.

1.6 Calculate the mean of groupeddata.

1.7 Calculate the median of groupeddata from cumulative frequencydistribution tables.

1.8 Estimate the median of groupeddata from an ogive.

1.9 Determine the effects on mode,median and mean for a set ofdata when:a) each data is changed

uniformly;b) extreme values exist;c) certain data is added or

removed.

1.10 Determine the most suitablemeasure of central tendency forgiven data.


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2. Understand anduse the concept ofmeasures ofdispersion to solveproblems.

2.1 Find the range of ungroupeddata.

2.2 Find the interquartile range ofungrouped data.

2.3 Find the range of groupeddata.

2.4 Find the interquartile range ofgrouped data from thecumulative frequency table.

2.5 Determine the interquartile rangeof grouped data from an ogive.

2.6 Determine the variance ofa) ungrouped data;b) grouped data.

2.7 Determine the standard deviationof:a) ungrouped data

b) grouped data.

2.8 Determine the effects on range,interquartile range, variance andstandard deviation for a set of

data when:a) each data is changeduniformly;

b) extreme values exist;c) certain data is added or

removed.

2.9 Compare measures of centraltendency and dispersionbetween two sets of data.

2

CIRCULAR

MEASURES

1. Understand the

concept of

radian.

Use dynamic

geometry software such

as the Geometers

Sketchpad to explore the

concept of circular

measure.

1.1 Convert measurements inradians to degrees and viceversa.


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2. Understand and

use the concept

of length of arc of

a circle to solveproblems.

Use examples of


explore circular

measure.

2.1 Determine:a) length of arc;b) radius; and

c) angle subtended at thecentre of a circlebased on given information.

2.2 Find perimeter of segments ofcircles.

2.3 Solve problems involvinglengths of arcs.

3. Understand anduse the concept

of area of sector

of a circle to

solve problems.

3.1 Determine the:a) area of sector;b) radius; and c) angle subtended at the

centre of a circlebased on given information.

3.2 Find the area of segments ofcircles.

3.3 Solve problems involving areas ofsectors.

5

DIFFERNTATIONS

1. Understand and

use the concept

of gradients of

curve and

differentiation.

Use


dynamic geometry

software such as

Geometers


the concept of

differentiation.

1.1 Determine the value of a functionwhen its variable approaches acertain value.

1.2 Find the gradient of a chordjoining two points on a curve.

1.3 Find the first derivative of afunction y = f(x), as the gradientof tangent to its graph.

1.4 Find the first derivative ofpolynomials using the firstprinciples.


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1.5 Deduce the formula for firstderivative of the function y = f(x)by induction.

2. Understand and

use the concept

of first derivative

of polynomial

functions to solve

problems.

2.1 Determine the first derivative ofthe function y = axnusingformula.

2.2 Determine value of the firstderivative of the function y = axn

for a given value of x.

2.3 Determine first derivative of afunction involving:a) addition, or b) subtractionof algebraic terms.

2.4 Determine the first derivative of aproduct of two polynomials.

2.5 Determine the first derivative of aquotient of two polynomials.

2.6 Determine the first derivative ofcomposite function using chainrule.

2.7 Determine the gradient oftangent at a point on a curve.

2.8 Determine the equation oftangent at a point on a curve.

2.9 Determine the equation ofnormal at a point on a curve.

3. Understand and

use the concept

of maximum and

minimum values

Use


dynamic geometry

software to explore the

3.1 Determine coordinates of turningpoints of a curve.


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to solve

problems.

concept of maximum

and minimum values

3.2 Determine whether a turningpoint is a maximum or a

minimum point.

3.3 Solve problems involvingmaximum or minimum values.

4. Understand and

use the concept

of rates of

change to solve

problems.

Use graphing

calculators with

computer base ranger

to explore the concept

of rates of change.

4.1 Determine rates of change forrelated quantities.

5. Understand and

use the concept

of small changes

and

approximations

to solveproblems.

5.1 Determine small changes inquantities.

5.2 Determine approximate valuesusing differentiation.

6. Understand and

use the concept

of second

derivative to

solve problems.

6.1 Determine the second derivativeof function y = f (x0

6.2 Determine whether a turningpoint is maximum or minimumpoint of a curve using the secondderivative.

2

SOLUTION OF

TRIANGLES

1. Understand and

use the concept

of sine rule to

solve problems.

Use

dynamic geometry


Geometers


the sine rule.

1.1 Verify sine rule.

1.2 Use sine rule to find unknownsides or angles of a triangle.

1.3 Find the unknown sides andangles of a triangle involving


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Use examples of


explore the sine rule.

ambiguous case.

1.4 Solve problems involving thesine rule.

2. Understand anduse the concept

of cosine rule to

solve problems.

Usedynamic geometry


Geometers


the cosine rule.

Use examples of

real-life


the cosine

rule.

.

2.1 Verify cosine rule.

2.2 Use cosine rule to find unknownsides or angles of a triangle.

2.3 Solve problems involving cosinerule.

2.4 Solve problems involving sineand cosine rules.

3. Understand and

use the formula

for areas of

triangles to solve

problems.

Use

dynamic geometry


Geometers


the concept of areas

of triangles.

Use examples of


explore area of

triangles.

3.1 Find the area of triangles using

the formula2

1ab sin C or its

equivalent.

3.2 Solve problems involving three-dimensional objects.

2

INDEX NUMBER

1. Understand and

use the concept

of index number

to solve

problems.

Use examples of


explore index

numbers.

1.1 Calculate index number.

1.2 Calculate price index.

1.3 Find Q0or Q 1 given relevantinformation.


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2. Understand anduse the concept ofcomposite index tosolve problems

Use



composite index.

2.1 Calculate composite index.

2.2 Find index number or weightagegiven relevant information.

2.3 Solve problems involving indexnumber and composite index.

PROJECT WORK

1. Carry out projectwork.

Use scientificcalculators, graphingcalculators orcomputer software tocarry out project work.

Students areallowed to carry outproject work in groupsbut written reportsmust be doneindividually.

Students should begiven opportunity togive oral presentationof their project work.

1.1 Define the problem/situation tobe studied.

1.2 State relevant conjectures.

1.3 Use problem solving strategies

to solve problems.1.4 Interpret and discuss results.

1.5 Draw conclusions and/orgeneralisations based on criticalevaluation of results.

1.6 Present systematic andcomprehensive written reports.

add maths - form 4 - year-plan

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