add maths - form 4 - year-plan
TRANSCRIPT
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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
graphing calculators or
dynamic geometry
software such as the
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
graphing calculators or
dynamic geometry
software such as the
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
graphing calculators or
dynamic geometry
software such as the
Geometers
Sketchpad to explore
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
software such as the
Geometers
Sketchpad to explore
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
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using formula.
4. Understand and
use the concept
of equation of astraight line.
Use
dynamic geometry
software such as theGeometers
Sketchpad to explore
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
Sketchpad to explore
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
examples of real-life
situations to explore
equation of locusinvolving distance
between two points.
Use
graphic calculators
and dynamic geometry
software such as the
Geometers
Sketchpad to explore
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
real-life situations to
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
real-life situations to
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
graphing calculators or
dynamic geometry
software such as
Geometers
Sketchpad to explore
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
graphing calculators or
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
software such as the
Geometers
Sketchpad to explore
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
real-life situations to
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
software such as the
Geometers
Sketchpad to explore
the cosine rule.
Use examples of
real-life
situations to explore
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
software such as the
Geometers
Sketchpad to explore
the concept of areas
of triangles.
Use examples of
real-life situations to
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
real-life situations to
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
examples of real-life
situations to explore
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.