1. ANNUAL PLANNING FOR ADDITIONAL MATHEMATICS FORM 4 / 2011
WEEK TOPICS/LEARNING AREA LEARNING OUTCOMES POINTS TO NOTE
3 Jan – • Registration Day
7 Jan • Orientation Week

2. 3 A1 FUNCTIONS Students should be able to :
WEEKS
(10 Jan – 1.0 Understand the concept of 1.1 Represent a relation using  Discuss the idea of set and
28 Jan) relations a) arrow diagram introduce set notation
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 or many to many
relation.
2.0 Understand the concept of 2.1 Recognise function as a special  Represent functions using
functions relation. arrow diagram, ordered
2.2 Express functions using function pairs or graph.
notation.  Examples of functions
2.3 Determine domain, object, image include algebraic (linear and
and range of a function. quadratic), trigonometric
2.4 Determine image of a function and absolute value.
given the object and vice versa.  Define and sketch absolute
value function.
3.0 Understand the concept of 3.1 Determine composition of two  Involve algebraic functions
composite functions functions. only.
3.2 Determine image of composite  Images of composite
functions given the object and function include arrange of
vice versa. values.
3.3 Determine one of the function in
a given composite function given
the other related function.
4.0 Understand the concept of inverse 4.1 Find object by inverse mapping  Limit to algebraic function.
functions given its image and function. Exclude inverse of
4.2 Determine inverse function using composite function.
algebra.  Emphasise that inverse of a
4.3 Determine and state the function is not necessarily a
condition for existence of an function.
inverse function.

3. 3 A2 QUADRATIC EQUATIONS Students should be able to:
WEEKS
(31 1.0 Understand the concept of 1.1 Recognise quadratic equation  Questions for 1.2(b) are
Jan-11 quadratic equations and its roots and express it in general form. given in the form
Feb)
1.2 Determine whether a given value ( x + a)( x + b) = 0 a, b are
is the root of a quadratic numerical values.
equation by:  Involve the use of α and
a) substitution β
b) inspection
1.3 Determine the roots of a
quadratic equation by trial and
improvement method.
2.0 Understand the concept of 2.1 Determine the roots of a
quadratic equations quadratic equation by
a) factorization
b) completing the square
c) using the formula
2.2 Form a quadratic equation from
given roots.
3.0 Understand and use the conditions 3.1 Determine types of roots of  b 2 − 4ac > 0
for quadratic equations to have quadratic equations from the  b 2 − 4ac = 0
a) two different roots value of b 2 − 4ac .  b 2 − 4ac < 0
b) two equal roots 3.2 Solve problems involving
c) no roots b − 4ac
2
in quadratic
equations to
a) find an unknown value
b) derive a relation
4 A3 QUADRATIC FUNCTIONS Students should be able to :
WEEKS
(14 Feb-4 1.0 Understand the concept of 1.1 Recognise quadratic functions.  Discuss cases where
Mac) quadratic functions and their 1.2 Plot quadratic function graphs a > 0 and a < 0 for
graphs a) based on given tabulated f ( x) = ax 2 + bx + c = 0
values
b) by tabulating values based
on given functions
1.3 Recognise shapes of graphs of
quadratic functions.
1.4 Relate the position of quadratic
function graphs with types of
roots for f(x) = 0.

4. TEST 1 Will be prepared by:
(7 Mac – 11 Mac) PN. SURIANI
(21 Mar – 2.0 Find maximum and minimum 2.1 Determine the maximum or  Emphasise the marking of
25 Mar) values of quadratic functions minimum value of a quadratic maximum or minimum and
function by completing the two other points on the
square graphs drawn or finding the
axis of symmetry and the
(28 Mar 3.0 Sketch graphs of quadratic 3.1 Sketch quadratic function graphs intersection with y-axis.
– 1 Apr) functions by determining the maximum or
minimum point and two other  Emphasise on sketching
points graphs and use number
lines when necessary
(4 Apr – 4.0 Understand and use the concept of 4.1 Determine the ranges of values
8 Apr)
quadratic inequalities of x that satisfies quadratic
inequalities
2 A4 SIMULTANEOUS EQUATIONS Students should be able to:
WEEKS
(11 Apr 1.0 Solve simultaneous equations in 1.1 Solve simultaneous equations  Limit non-linear equations
-22 Apr) two unknowns: one linear equation using the substitution method up to second degree only
and one non-linear equation 1.2 Solve simultaneous equations
involving real-life situations
2 A5 INDICES AND LOGARITHM Students should be able to:
WEEKS
(25 Apr 1.0 Understand and use the concept 1.1 Find the values of numbers given  Discuss zero index and
-6 May) of indices and laws of indices to in the form of negative indices
solve problems a) integer indices
b) fractional indices
1.2 Use laws of indices to find the
values of numbers in index form
that are multiplied, divided or
raised to a power
1.3 Use laws of indices to simplify
algebraic expressions

5. 2.0 Understand and use concept of 2.1 Express equation in index form to  Explain definition of
logarithms and laws of logarithm form and vice versa logarithm
logarithms to solve problems 2.2 Find logarithm of a number N = a x ; log a N = x
2.3 Find logarithm of numbers by  Emphasise that
using laws of logarithms log a 1 = 0 ; log a a = 1
2.4 Simplify logarithmic expressions
 Discuss cases where the
to the simplest form
given number is in
a) index form
b) numerical form
 Discuss laws of logarithms
3.0 Understand and use the change 3.1 Find the logarithm of a number  Discuss:
of base of logarithms to solve by changing the base of the 1
log a b =
problems logarithm to a suitable base log b a
3.2 Solve problems involving the
change of base and laws of
logarithms
4.0 Solve equations involving indices 4.1 Solve equations involving indices.  Equations that involve
and logarithms 4.2 Solve equations involving indices and logarithms are
logarithms. limited to equations with
single solution only.
 Solve equations involving
indices by:
a) comparison of indices
and bases
b) using logarithms
MID YEAR EXAM Will be prepared by:
(9 MAY – 27 MAY) PN. SURIANI

6. 3 G1 COORDINATE GEOMETRY Students should be able to:
WEEKS
(13 1.0 Find distance between two points 1.1 Find distance between two  Use Pythagoras’ theorem to
June-1 points using formula find the formula for
July)
distance between two
2.0 Understand the concept of division 2.1 Find midpoint of two given points.
of a line segment points.  Limit to cases where m and
2.2 Find coordinates of a point that n are positive.
divides a line according to a  Derivation of the formula
given ration m:n  nx1 + mx 2 ny1 + my 2 
 , 
3.0 Find areas of polygons 3.1 Find area of triangle based on  m+n m+n 
the area specific geometrical is not required
shapes.  Limit to numerical values
3.2 Find area of a triangle by using  Emphasise the
formula. relationship between the
3.3 Find area of a quadrilateral sign of the value for area
using formula. obtained with the order of
the vertices used
4.0 Understand and use the concept of 4.1 Determine the x-intercept and  Derivation of the formula:
equation of a straight line the y-intercept of a line. 1
( x1 y 2 + x 2 y 3 + x3 y1 ) −
4.2 Find the gradient of a straight 2
line that passes through two ( x 2 y1 − x3 y 2 − x1 y 3 )
points. is not required.
4.3 Find the gradient of a straight  Emphasise that when area
line using the x-intercept and y- of polygon is zero, the
intercept. given points are collinear.
4.4 Find the equation of a straight  Answers for learning
line given: outcomes 4.4(a) and 4.4(b)
a) gradient and one point must be stated in the
b) two points simplest form.
c) x-intercept and y-intercept  Involve changing the
4.5 Find the gradient and the equation into gradient and
intercepts of a straight line intercept form.
given the equation.
4.6 Change the equation of a
straight line to the general
form.
4.7 Find the point of intersection of
two lines.
5.0 Understand and use the concept of 5.1 Determine whether two straight  Emphasise that for parallel
parallel and perpendicular lines lines are parallel when lines:
gradients of both lines are m1 = m2
known and vice versa.  Emphasise that for
5.2 Find the equation of a straight perpendicular lines

7. 3 S1 STATISTICS Students should be able to:
WEEKS
(4 1.0 Understand and use the concept 1.1 Calculate mean of ungrouped  Discuss grouped data and
July-22 of measures of tendency to solve data. ungrouped data.
July)
problems 1.2 Determine mode of ungrouped
data.
1.3 Determine median of ungrouped
data.
1.4 Determine modal class of  Involve uniform class
grouped data from the intervals only.
frequency distribution table.
1.5 Find mode from histogram.
1.6 Calculate mean of grouped data.  Derivation of the median
1.7 Calculate median of grouped formula is not required.
data from the cumulative
frequency distribution table.
1.8 Estimate median of grouped  Ogive is also known as
data from an ogive. cumulative frequency
1.9 Determine the effects on mode, curve.
median and mean for a set of
data.
1.10 Determine the most suitable  Involve grouped and
measure of central tendency for ungrouped data.
given data.
2.0 Understand and use the concept 2.1 Find the range of ungrouped
of measures of dispersion to data.
solve problems. 2.2 Find the interquartile range of
ungrouped data.
2.3 Find the range of grouped data.
2.4 Find the interquartile range of  Determine upper and
grouped data from the lower quartiles by using
cumulative frequency table. the first principle.
2.5 Determine the interquartile
range of grouped data from an
ogive.
2.6 Determine the variance of:
a) ungrouped data;
b) grouped data
2.7 Determine standard deviation of
ungrouped data and grouped
data.
2.8 Determine the effect on range,
interquartile range, variance
and standard deviation for a set

8. of data when:
a) each data is changed
uniformly
b) extreme values exist
c) certain data is added or
removed
2.9 Compare the measures of  Emphasise that
central tendency and dispersion comparison between two
between two sets of data. sets of data using only
measures of central
tendency is not sufficient.
4 T1 CIRCULAR MEASURES Students should be able to:
WEEKS
(25 1.0 Understand the concept of radian. 1.1 Convert measurement in  Discuss the definition of
July-5 radians to degrees and vice one radian.
Aug)
versa.  ‘rad’ is the abbreviation of
radian.
2.0 Understand and use the concept 2.1 Determine:  Include measurements in
of length of arc of a circle to solve a) length of arc radians expressed in term
problems. b) radius and of π.
c) angle subtended at the
centre of a circle
based on given information.
2.2 Find perimeter of segments of
circles.
2.3 Solve problems involving lengths
of arcs.
TEST 2 Will be prepared by:
(8 AUG – 12 AUG) PN. SURIANI

9. (15 Aug – 3.0 Understand and use the concept 3.1 Determine:
26 Aug ) of area of sector of a circle to a) area of sector
solve problems b) radius and
c) angle subtended at the
centre of circle
based on given information.
3.2 Find area of segments of
circles.
3.3 Solve problems involving area of
sectors.

10. 3 C1 DIFFERENTIATION Students should be able to:
WEEKS
(5 Sept 1.0 Understand the concept of radian 1.1 Determine value of a function  Idea of limit to a function
-23 when its variable approaches a can be illustrated using
Sept)
certain value. graphs.
1.2 Find gradient of a chord joining  Concept of first derivative
two points on a curve. of a function is explained
1.3 Find the first derivative of a as a tangent to a curve
function y=f(x) as gradient of can be illustrated using
tangent to its graph. graphs.
1.4 Find the first derivative for  Limit to
polynomial using first principles. y = ax n ; a, n are constant,
1.5 Deduce the formula for first n=1,2,3
derivative of function y=f(x) by  Notation of f ' ( x) is
induction. dy
equaivalent to when
dx
2.0 Understand and use the concept 2.1 Determine first derivative of the
y = f (x) . f ' ( x) read
of first derivative of polynomial function y = ax n using
functions to solve problems as ‘f prime x’.
formula.
2.2 Determine value of the first
derivative of the function
y = ax n for a given value of x.
2.3 Determine first derivative of a
function involving:
a) addition, or
b) subtraction
of algebraic terms.
2.4 Determine first derivative of a
product of two polynomials.
2.5 Determine first derivative of a
quotient of two polynomials.
2.6 Determine the first derivative of
composite function using chain
rule.
2.7 Determine gradient of tangent  Limit cases in learning
at a point on a curve. outcomes 2.7 – 2.9 to
2.8 Determine equation of tangent rules introduced in 2.4 –
at a point on a curve. 2.6.
2.9 Determine equation of normal at
a point on a curve.
3.0 Understand and use the concept 3.1 Determine coordinates of  Emphasise the use of first
of maximum and minimum values turning points of a curve. derivative to determine
to solve problems. 3.2 Determine whether a turning turning points.
point is a maximum or minimum  Exclude points of inflextion.

11. 2 AST1 SOLUTION OF TRIANGLES Students should be able to:
WEEKS
(26 Sept 1.0 Understand and use the concept of 1.1 Verify sine rule.
- 7 Oct) sine rule to solve problems 1.2 Use sine rule to find unknown  Include obtuse-angled
sides or angles of triangle. triangles
1.3 Find unknown sides and angles
of triangle in ambiguous case.
1.4 Solve problems involving the
sine rule.
2.0 Understand and use the concept 2.1 Verify cosine rule.  Include obtuse-angled
of cosine rule to solve problems 2.2 Use cosine rule to find unknown triangles
sides or angles of a triangle.
2.3 Solve problems involving cosine
rule.
2.4 Solve problems involving sine
and cosine rules.
3.0 Understand and use the formula 3.1 Find area of triangles using
for area of triangles to solve 1
formula ab sin C or its
problems 2
equivalent.
3.2 Solve problems involving three-
dimensional objects.
2 ASS1 INDEX NUMBER Students should be able to:
WEEKS
(10 1.0 Understand and use the concept 1.1 Calculate index number.  Explain index number.
Oct-14 of index number to solve 1.2 Calculate price index.  Q0 = quantity at base
Oct)
problems 1.3 Find Q0 orQ1 given relevant time
information.  Q1 = quantity at specific
time
2.0 Understand and use the concept 2.1 Calculate composite index.
of composite index to solve 2.2 Find index number or weightage  Explain weightage and
problems. given relevant information. composite index
2.3 Solve problems involving index
number and composite index.
• REVISION
• FINAL EXAM PPSMI
(17 OKT – 4 NOV)