yearly plan add maths form 4-edit kuching[1]
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8/8/2019 Yearly Plan Add Maths Form 4-Edit Kuching[1]
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Topic/Learning Area Al : FUNCTION --- 3 weeks
First Term
1 1. Understand theconcept of relations.
1.1 Represent relations using
1 arrow diagrams
2 ordered pairs
3 graphs
1.2 Identify domain, co domain,
object, image and range of arelation.
1.3 Classify a relation shown
on a mapped diagram as: oneto one, many to one, one to
many or many to manyrelation.
1
1
Use pictures, role-play and
computer software to introduce the
concept of relations.
Skill : Interpretation, observe
connection between domain, codomain, object, image and range ofa relation.
Discuss the idea of set and
introduce set notation.
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 a
function.
2.4 Determine the image of a
function given the object and
vice versa.
1
1
Give examples of finding images
given the object and vice versa.(a) Given f : x 4x x2. Find
image of 5.
(b) Given function h : x 3x
12. Find object with image =
0.
Use graphing calculators and
computer software to explore the
image of functions.
Represent functions using arrow
diagrams, ordered pairs or
graphs, e.g.
( ) xxfxxf 2,2: = xxf 2: is read as
functionfmapsx to 2x.
( ) xxf 2= is read as 2x isthe image of x under the
functionf.
Include examples of functions that
are not mathematically based.
Examples of functions includealgebraic (linear and quadratic),
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Yearly Plan Additional Mathematics Form 4
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trigonometric and absolute value.
Define and sketch absolute value
functions.
2 3. Understand theconcept ofcomposite
functions.
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 thefunctions in a given
composite function given the
other related function.
1
1
2
Use arrow diagrams or algebraic
method to determine composite
functions.
Give examples of finding images
given the object and vice versa for
composite functions
For example :
Given f : x
3x 4. Find(a) ff(2),
(b) range of value of x if ff(x) > 8.
Give examples for finding a
function when the composite
function is given and one other
function is also given.
Example :
Given f : x2x 1. find function
g ifa. The composite function fg is
given as fg : x7 6x
b. composite function gf is given as
gf : x 5/2x.
Involve algebraic functions only.
Images of composite functions
include a range of values. (Limit to
linear composite functions).
Define composite functions
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3 4. Understand the
concept of inversefunctions.
4.1 Find the object by inverse
mapping given its image and
function.
4.2 Determine inverse functions
using algebra.
4.3 Determine and state the
condition for existence of an
inverse function
Additional Exercises
1
1
1
1
Use sketches of graphs to show the
relationship between a function and
its inverse.
Examples :
Given f: x 23 + x , find 1f
Limit to algebraic functions.
Exclude inverse of composite
functions.
Emphasise that the inverse of a
function is not necessarily a
function.
Topic A2 : Quadratic Equations ---3 weeks
41. Understand the
concept ofquadraticequations andtheir roots.
1.1 Recognise a quadraticequation and express it ingeneral form.
1. 2 Determine whether agiven value is the root of a
quadratic equation by4 substitution;
a) inspection.
1.3 Determine roots ofquadratic equations bytrial and improvementmethod.
1
1
Use graphing calculators orcomputer software such as theGeometers Sketchpad andspreadsheet to explore the conceptof quadratic equations
Values : Logical thinkingSkills : seeing connection, usingtrial and error methods
Questions for 1..2(b) are givenin the form of( ) ( ) 0=++ bxax ; a and b arenumerical values.
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5
2. Understand theconcept ofquadratic
equations.
2.1 Determine the roots of aquadratic equation by
a) factorisation;
b) completing thesquare
c) using the formula.
2.2 Form a quadratic equationfrom given roots.
1
1
2
Ifx =p andx = q are the roots, thenthe quadratic equation is( ) ( ) 0= qxpx , that is
( ) 02 =++ pqxqpx .
Involve the use of:
a
b=+ and
a
c=
where andare roots of the
quadratic equation02 =++ cbxax
Skills : Mental process, trial anderror
Discuss when( ) ( ) 0= qxpx , hence
0= px or 0=qx .
Include cases whenp = q.
Derivation of formula for 2.1cis not required.
6
3. Understand anduse the conditionsfor quadraticequations to have
a) two different roots;b) two equal roots;
c) no roots.
a)dua punca berbeza;
3.1 Determine types of roots of
quadratic equations from the
value of acb 42 .
3.2 Solve problems
involving acb 42 in
quadratic equations to:
a) find an unknown value;
b) derive a relation.
Additional Exercises
2
2
2
Giving quadratic equations with the
following conditions : 042 > acb04
2 = acb , 042
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Topic A3 : Quadratics Functions---3 weeks
71. Understand the
concept of
quadraticfunctions andtheir graphs.
1.1 Recognise quadraticfunctions
1 1) Use graphing calculators or
computer software such as
Geometers Sketchpad to explore the
graphs of quadratic functions.
a) f(x) = ax2 + bx + c
b) f(x) = ax2 + bx
c) f(x) = ax2 + c
* pedagogy : Constructivism
Skills : making comparison
& making conclusion
1.2 Plot quadratic functiongraphs:
a)based on giventabulated
values;
1b) by tabulating values
2based on given functions.
2
1) Use examples of everyday
situations to introduce graphs of
quadratic functions.
Contextual learning
1.3 Recognise shapes ofgraphs of quadraticfunctions.
1
Discuss the form of graph ifa > 0 and a < 0 for
( ) cbxaxxf ++= 2
Explain the term parabola.
81.4 Relate the position of
quadratic function graphs
with types of roots for2
Recall the type of roots if :
a) b2 4ac > 0
b) b2 4ac < 0
Relate the type of roots with
the position of the graphs.
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( ) 0=xf . c) b2 4ac = 0
2. Find themaximum andminimum valuesof quadraticfunctions.
2.1 Determine the maximumor minimum value of aquadratic function bycompleting the square.
2
Use graphing calculators or dynamicgeometry software such as theGeometers Sketchpad to explore thegraphs of quadratic functions
Skills : mental process ,interpretation
Students be reminded of the steps
involved in completing square and
how to deduce maximum or
minimum value from the function
and also the corresponding values
of x.
9 3. Sketch graphs of quadratic functions. 3.1 Sketch quadratic functiongraphs by determining the
maximum or minimum point
and two other points.
2 Use graphing calculators ordynamic geometry software suchas the Geometers Sketchpad toreinforce the understanding ofgraphs of quadratic functions.
Steps to sketch quadratic graphs:
a) Determining the form or
b) finding maximum or minimum
point and axis of symmetry.
c) finding the intercept with x-axis
and y-axis.d) plot all points
e) write the equation of the axis of
symmetry
Emphasise the marking ofmaximum or minimum point andtwo other points on the graphsdrawn or by finding the axis ofsymmetry and the intersectionwith they-axis.
Determine other points by finding
the intersection with thex-axis (if
it exists).
4. Understand and usethe concept of
quadratic inequalities.
4.1 Determine the ranges of
values ofx that satisfies
quadratic inequalities.
2
Use graphing calculators or
dynamic geometry software such as
the Geometers Sketchpad to
explore the concept of quadratic
Emphasise on sketching graphs
and use of number lines when
necessary.
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inequalities.
Topic A4: SIMULTANEOUS EQUATIONS---2 weeks
101. Solve
simultaneousequations in twounknowns: one
linear equationand one non-
linear equation.
1.1 Solve simultaneousequations using thesubstitution method.
4 Use graphing calculators or dynamic
geometry software such as the
Geometers Sketchpad to explore the
concept of simultaneous equations.
Value: systematic
Skills: interpretation of mathematical
problem
Limit non-linear equations up to
second degree only.
111.2Solve simultaneous
equations involving real-
life situations.
Additional Exercises
2
2
Use examples in real-lifesituations such as area, perimeter
and others.
Pedagogy: Contextual LearningValues : Connection between
mathematics and other subjects
Topic G1. Coordinate Geometry---5 weeks
121. Find distance
between twopoints.
1.1 Find the distance between
two points ( )11 , yx ,( )22 , yx using formula
1 Skill : Use of formula
Use the Pythagoras Theorem to
find the formula for distance
between two points.
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2.Understand theconcept ofdivision of linesegments
2.1Find the midpoint of twogiven points.
2.2Find the coordinates of apoint that divides a line
according to a given ratiom : n.
1
2
Skill : Use of formula
Value : Accurate & neat work
Limit to cases where m and n are
positive.Derivation of the formula
++
++
nm
myny
nm
mxnx 2121 ,
is not required.
13 3 Find areas of polygons.
3.1 Find the area of a triangle
based on the area ofspecific geometrical
shapes.
3.2 Find the area of a triangleby using formula.
1
2x1
x2
y1
y2
x3 x1y3
y1
3.3 Find the area of aquadrilateral usingformula.
1
1
Values : Systematic & neat
Skills : use of formula , recognise
relationship and patterns
Limit to numerical values.
Emphasise the relationship
between the sign of the value for
area obtained with the order of the
vertices used.
Derivation of the formula:
++
3123
12133211
2
1
yxyx
yxyxyxyxis
not required.
Emphasise that when the area of
polygon is zero, the given points
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are collinear.
14
4 Understand anduse the conceptof equation of astraight line.
4.1 Determine thex-interceptand they-intercept of aline.
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 andy-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 a straight linegiven the equation.
4.6Change the equation of astraight line to the generalform
4.7Find the point ofintersection of two lines.
1
1
2
1
1
Use dynamic geometry software suchas the Geometers Sketchpad toexplore the concept of equation of astraight line.
Skills : drawing relevant diagrams,
using formula, recognisingrelationship, compare and contrast.
Values : Neat & systematic
Pedagogy: contextual learning
Finding point of intersection of twolines by solving simultaneousequations
Answers for learning outcomes4.4(a) and 4.4(b) must be stated inthe simplest form.Involve changing the equation into
gradient and intercept form
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15
16
5. Understand and
use the conceptof parallel and
perpendicular
lines.
5.1 Determine whether two
straight lines are parallelwhen the gradients of
both lines are known and
vice versa.
5.2 Find the equation of astraight line that passes
through a fixed point andparallel to a given line.
5.3 Determine whether twostraight lines are
perpendicular when thegradients of both lines areknown and vice versa.
5.4 Determine the equation ofa straight line that passesthrough a fixed point and
perpendicular to a givenline.
5.5 Solve problems involvingequations of straightlines.
1
1
1
1
2
Use examples of real-life situations to
explore parallel and perpendicularlines.
Skill: Use of formula; makingcomparison
Students to be exposed to SPMexam type of questions.
Values : hard work, cooperative
Pedagogy : Mastery learning
Emphasise that for parallel lines:
21 mm = .
Emphasise that for perpendicularlines
121 =mm .Derivation of 121 =mm is notrequired.
6 Understand anduse the conceptof equation oflocus involvingdistance
6.1 Find the equation oflocus that satisfies thecondition if:
a)the distance of a movingpoint from a fixed point is
1 Use examples of real-life situations toexplore equation of locus involvingdistance between two points.Use graphic calculators and dynamicgeometry software such as the
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between twopoints.
constant;
b) the ratio of the distancesof a moving point from
two fixed points isconstant
6.2 Solve problems involvingloci.
1
2
Geometers Sketchpad to explore theconcept of parallel and perpendicular
lines.
Value : Patience, hard working
Pedagogy: contextual learningSkill : drawing relevant diagrams
Topic T1: Circular Measures---3 weeks
171. Understand the
concept ofradian.
1.1 Convert measurements in
radians to degrees andvice versa.
1 Use dynamic geometry software such
as the Geometers Sketchpad to
explore the concept of circular
measure.
Students measure angle subtended at
the centre by an arc length equal thelength of radius. Repeat with different
radius.
Skill : contextual learning
Value : Accurate, making conclusion.
Discuss the definition of oneradian.rad is the abbreviation of radian.
Include measurements in radians
expressed in terms of .
rad = 1800
2. Understand and use
the concept of length
2.1 Determine:
i) length of arc;
2 Use examples of real-life situations toexplore circular measure.
Major and minor arc lengthsdiscussed
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of arc of a circle to
solve problems.
bulatan
radius; and
iii) angle subtended atthe centre of a circle
based on given information.
Derivation of S = j by use of ratio orby deduction using definition of
radian.Skill : Making conclusion ordeduction, application of formula
Emphasize that the angle must be
in radian.Students can also use formula
S= 2360
xj
when the angle
given is in degree
18
2.2 Find perimeter of segments
of circles.
Solve problems involving
lengths of arcs.
1
1
19
3. Understand anduse the conceptof area of sectorof a circle tosolve problems
3.1 Determine the:
a) area of sector;
b)radius; and
c)angle subtended at thecentre of a circle
based on given information.
3.2 Find the area of segmentsof circles.
3.3 Solve problemsinvolving areas of sectors.
2
2
2
Deriving the formula L= j2 Using ratioSkill : drawing relevant diagrams ,recognising relationship & makingconclusionValue : Systematic & logical
Emphasize that the angle must bein radian.Area of major sektor need to bediscussedStudents can also use formula
L=2
360
xj
if the angle given
is in degree.
Topic A5 : INDICES AND LOGARITHMS---4 weeks
Second Term
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1. Understand and
use the conceptof indices andlaws of indices
to solveproblems.
1.1 Find the value of numbersgiven in the form of:
integer indices.
fractional indices.
1.2 Use laws of indices to findthe value of numbers inindex form that aremultiplied, divided orraised to a power.
1
1
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.
Pedagogy : Constructivism
Skill : making inference, use of laws
Value : systematic, logical thinking
Discuss zero index and negative
indices.
1.3 Use laws of indices tosimplify algebraicexpressions
1
2. Understand anduse the conceptof logarithmsand laws oflogarithms to
solve problems.
2.1 Express equation in indexform to logarithm formand vice versa.
2.2 Find logarithm of a
number
1 Use scientific calculators to enhance
the understanding of the concept of
logarithm.
Explain definition of logarithm.N= ax; logaN=x with a > 0, a 1.
Value : systematic, abide by the laws
Pedagogy:Mastery learning
Emphasise that:loga 1 = 0; logaa = 1.
Emphasise that:a) logarithm of negative numbers
is undefined;b) logarithm of zero is undefined.Discuss cases where the givennumber is in:a) index form
b) numerical form.
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2.3 Find logarithm of
numbers by using laws oflogarithms
2.4 Simplify logarithmic
expressions to thesimplest form.
2
1
Activities : Demonstration
Value : systematic and organised
Skill : recognising pattern and
relationship, application of laws
Discuss laws of logarithms
3 Understand and
use the changeof base of
logarithms tosolve problems.
3.1 Find the logarithm of a
number by changing thebase of the logarithm to a
suitable base.
1 Aktivities : Demonstration
Pedagogy: Mastery learning, problem solving
Discuss:
ab
b
alog
1log =
33.2 Solve problems involving
the change of base and
laws of logarithms.
2Aktivities : DemonstrationPedagogy: Mastery learning
, problem solving.
4. Solve equationsinvolvingindices andlogarithms
4.1 Solve equationsinvolving indices.
2 Aktivities : Demonstration
Pedagogy: Mastery learning
, problem solving.
Equations that involve indices andlogarithms are limited to equations
with single solution only.Solve equations involving indices
by:
a) comparison of indices andbases;
b) using logarithms.
4
. 4.2 Solve equations involving
logarithms.
Additional/reinforcementExercises on this topic
2
2
Values : Systematic & logical
thinking
Topic S1: Statistics ---4 Weeks
1 Understand and 1.1 Calculate the mean of 1
Use scientific calculators, graphing
calculators and spreadsheets to Discuss grouped data and
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5
6
use the conceptof measures of
central tendencyto solve
problems.
ungrouped data.
1.2 Determine the mode of
ungrouped data.1.3 Determine the median of
ungrouped data
1.4Determine the modal class of
grouped data from frequency
distribution tables.1.5 Find the mode from
histograms.
1.6 Calculate the mean of
grouped data
1.7 Calculate the median ofgrouped data from
cumulative frequency
distribution tables.
1.8 Estimate the median of
grouped data from an ogive
1.9 Determine the effects onmode, median and mean fora set of data when:
i) each data is changed uniformly;
ii) extreme valuesexist;
iii) certain data is added or
removed
1.10 Determine the most suitable
2
1
1
2
1
explore measures of central tendency.
Students collect data from real-lifesituations to investigate measures of
central tendency.
Eg. 1) Length of leaves in school
compound
2). Marks for Add maths in the class.
Values : Cooperative; honest , logical
thinking
Skill : classification, making
conclusion
Pedagogy :
1. Contextual learning
2. Constructivism
3. Multiple intelligence
Skills : Classification; observing
relationship, course and effect, able to
analise and make conclusion
ungrouped data.
Involve uniform class intervals
only.
Derivation of the median formula
is not required.
Ogive is also known as cumulative
frequency curve.
Involve grouped and ungrouped
data
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measure of central tendency
for given data.
72. Understand and
use the conceptof measures ofdispersion to
solve problems.
2.1 Find the range ofungrouped data.
2.2 Find the interquartile
range of ungrouped data.
2.3 Find the range ofgrouped data
1 Activities :1. Teacher gives real life exampleswhere values of mean, mode adnmedium are more or less the same and
not sufficient to determine theconsistency of the data and that lead
to the need of finding measures ofdispersion
2.4 Find the interquartilerange of grouped datafrom the cumulative
frequency table
2.5 Determine theinterquartile range ofgrouped data from anogive.
2.6Determine the variance of
a)ungrouped data;
b)grouped data.2.7 Determine the standard
deviation of:
ii) ungrouped data
1
1
2
Values :1. Honest2. cooperative
Pedagogy : Contextual learning
Determine the upper and lowerquartiles by using the first
principle.
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grouped data.
82.8 Determine the effects onrange, interquartile range,
variance and standarddeviation 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 and
dispersion between two sets
of data.
2
2
Skills :1. Compare and contrast
2. Classification3. Problem Solving
4. Sorting data from small to big
Pedagogy : Contextual learning
Values : Logical thinking Emphasise that comparison
between two sets of data usingonly measures of central tendency
is not sufficient.
Topic AST1: SOLUTION OF TRIANGLES---2 weeks
91. Understand and
use the conceptof sine rule tosolve problems.
1.1Verify sine rule.
1.2Use sine rule to find
unknown sides or angles of a
triangle.
1.3Find the unknown sides and
angles of a triangle involving
ambiguous case
1
1
1
Use dynamic geometry software suchas the Geometers Sketchpad toexplore the sine rule.
Use examples of real-life situations to
explore the sine rule.
Skill : Interpretation of problem
Include obtuse-angled triangles
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1.4Solve problems involving the
sine rule. 1Value : Accuracy
10
2. Understand and usethe concept ofcosine rule tosolve 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 and
cosine rules
1
1
2
Use dynamic geometry software suchas the Geometers Sketchpad toexplore the cosine rule.
Use examples of real-life situations toexplore the cosine rule.
Acticities : Demonstration
Skill : Interpretation of datas given
Value : Accuracy.
Include obtuse-angled triangles
11 3. Understand and usethe 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.
Additional Exercises
1
2
1
Use dynamic geometry software such
as the Geometers Sketchpad toexplore the concept of areas of
triangles.
Use dynamic geometry software suchas the Geometers Sketchpad toexplore the concept of areas oftriangles.
Skills : Recognising RelationshipAnalising dataUse examples of real-life situations toexplore area of triangles.
Value : Systematic
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Learning Outcomes
Pupils will be able to
No of
Periods
Suggested Teaching & Learning
activities/Learning Skills/Values
Points to Note
Topic ASS1: INDEX NUMBER---1 week
121. Understand and use
the concept of
index number tosolve problems
1.1 Calculate index number.
1.2 Calculate price index.
Find Q0 orQ1 given relevant
information.
1
1
Use examples of real-life situations toexplore index numbers.
Skill : Analise, problem solvingValue : Systematic Q0 = Quantity at base time.
Q1 = Quantity at specific time.
13
2. Understand and usethe concept of
composite index tosolve problems
2.1 Calculate composite index.2.2 Find index number or
weightage given relevantinformation.
2.3 Solve problems involving
index number and composite
index.
Additional Exercises or
past year questions
2
2
2
Use examples of real-life situations toexplore composite index. Eg
Composite index of share.
Skill : Analise, problem solvingValue : Systematic
Explain weightage and compositeindex.
Topic K1 : Differentiation---5 Weeks
14 1. Understand anduse the conceptof gradients ofcurve anddifferentiation.
1.1Determine the value of afunction when its variableapproaches a certainvalue.
1.2Find the gradient of achord joining two pointson a curve.
1.3Find the first derivative of
1
1
Use graphing calculators or dynamicgeometry software such asGeometers Sketchpad to explore theconcept of differentiation.
Skills : Logical Thinking,relationship, application of rules,making inference, making deduction
Idea of limit to a function can beillustrated using graphs.
The concept of first derivative of a
function is explained as a tangent
to a curve can be illustrated using
graphs.
Limit to naxy = ;
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Suggested Teaching & Learning
activities/Learning Skills/Values
Points to Note
a function ( )xfy = , asthe gradient of tangent to
its graph.
1.3 Find the first derivative ofpolynomials using the first
principles.
1.4 Deduce the formula for firstderivative of the function
( )xfy = by induction.
2
Pedagogy : Constructivism
Activities : Explanation &demonstration
a, n are constants, n = 1, 2, 3.
Notation of ( )xf' is equivalent
todx
dywhen ( )xfy = ,
( )xf' read as fprimex.
15
&
16
2. Understand and usethe concept of first
derivative of
polynomial
functions to solve
problems.
2.1 Determine the first
derivative of the functionnaxy = using formula.
2.2 Determine value of thefirst derivative of the
function naxy = for a
given value ofx.
2.3Determine first derivativeof
a function involving:
a) addition, or
b) subtractionof algebraic terms.
2.4Determine the firstderivative of a product oftwo polynomials.
2.5 Determine the firstderivative of a quotient oftwo polynomials.
1
1
1
1
1
Pedagogy : ConstructivismSkills : Logical Thinking,relationship, application of rules,making inference, making deductionValue : Logical thinking
Activities : Explanation anddemonstration by teacher
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Suggested Teaching & Learning
activities/Learning Skills/Values
Points to Note
2.6Determine the first
derivative of compositefunction using chain rule.
2.7Determine the gradient oftangent at a point on a
curve.2.8Determine the equation
of tangent at a point on acurve.
2.9 Determine the equation
of normal at a point on acurve
1
1
1
Limit cases in Learning Outcomes 2.7through 2.9 to rules introduced in 2.4
through 2.6.
173. Understand and
use the concept
of maximumand minimumvalues to solve
problems.
3.1 Determine coordinates of
turning points of a curve.
3.2 Determine whether aturning point is a maximumor a minimum point.
3.3 Solve problems involving
maximum or minimum
values.
2
1
Use graphing calculators or dynamicgeometry software to explore the
concept of maximum and minimumvaluesPedagogy : Constructivism
Skills : Interpretation of problem; Application of appropratemethod/formula
Emphasise the use of first
derivative to determine the turning
points.Limit problems to two variables
only.
Exclude points of inflexion.
Limit problems to two variables
only
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No of
Periods
Suggested Teaching & Learning
activities/Learning Skills/Values
Points to Note
4. Understand and
use the conceptof rates ofchange to solve
problems.
4.1 Determine rates of
change for relatedquantities.
1 Use graphing calculators with
computer base ranger to explore theconcept of rates of change.Skills : Interpretation of problem
; Application of appropratemethod/formula
Limit problems to 3 variables only.
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5. Understand and
use the concept of
small changes and
approximations tosolve problems.
5.1 Determine small changes in
quantities
5.2 Determine approximate
values using
differentiation.
1 Skills : Interpretation of problem; Application of approprate
method/formula
Exclude cases involvingpercentage change.
6. Understand and
use the concept
of second
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
using the second derivative
1
1
Mathematical logic
Value : systematic problem solving
Introduce2
2
dx
ydas
dx
dy
dx
dor
( ) ( )( )xfdx
dxf ''' =
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