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ANNUAL PLANNING FORMATHEMATICS FORM 4 /
2013
WEEK TOPICS/LEARNING
AREA
LEARNING OUTCOMES POINTS TO NOTE
7 Jan
9
Jan
Registration
Day
Orientation
Week
1
WEEK
(10
Jan
18
Jan)
CHAPTER 1 :
STANDARD FORM
Students will be
taught to understand
and use the concept
of significant figure
Students will be able to:
i. Round off positive
numbers to a given
number of significant
figures when the
numbers are
a. greater than 1
b. less than 1
ii. Perform operations of
addition, subtraction,
multiplication and
division involving a few
numbers and state the
answer in specific
significant figures.
iii. solve problems
involving significant
figures.
Discuss the significance
of zero in a number.
Discuss the use of
significant figures in
everyday life and other
areas
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Students will be
taught to understand
and use the concept
of standard form to
solve problems
Students will be able to:
i. State positive numbers
in standard form when
the numbers are
a) greater than or
equal to 10
b) less than 1
ii. convert numbers in
standard form to single
numbers
iii. perform operations of
addition, subtraction,
multiplication and
division involving any
two numbers and state
the answers in standard
form
iv. solve problems
involving numbers instandard form
Use everyday life
situations such as in
health, technology,
industry, construction
and business involving
numbers in standard
form
Use the scientific
calculator to explore
numbers in standard
form
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2
WEEKS
(21
Jan 1 Jan)
CHAPTER 2 :
QUADRATIC
EXPRESSIONS AND
EQUATIONS
Students will be
taught to understand
the concept of
quadratic expressions
Students will be able to :i. Identify quadratic
expressions
ii. Form quadratic
expressions by
multiplying any two
linear expressions
iii. Form quadratic
expressions based on
specific situations
Discuss the characteristicsof quadratic expressions
of the form ax2 + bx +
c = 0 where a, b and are
constants, a 0 and x is
an unknown
Students will be
taught how to
factorise quadratic
expressions
Students will be able to :
i. Factorise quadratic
expressions of the form
ax2+bx+c =0or c=0;ii. Factorise quadratic
expressions of the form
px2-q, pand qare
perfect squares;
iii. Factorise quadratic
expressions of the form
ax2+bx+c, where a, b
and c not equal to
zero;
iv. Factorise quadratic
expressions containing
coefficients with
Discuss the various
methods to obtain the
desired product.
Begin with the case a=1.
Explore the use of
graphing calculator to
factorise quadratic
expressions
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common factors;
Students will be
taught to
understand the
concept of quadratic
equation
Students will be able to :
i. Identify quadratic
equations with one
unknown;
ii. write quadratic
equations in general
form i.e.
ax2+ bx + c = 0 ;
iii. form quadratic
equations based on
specific situations ;
Discuss the characteristics
of quadratic equations.
Students will be
taught to
understand and use
the concept of roots
of quadraticequations to solve
problems.
Students will be able to :
i. Determine whether a
given value is a root of
a specific quadratic
equationii. Determine the solutions
for quadratic equations
by:
a) trial and error method
Discuss the number of
roots of a quadratic
equation.
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;
b) factorization ;
iii. solve the problems
involving quadraticequations
Use everyday life
situations.
3
WEEKS
(31
Jan
18
Feb)
CHAPTER 3 : SETS
Students will be
taught to
understand the
concept of set
Students will be able to :
i. sort given objects into
group
ii. define set by :
a. descriptions;
b. using set notation;
iii. identify whether a
given object is
anelement of a set
and use the symbol
or ;iv. represent sets by
using Venn diagrams;
v. list the element and
state the number of
element of a set;
vi. determine whether a
set is an empty set;
vii. determine whether
two sets are equal;
Use everyday life
examples to introduce
the concept of set.
Discuss the difference
between the
representation of
element and the number
of element in Venn
diagrams.
Discuss why { 0 } and {
} are not empty sets.
Students will be Students will be able to : Begin with everyday life
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taught to
understand and use
the concept of
subset, universal setand the complement
of a set
i. determine whether a
given set is a subset of
a specific set and use
the symbol
or
;ii. represent subset using
Venn diagram;
iii. list the subsets for a
specific set;
iv. illustrate the
relationship between
set and universal set
using Venn diagram;
v. determine the
complement of a given
set ;
vi. determine the
relationship between
set, subset, universal set
and the complement ofa set;
situations.
Discuss the relationship
between sets and
universal sets.
Students will be
taught to perform
operations on sets:
the intersection
of sets;
the union of sets
Students will be able to:
i. determine the
intersection of:
a) two sets;
b) three sets;
and use the symbol
;
ii. represent the
intersection of sets
Discuss cases when:
BA =
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using Venn diagram;
iii. state the relationship
between
i.
BA
andA
,ii. BA and B ;
iv. determine the
complement of the
intersection of sets;
v. solve problems
involving the
intersection of sets;
vi. determine the union of
a) two sets;
b) three sets;
and use the symbol
;
vii. represent the union of
sets using
Venn diagram;viii. state the relationship
between
a) BA and A ,
b) BA and B ;
ix. determine the
complement of the
union of sets
x. solve problems
involving the union of
sets
xi. determine the outcome
of combined operations
BA
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on sets
xii solve problems
involving combined
operations on sets2
WEEKS
(21
Feb
4
March)
CHAPTER 4 :
MATHEMATICAL
REASONING
Students will be
taught to understand
the concept ofstatement;
Students will be able to:
i. determine whether a
given sentence is a
statement;
ii. determine whether a
given statement is true
or false;
iii. construct true or false
statement using given
numbers and
mathematical symbols;
Introduce this topic using
everyday life situations
Focus on mathematical
sentences
Discuss sentences
consisting of:
words only;
numbers and words;
numbers and
mathematical symbols;.
Students will be
taught understand
the concept of
quantifiers all and
some;
Students will be able to:
i. construct statements
using the quantifier:
a)all;
b)some;
ii. determine whether a
Start with everyday life
situations.
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statement that contains
the quantifier all is
true or false;
iii. determine whether astatement can be
generalised to cover all
cases by using the
quantifier all;
iv. construct a true
statement using the
quantifier all or
some, given an object
and a property.
TEST 1
(7 Mac 11 Mac)
Will be prepared by:
PN. SURIANI
2
WEEKS
(21
Mar
1 Apr)
Students will be
taught to perform
operations involving
the words not or
no, and and or
on statements;
Students will be able to :
i.
change the truth valueof a given statement by
placing the word not
into the original
statement;
ii. identify two statements
from a compound
statement that contains
the word and;
iii. form a compound
statement by combining
two given statements
Begin with everyday life
situations.
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using the word and;
iv. identify two statement
from a compound
statement that containsthe word or ;
v. form a compound
statement by combining
two given statements
using the word or;
vi. determine the truth
value of a compoundstatement which is the
combination of two
statements with the
word and;
vii. determine the truth
value of a compound
statement which is the
combination of two
statements with the
word or.
Students will be
taught to understand
the concept of
implication;
Students will be able to;
i.
identify the antecedentand consequent of an
implication ifp, then
q;
ii. write two implications
Start with everyday life
situations.
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from a compound
statement containing if
and only if
iii. construct mathematicalstatements in the form
of implication
a) Ifp, then q;
b) pif and only ifq
v. determine the converse
of a given implication;
vi. determine whether the
converse of an
implication is true or
false
Students will betaught to understand
the concept of
argument;
Students will be able to:
i. identify the premise
and conclusion of a
given simple argument;
ii. make a conclusion
based on two given
premises for
a) Argument Form I;
b) Argument Form II;
c) Argument Form III;
iii. complete an argument
given a premise and the
Start with everyday life
situations.
Encourage students to
produce arguments
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conclusion. based on previous
knowledge.
Students will be
taught to understand
and use the concept
of deduction and
induction to solve
problems.
Students will be able to:i. determine whether a
conclusion is made
through:
a) reasoning by
deduction;
b) reasoning by
induction;
ii. make a conclusion for a
specific case based on a
given general
statement, by
deduction;
iii. make a generalization
based on the pattern of
a numerical sequence,
by induction;
iv. use deduction and
induction in problem
solving.
Use specific
examples/activities to
introduce the concept.
3
WEEKS
(4 Apr
-22
Apr)
CHAPTER 5 : THE
STRAIGHT LINE
Students will be
taught to
understand the
Students will be able to:
i. determine the vertical
and horizontal distances
between two given
Use technology such as
the Geometer's
Sketchpad , graphing
calculators, graph boards,
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concept of gradient
of a straight line
points on a straight line
ii.
determine the ratio ofvertical distance to
horizontal distance
magnetic boards, topo
maps as teaching aid
where appropriate.
Begin with concrete
examples /daily situations
to introduce the concept
of gradient.
Horizontal distance
Discuss:
the relationship
between gradient
and tan
the steepness of th
straight line with
different values of
gradient
Carry out activities to
find the ratios of vertical
distance to horizontal
distance for several pairs
of points on a straight
Vertical
distance
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line to conclude that the
ratio is constant.
Students will be
taught to understand
the concept of
gradient of a straight
line in Cartesian
coordinates
Students will be able to:
i. derive the formula for
the gradient of a
straight line
ii. calculate the gradient
of a straight linepassing through two
points;
iii. determine the
relationship between
the value of the
gradient and the :
a) steepness;
b) direction of
inclination, of a straight
line
Discuss the value of
gradient if
P is chosen as (x1
,y1 ) and Q is (x2
,y2 ) ;
P is chosen as (x2,y2 ) and Q is (x1
,y1 )
Students will be
taught to
understand the
concept of intercept;
Students will be able to:
i. determine the x-
intercept and the y-
intercept of a straight
line
ii. derive the formula for
Students will be taught
to understand the
concept of intercept;
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the gradient of a
straight line in terms of
the x-intercept and the
y-interceptiii. perform calculations
involving gradient, x-
intercept and y-
intercept
Students will be
taught to
understand and use
equation of a straight
line;
i. Find the equation of the
straight line which:
a. is parallel to the x-axis;
b. is parallel to the y-axis;
c. passes through a given
point
and has a specific
gradient;
d. passes through two givenpoints;
ii. find the point of
intersection of two
straight lines by;
a) drawing the two
straight lines;
b) solving simultaneous
equations
Discuss and concludethat the point of
intersection is the only
point that satisfies both
equations
Use the graphing
calculator and
Geometer's Sketchpad or
other teaching aids to
find the point of
intersection
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2
WEEKS
(25
Apr
6 May
Students will be
taught to
understand and usethe concept of
parallel lines
Students will be able to:
i. verify that two parallel
lines have the samegradient and vice versa;
ii. determine from the
given equation whether
two straight lines are
parallel;
iii. find the equation of the
straight line which
passes through a given
point and is parallel to
another straight line;
iv. solve problems
involving equations of
straight lines
Explore properties of
parallel lines using thegraphing calculator and
Geometer's Sketchpad or
other teaching aids.
CHAPTER 6 :
STATISTICS III
Students will be
taught to understand
the concept of class
interval.
Students will be able to:
i. Complete the class
interval for a set of data
given one of the class
intervals;
ii. Determine
a) the upper limit and
lower limit;
b) the upper boundary
and lower boundary
Use data obtained from
activities and other
sources such as research
studies to introduce the
concept of class interval .
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of a class in a
grouped data;
iii. Calculate the size of a
class interval;iv. Determine the class
interval, given a set of
data and the number of
classes;
v. Determine a suitable
class interval for a given
set of data ;
vi. Construct a frequency
table for a given set of
data
Discuss criteria for
suitable class intervals
Students will be
taught to understand
and use the
concept of mode andmean of grouped
data ;
Students will be able to:
i. Determine the modal
class from the
frequency table ofgrouped data ;
ii. Calculate the midpoint
of a class;
iii. Verify the formula for
the mean of grouped
data ;
iv. Calculate the mean
from the frequency
table of grouped data
v. Discuss the effect of the
size of class interval on
the accuracy of the
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mean for a specific set
of grouped data
Students will be
taught to represent
and interpret
data in histogramswith
class intervals of the
same
size to solve
problems ;
Students will be able to:
i. Draw a histogram
based on the frequency
table of a grouped dataii. Interpret information
from a given histogram;
iii. Solve problems
involving histograms.
Discuss the difference
between histogram and
bar chart.
Use graphing calculator
to explore the effect of
different class interval on
histogram.
Students will be
taught to represent
and interpret data in
frequency polygons
to solve
problems.
Students will be able to:
i. Draw the frequency
polygon based on
a) a histogram ;
b) a frequency table ;
ii. Interpret information
from a given frequency
polygon ;
iii. Solve problems
involving frequency
polygon.
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Students will be
taught to understand
the concept ofcumulative frequency
Students will be able to:
i. Construct the
cumulative frequencytable for
a) ungrouped data
b) grouped data
ii. Draw the ogive for :
a) ungrouped data
b) grouped data
Students will be
taught to understand
and use the concept
of measures of
dispersion to solve
problems
Students will be able to:
i. Determine the range of
a set of data
ii. Determine
a) the median ;
b) the first quartile;
c) the third quartile ;
d) the interquartile
range ;
from the ogive .
iii. interpret information
Discuss the meaning of
dispersion by comparing
a few sets of data.
Graphing calculator can
be used for this purpose
.
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from an ogive
iv. solve problems
involving data
representations andmeasures of dispersion
Carry out a project
/research and analyse as
well as interpret the data
.Present the findings ofthe project/research.
Emphasise the
importance of honesty
and accuracy in
managing statistical
research .
MID YEAR EXAM
(9 MAY 27 MAY)
Will be prepared by:
PN. SURIANI & PN.
SAIDANORLAILI
2
WEEKS
(13
June
24
June)
CHAPTER 7 :
PROBABILITY
Students will be
taught to understand
the concept o
sample space.
Students will be able to:
i. Determine whether
an outcome is a
possible outcome of
an experiment;
ii. List all the possible
outcomes of an
experiment ;
a) from activities;
b) by reasoning;
iii. Determine the sample
space of an
experiment;
iv. Write the sample
space by using set
notations.
Use concrete examples
such as drawing a die
and tossing a coin.
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Students will be
taught tounderstand the
concept of
events.
Students will be able to:
i.
identify the elementsof a sample space
which satisfy given
conditions;
ii. list all the element of
a sample space which
satisfy certain condition
using set notations.
iii. determine whether an
event is
possible for a
sample space.
Discuss that an event
is a subset of thesample space
Discuss also impossible
events for a sample
space.
Discuss that the
sample space itself is
an event.
Students will be
taught to understand
and use the
concept of
probability of an
event to solve
problems
Students will be able to:
i. find the ratio of the
number of
times an event
occurs to the number
of trials.
ii. find the probability of
an event from a big
enough number of
trials;
iii. calculate the
expected number of
times an event will
occur given the
probability of the
Carry out activities to
introduce the concept
of probability . The
graphing calculator can
be used to simulate
such activities.
Discuss situation which
results in:
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event an number of
trials;
iv. solve problems
involving probability;v. predict the
occurrence of an
outcome and make a
decision based on
known information.
probability of
event = 1
probability of
event = 0
Emphasise that the value
of probability is
between 0 and 1.
Predict possible events
which might occur in
daily situations
2
WEEKS
(27
June
8 July)
CHAPTER 8 :
CIRCLES III
Students will be
taught to understand
and use the concept
of tangent to a circle.
Students will be able to:
i. identify tangent to a
circle;
ii. make inference that
the tangent to a circle
is a straight lineperpendicular to the
radius that passes
through the contact
point;
iii. construct the tangent
to a circle passing
through a point:
a) on the
circumference of
the circle;
b) outside the circle;
iv. determine the
Develop concepts and
abilities through activities
using technology such as
the Geometer`s
Sketchpad and graphing
calculator.
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properties related to
two tangent to a circle
from a given point
outside the circle;v. solve problems
involving tangent to a
circle.
Students will be
taught understand
and use theproperties of angle
between tangent and
chord to solve
problems.
Students will be able to:
i. identify the angle in
the alternate segmentwhich is subtended by
the chord through the
contact point of the
tangent;
ii. verify the relationship
between the angle
formed by the tangent
and the chord with the
angle in the alternate
segment which is
subtended by the
chord;
Explore the properties of
angle in alternatesegment using
Geometer`s Sketchpad or
other teaching aids.
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iii. perform calculations
involving the angle in
alternate segment;
iv.
solve problemsinvolving tangent to a
circle and angle in
alternate segment.
Students will taught
to understand and
use the properties of
common tangents to
solve problems
Students will be able to:
i. determine the number of
common tangents which
can be drawn to two
circles which:
a) intersect at two
points;
b) intersect only at one
point;
c) do not intersect;
ii. determine the propertiesrelated the common
tangent to two circles
which:
a) intersect at two
points;
b) intersect only at one
point;
c) do not intersect;
iii. solve problems involving
common tangents to two
circles;
iv. solve problems involving
Discuss the maximum
number of common
tangents for the three
cases.
Include daily situations.
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tangents and common
tangents.
Students will be
taught to
understand and use
the concept of the
values of sin ,
kos , and tan
(0 360) to
solve problems.
i. find the values of sine,
cosine and tangent of
the angles between
90 and 360
ii. find the angles
between 0 and 360,
given the values of
sine, cosine or
tangent
iii. solve problems
involving sine, cosine
and tangent
Relate the daily situation
Students will be
taught to draw and
use the graphs of
sine, cosine and
tangent.
Students will be able to:
i. Draw the graphs of
sine, cosine and
tangent for angles
between 0o and 360o;
ii. Compare the graphs of
sine, cosine and
tangent for angles
between 0o and 360o;
iii. Solve problems
involving graphs of
sine, cosine and
tangent.
Use the graphing
calculator and
Geometers Sketchpad to
explore the feature of the
graphs of
tan,cos,sin yyy
Discuss the feature of the
graphs of
tan,cos,sin yyy
Discuss the examples of
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these graphs in other
area.
3
WEEKS
(11
July -
29
July)
CHAPTER 10 :
ANGLES OF
ELEVATION AND
DEPRESSIONS
Students will be
taught to understand
and use the concept
of angle of elevation
and angle of
depression to solve
problems
Students will be able to:
i. identify
a) the horizontal line
b) the angle of
elevation
c) the angle of
depression
for a particular
situation
ii. Represent a particular
situation involving
a)the angle ofelevation
b) the angle of
depression,
using diagrams
iii. Solve problems
involving the angle of
elevation and the
angle of depression
Use daily situations to
introduce the concept
(1 Aug
5
Aug)
REVISION
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TEST 2
(8 AUG 12 AUG)
Will be prepared by:
PN. SAIDANORLAILI
2
WEEKS(15
Aug
26
Aug)
CHAPTER 11 :
LINES AND PLANESIN 3 DIMENSIONS
Students will be
taught to understand
and use the concept
of angle between
lines and planes to
solve problems
Students will be able to
i. identify planes
ii. identify horizontal
planes and inclined
planes
iii. sketch a three
dimensional shape and
identify the specific
planes.
iv. Identify :
a) lines that lies on a
plane.
b) Lines that intersectwith a plane,
v. Identify normals to a
given plane,
vi. Determine the
orthogonal projection
of a line on a plane
vii. Draw and the name
the orthogonal
projection of a line on
a plane
viii. Determine the angle
between a line and a
Carry out activities using
daily situation and 3-
dimensional models.
Differentiate between 2-
dimensional an d 3-
dimensional shapes.
Involve planes found in
natural surroundings.
Begin with 3-dimensional
models.
Use 3-dimensional
models to give clearer
pictures.
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plane
ix. Solve problems
involving the angle
between a line and aplane.
Students will be
taught to
understand and
use the conceptof angle between
two planes to
solve problems
Students will be able to :
i. identify the line
intersection between
two planes,ii. draw a line on each
plane which is
perpendicular to the
line of intersection of
the two planes at a
point on the line of
intersection
iii. determine the angle
between two planes on
a model and a given
diagram.
iv. Solve problems
involving lines and
planes in 3-
dimensional shapes.
Use 3-dimensional
models to give clearer
pictures.
(5
Sept
14
REVISION
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Oct)
FINAL EXAM
(17 OKT 4
NOV)
Will be prepared by:
PN. SURIANI & PN.
SUNITA
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