Download - Yearly Plan Add Math f4 2013
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7/27/2019 Yearly Plan Add Math f4 2013
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Topic A4: SIMULTANEOUS EQUATIONS---3 weeks
1 1. Solve simultaneous equations in twounknowns: one linear equation andone non-linear equation.
1.1 Solve simultaneous equations using thesubstitution method.
4 Limit non-linear equations up tosecond degree only.
2-3 1.2Solve simultaneous equations involving real-life situations.
Additional Exercises
2
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Topic ASS1: INDEX NUMBER---2 week
41. Understand and use the concept of index
number to solve problems1.1 Calculate index number.1.2 Calculate price index.
Find Q0 orQ1 given relevant information.
11
Q0 = Quantity at base time.Q1 = Quantity at specific time.
5
2. Understand and use the concept ofcomposite index to solve problems
2.1 Calculate composite index.
2.2 Find index number orweightage given relevantinformation.
2.3 Solve problems involving index number andcomposite index.
Additional Exercises orpast year questions
2
2
2
Explain weightage and compositeindex.
Topic/Learning Area Al : FUNCTION --- 3 weeks
First Term
6 1. Understand the concept of relations. 0.1 Represent relations usinga) arrow diagramsb) ordered pairs
c) graphs
1 Discuss the idea of set andintroduce set notation.
1
Yearly Plan Additional Mathematics Form 4
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0.2 Identify domain, co domain, object, image andrange of a relation.
1.3 Classify a relation shown on a mapped
diagram as: one to one, many to one, one tomany or many to many relation.
1
2. Understand the concept of functions. 2.1 Recognise functions as a special relation.
2.2 Express functions using function notation.
2.3 Determine domain, object, image and range of afunction.
2.4 Determine the image of a function given the
object and vice versa.
1
1
Represent functions using arrow
diagrams, ordered pairs orgraphs, e.g.
( ) xxfxxf 2,2: = xxf 2: is read asfunction fmaps x to 2x.
( ) xxf 2= is read as 2x isthe image of x under the
function f.
7 3. Understand the concept of compositefunctions.
3.1 Determine composition of two functions.
3.2 Determine the image of composite functions
given the object and vice versa
3.3 Determine one of the functions in a givencomposite function given the other relatedfunction.
1
1
2
Involve algebraic functions only.
Images of composite functions
include a range of values. (Limit tolinear composite functions).Define composite functions
84. Understand the
concept of inversefunctions.
4.1 Find the object by inverse mapping given itsimage and function.
4.2 Determine inverse functions using algebra.
4.3 Determine and state the condition for existence
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1
Limit to algebraic functions.
Exclude inverse of composite
functions.
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of an inverse functionAdditional Exercises
1
1
Emphasise that the inverse of a
function is not necessarily afunction.
Topic A2 : Quadratic Equations ---3 weeks
9 1. Understand the concept of quadraticequations and their roots.
1.1 Recognise a quadratic equation and express itin general form.
1. 2 Determine whether a given value is the rootof a quadratic equation by
a) substitution;
b) inspection.
1.3 Determine roots of quadratic equations by
trial and improvement method.
1
1
Questions for 1..2(b) are givenin the form of( ) ( ) 0=++ bxax ; a and b arenumerical values.
10
2. Understand the concept of quadratic
equations.
2.1 Determine the roots of a quadratic equation
bya) factorisation;
b) completing the squarec) using the formula.
2.2 Form a quadratic equation from given roots.
1
1
2
Discuss when( ) ( ) 0= qxpx , hence
0=px or 0=qx .
Include cases when p = q.
Derivation of formula for 2.1cis not required.
3. Understand and use the conditionsfor quadratic equations to have
a) two different roots;b) two equal roots;c) no roots.
3.1 Determine types of roots of quadratic equations
from the value of acb 42 .
3.2 Solve problems involving acb 42 in
2 Explain that no roots means noreal roots.
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11 quadratic equations to:a) find an unknown value;b) derive a relation.
Additional Exercise
2
2
Topic A3 : Quadratics Functions---3 weeks
12 1. Understand the concept of quadraticfunctions and their graphs.
1.1 Recognise quadratic functions 1
1.2 Plot quadratic functiongraphs:
a)based on given tabulatedvalues;
1 b) by tabulating values
2 based on given functions.
2
2
1.3 Recognise shapes of graphs of quadraticfunctions. 1
Discuss the form of graph ifa > 0 and a < 0 for
( ) cbxaxxf ++= 2
Explain the term parabola.
1.4 Relate the position of quadratic function
graphs with types of roots for ( ) 0=xf . 1 Relate the type of roots with the
position of the graphs.
13 2. Find the maximum and minimum
values of quadratic functions.
2.1 Determine the maximum or minimum value
of a quadratic function by completing thesquare.
2
Students be reminded of the steps
involved in completing square andhow to deduce maximum orminimum value from the functionand also the corresponding valuesof x.
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3. Sketch graphs of quadratic functions. 3.1 Sketch quadratic function graphs by determiningthe maximum or minimum point and two other
points.
2Emphasise the marking ofmaximum or minimum point andtwo other points on the graphs
drawn or by finding the axis ofsymmetry and the intersection withthey-axis.
Determine other points by finding
the intersection with the x-axis (ifit exists).
14 4. Understand and use
the concept of quadratic inequalities.
4.1 Determine the ranges of values ofx that satisfies
quadratic inequalities. 2
Emphasise on sketching graphs
and use of number lines whennecessary.
Topic G1. Coordinate Geometry---5 weeks
1. Find distance between two points. 1.1 Find the distance between two points ( )11 , yx ,
( )22 , yx using formula
1 Use the Pythagoras Theorem tofind the formula for distance
between two points.
152.Understand the concept of division
of line segments2.1Find the midpoint of two given points.
2.2Find the coordinates of a point that divides aline according to a given ratio m : n.
12
Limit to cases where m and n are
positive.Derivation of the formula
++
++
nm
myny
nm
mxnx 2121,
is not required.
3 Find areas of polygons. 3.1 Find the area of a triangle based on the areaof specific geometrical shapes.
3.2 Find the area of a triangle by using formula.
13
13
21
21
2
1
yy
xx
yy
xx
1
1
Limit to numerical values.Emphasise the relationship
between the sign of the value forarea obtained with the order of the
vertices used.Emphasise that when the area of
polygon is zero, the given points
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3.3 Find the area of a quadrilateral usingformula.
are collinear.
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4 Understand and use the concept ofequation of a straight line.
4.1 Determine the x-intercept and the y-intercept ofa line.
4.2 Find the gradient of a straight line that passesthrough two points.
4.3 Find the gradient of a straight line using thex-
intercept and y-intercept
4.4 Find the equation of astraight line given:
a) gradient and one point;b) two points;
c) x-intercept andy-intercept.
4.5Find the gradient and the intercepts of astraight line given the equation.
4.6Change the equation of a straight line to thegeneral form
4.7Find the point of intersection of two lines.
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Answers for learning outcomes4.4(a) and 4.4(b) must be stated in
the simplest form.
Involve changing the equationintogradient and intercept form
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18 5. Understand and use the concept ofparallel and perpendicular lines.
5.1 Determine whether two straight lines areparallel when the gradients of both lines are
known and vice versa.
5.2 Find the equation of a straight line that
passes through a fixed point and parallel to agiven line.
5.3 Determine whether two straight lines are
perpendicular when the gradients of bothlines are known and vice versa.
5.4 Determine the equation of a straight line that
passes through a fixed point andperpendicular to a given line.
5.5 Solve problems involving equations ofstraight lines.
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2
Emphasise that for parallel lines:
21 mm = .
Emphasise that for perpendicular
lines
121 =mm .Derivation of 121 =mm is notrequired.
PEPERIKSAAN PERTENGAHAN TAHUN 2013(13-23 mei 2013)
21 6 Understand and use the concept of equation of locus involving distance
between two points.
6.1 Find the equation of locus that satisfies thecondition 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
6.2 Solve problems involving loci.
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1
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Topic T1: Circular Measures---3 weeks
22 1. Understand the concept of radian. 1.1 Convert measurements inradians to degrees andvice versa.
1 Discuss the definition of oneradian.rad is the abbreviation of radian.Include measurements in radiansexpressed in terms of .
rad = 1800
2. Understand and use the concept oflength of arc of a circle to solve problems.
bulatan
2.1 Determine:i) length of arc;ii) radius; andiii) angle subtended at the centre of a circle
based on given information.
2 Major and minor arc lengthsdiscussed
Emphasize that the angle must bein radian.Students can also use formula
S= 2360
xj
when the angle
given is in degree
23
2.2 Find perimeter of segments of circles.
Solve problems involving lengths of arcs
1
1
24
3. Understand and use the concept of
area of sector of a circle to solveproblems
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 of circles.
3.3 Solve problems involving areas of sectors
2
2
2
Emphasize that the angle must be
in radian.Area of major sektor need to be
discussedStudents can also use formula
L=2
360
xj
if the angle given
is in degree.
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Topic A5 : INDICES AND LOGARITHMS---4 weeks
Second Term
25 1. Understand and use the concept of
indices and laws of indices to solveproblems.
1.1 Find the value of numbers given in the form
of:i. integer indices.ii. fractional indices.
1.2 Use laws of indices to find the value of numbers
in index form that are multiplied, divided orraised to a power.
1
1
Discuss zero index and negative
indices.
1.3 Use laws of indices to simplify algebraicexpressions 1
2. Understand and use the concept oflogarithms and laws of logarithmsto solve problems.
2.1 Express equation in index form to logarithmform and vice versa.
2.2 Find logarithm of a number
1Emphasise that:loga 1 = 0; logaa = 1.
Emphasise that:
a) logarithm of negative numbersis undefined;
b) logarithm of zero is undefined.Discuss cases where the given
number is in:a) index form
b) numerical form.
UJIAN BULANAN 2 (17-19 JULAI 2013)
27 2.3 Find logarithm of numbers by using laws of logarithms
2.4 Simplify logarithmic expressions to thesimplest form.
2
1
Discuss laws of logarithms
3 Understand and use the change ofbase of logarithms to solve problems.
3.1 Find the logarithm of a number by changingthe base of the logarithm to a suitable base.
1 Discuss:
ab
b
alog
1log =
28 3.2 Solve problems involving the change of baseand laws of logarithms.
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4. Solve equation involving indices andlogarithms
4.1 Solve equations involving indices. 2 Equations that involve indices andlogarithms are limited to equationswith single solution only.
Solve equations involving indicesby:a) comparison of indices and
bases;b) using logarithms.
29 . 4.2 Solve equations involving logarithms.
Additional/reinforcement Exercises on thistopic
2
2
Topic S1: Statistics ---4 Weeks
30
31
1 Understand and use the concept ofmeasures of central tendency to solve
problems.
1.1 Calculate the mean of ungrouped data.1.2 Determine the mode of ungrouped data.1.3 Determine the median of ungrouped data1.4Determine the modal class of grouped data from
frequency distribution tables.1.5 Find the mode from histograms.
1.6 Calculate the mean of grouped data1.7 Calculate the median of grouped data from
cumulative frequency distribution tables.
1.8 Estimate the median ofgrouped data from an ogive
1.9 Determine the effects on
mode, median and mean fora set of data when:
i) each data is changeduniformly;
ii) extreme values exist;iii) certain data is added or
removed
1.10 Determine the most suitablemeasure of central tendency
1
2
1
1
2
1
Discuss grouped data andungrouped data.
Involve uniform class intervalsonly.
Derivation of the median formulais not required.
Ogive is also known as cumulativefrequency curve
Involve grouped and ungroupeddata
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for given data.
32 2. Understand and use the concept ofmeasures of dispersion to solve
problems.
2.1 Find the range of ungrouped data.
2.2 Find the interquartilerange of ungrouped data.
2.3 Find the range of grouped data
1
2.4 Find the interquartile range of grouped datafrom the cumulative frequency table
2.5 Determine theinterquartile range of
grouped data from anogive.
2.6Determine the variance of
a)ungrouped data;b)grouped data.
2.7 Determine the standarddeviation of:
ii) ungrouped datagrouped data.
1
1
2
Determine the upper and lowerquartiles by using the first
principle.
2.8 Determine the effects on range, interquartilerange, 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.
2.9 Compare measures of central tendency anddispersion between two sets of data.
2
2Emphasise that comparison
between two sets of data usingonly measures of central tendencyis not sufficient.
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Topic AST1: SOLUTION OF TRIANGLES---2 weeks
291. Understand and use the concept of
sine rule to solve problems.1.1Verify sine rule.
1.2Use sine rule to findunknown sides or angles of atriangle.
1.3Find the unknown sides and
angles of a triangle involvingambiguous case
1.4Solve problems involving thesine rule.
1
1
1
1
Include obtuse-angled triangles
30
2. Understand and use the concept ofcosine rule to solve problems.
2.1 Verify cosine rule.2.2 Use cosine rule to find
unknown sides or anglesof a triangle.
2.3 Solve problemsinvolving cosine rule.
2.4Solve problemsinvolving sine andcosine rules
1
1
2
Include obtuse-angled triangles
31 3. Understand and use the formula forareas of triangles to solve problems.
3.1 Find the areas of triangles using the formula
Cab sin2
1or its equivalent
3.2.Solve problemsinvolving three-dimensional objects.
1
2
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Additional Exercises
1
33
Topic K1 : Differentiation---5 Weeks
34 1. Understand and use the concept ofgradients of curve and
differentiation.
1.1Determine the value of a function when itsvariable approaches a certain value.
1.2Find the gradient of a chord joining twopoints on a curve.
1.3Find the first derivative of a function( )xfy = , as the gradient of tangent to its
graph.
1.3 Find the first derivative of polynomials using
the first principles.1.4 Deduce the formula for first derivative of the
function( )xfy =
by induction.
1
1
2
Idea of limit to a function can beillustrated using graphs.
The concept of first derivative of afunction is explained as a tangentto a curve can be illustrated usinggraphs.
Limit to naxy = ;
a, n are constants, n = 1, 2, 3.
Notation of ( )xf' is equivalent
todx
dywhen ( )xfy = ,
( )xf'
read as fprime x.
35 2. Understand and use the concept of firstderivative of polynomial functions tosolve problems.
2.1 Determine the first derivative of the functionnaxy = using formula.
2.2 Determine value of the first derivative of the
function naxy = for a given value ofx.
1
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2.3Determine first derivative ofa function involving:a) addition, or
b) subtractionof algebraic terms.
2.4Determine the first derivative of a product of
two polynomials.2.5 Determine the first derivative of a quotient
of two polynomials.
2.6Determine the first derivative of compositefunction using chain rule.
2.7Determine the gradient of tangent at a point
on a curve.2.8Determine the equation of tangent at a point
on a curve.
2.9 Determine the equation of normal at a pointon a curve
1
1
1
1
1
1
1
3. Understand and use the concept ofmaximum and minimum values tosolve problems.
3.1 Determine coordinates of turning points of acurve.3.2 Determine whether a turning point is amaximum or a minimum point.
2
Emphasise the use of firstderivative to determine the turning
points.Limit problems to two variables
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3.3 Solve problems involving maximum orminimum values.
1
only.Exclude points of inflexion.
Limit problems to two variablesonly
4. Understand and use the concept ofrates of change to solve problems.
4.1 Determine rates of change for relatedquantities.
1 Limit problems to 3 variables only.
5. Understand and use the concept of small
changes and approximations to solveproblems.
5.1 Determine small changes in quantities5.2 Determine approximate values using
differentiation.
1 Exclude cases involvingpercentage change.
6. Understand and use the concept ofsecond derivative to solve problems.
6.1 Determine the second derivative of ( )xfy = .6.2 Determine whether a turning point is
maximum or minimum point of a curve usingthe second derivative
1
1
Introduce 2
2
dx
ydas
dx
dy
dx
dor
( ) ( )( )xfdx
dxf ''' =
PROJECT WORK
3
WEEKs
OUTSI
DE
SCHOO
L
HOURS
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Carry out project work In carrying out the project work1.1Define the problem/situation to be studied.
1.2 State relevant conjectures1.3 Use problem solving strategies to solve problems1.4 Interpret and discuss results.
1.5 Draw conclusions and/ormake generalisations based
on critical evaluation ofresults.
1.6 Present systematic and comprehensive writtenreports.
Usescientific
calculators,graphing
calculators
orcomputer
software tocarry out
projectwork.
Students
are allowedto carry out
projectwork in
groups butwrittenreportsmust be
doneindividuall
y.
Studentsshould be
givenopportunityto give oralpresentatio
n of theirproject
work.
Emphasise the use of Polyas four-step problem solving process.
Use at least two problem solvingstrategies.
Emphasise reasoning and effective
mathematical communication.
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