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YEARLY PLAN
~MATHEMATICS FORM 4~
2014
SMK TRIANG
n_wati/jan2013
TOPICSLEARNING
OBJECTIVESREMARKS
CHAPTER 1: i. Round off positive numbers to a given number of significant
figures when the numbers are :
(a) greater then 1 (b) less then 1
ii. Perform operations of addition, subtraction, multiplication and
W 1 division, involving a few numbers and state the answer in specific
3/1 - 5/1 significant figures
iii. Solve problems involving significant figures
i. State positive numbers in standard form when the numbers are :
(a) greater than or equal to 10 (b) less then 1
ii. Convert numbers in standard form to single numbers
iii. Perform operation of addition, subtraction, multiplication and
division, involving any two numbers and state the answer in
standard form
iv. Solve problems involving numbers in standard form
i. Identify quadratic expressions
CHAPTER 2 : ii. Form quadratic expressions by multiplying any two linear
expressions
iii. Form quadratic expressions base on specific situations
i. Factorise quadratic expressions of the form ax2 + bx + c ,
where b = 0 or c = 0
ii. Factorise quadratic expressions of the form px2 – q ,
1.2 Understand
and use the
concept of
standard form to
solve problems
2.1 Understand
the concept of
quadratic
expressions
2.2 Factorise
quadratic
expression
STANDARD
FORM
QUADRATIC
EXPRESSIONS
AND
EQUATIONS
1.1 Understand
and use the
concept of
significant figure
LEARNING OUTCOMES
Student will be able to:
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W 2, 3 p and q are perfect squares;
7/1 - 19/1 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 common factors.
i. Identify quadratic equations with one unknown
ii. Write quadratic equations in general form
i.e; ax2 + bx + c = 0
iii. Form quadratic equations base on specific situations
i. Determine whether a given value is a root of a
specific quadratic equations
ii. Determine the solutions for quadratic equations by
(a) trial and error method
(b) factorisations
iii. Solve problems involving quadratic equations
i. Sort given objects into groups
CHAPTER 3: ii. Define sets by :
SETS (a) descriptions (b) using set notation
iii. Identify whether the given object is an element of a
W 4, 5 set and use the symbol ∈ or ∉
21/1 - 1/2 iv. Represents sets by using Venn diagrams
v. List the elements and state the number of elements of a set
vi. Determine whether a set is an empty set
vii. determine whether two sets are equal
2.3 Understand
the concept of
quadratic
equations
2.4 Understand
and use the
concept of roots
of quadratic
equations to
solve problems
3.1 Understand
the concept of
set
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i. Determine whether a given set is a subsets of a
specific set and use the symbol ⊂ or ⊄
ii. Represents subsets by using Venn diagrams
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 the set,
subset, universal set and the complement of a set
i. Determine the intersection of :
(a) two sets; (b) three sets ;
and use the symbol ∩
ii. Represent the intersection of sets using Venn
diagrams
iii. State the relationship between
(a) A ∩ B and A ; (b) A ∩ B and B ;
iv. Determine the complement of the intersection of set
v. Solve problems involving the intersection of set
vi. Determine the union of
(a) two sets (b) three sets
vii. Represent the union of sets using Venn diagram
viii. State the relationship between
(a) A ∪ B and A (b) A ∪ B and B
ix. Determine the complement of the union of sets
* the
intersection of
set* the union of
set
3.2 Understand
the concept of
subset and the
compliment of a
set
3.3 Perform
operation of set;
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x. Solve problems involving the union of sets
xi. Determine the outcome of combined operations on
sets
xii. Solve problems involving combined operations on
sets
CHAPTER 6 : i. Complete the class interval for a set of data given one
STATISTICS of the class interval
ii. Determine
W 6, 8, 9 a) the upper limit and the lower limit
4/2 - 1/3 b) the upper boundary and lower boundary
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 the suitable class interval for a given set of
data
vi. Construct a frequency table for a given a set of data
i. Determine the modal class from the frequency table of
groped data
ii. Calculate a 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 mean for a specific sets of grouped data
6.2 Understand
and use the
concept of mode
and mean of
grouped data
6.1 Understand
the concept of
class interval
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i. Draw a histogram based on the frequency table of
grouped data
ii. Interpret information from a given histogram
iii. Solve problems involving histogram
i. Draw the frequency polygon based on :
a) a histogram
b) a frequency table ;
ii. Interpret information from a given frequency polygons
iii. Solve problems involving frequency polygons
i. Construct the cumulative frequency table for :
(a) ungrouped data (b) grouped data
ii. Draw the ogive for :
(a) ungrouped data (b) grouped data
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 from ogive
iv. Solve problems involving data representations and
measures of dispersion
6.4 Represent and
interpret data in
frequency
polygons to solve
problems
6.3 Represent &
interpret data in
histograms with class
intervals of the same
size to solve problems
6.5 Understand
the concept of
cumulative
frequency
6.6 Understand
& use the
concept of
measures of
dispersion to
solve problems
CHINESE NEW YEAR HOLIDAYW 7 (11/2 - 15/2)
W10 ( 4/3 - 8/3 )
W 11, 12 ( 11/3 - 22/3 )
REVISION WEEK
UP1
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i. Determine the vertical and horizontal distances
between two given points on a straight line
ii. Determine the ratio of vertical distance and horizontal
distance
W 14, 15, 16 i. Derive the formula for the gradient of a straight line
1/4 - 19/4 ii. Calculate the gradient of a straight line passing through
two points
iii. Determine the relationship between the value of
gradient and the :
(a) steepness, (b) direction of inclination, of a straight line
i. Determine the x-intercept and the y-intercept of a
straight line
ii. Derive the formula for the gradient of a straight line in
terms of the x-intercept and the y-intercept
iii. Perform calculations involving gradient , x-intercept and
the y-intercept
i. Draw the graph given an equation of the form y = mx + c
ii. Determine whether the given points lies on a specific
straight line
iii. Write the equation of the straight line given the
gradient and y-intercept
iv. Determine the gradient and y-intercept of the straight
5.4 Understand
and use
equationof a
straight line
5.3 Understand
the concept of
intercept
5.1 Understand
the concept of
gradient of a
straight line
5.2 Understand
the concept of
gradient of a
straight line in
Cartesian
coordinates
CHAPTER 5 :
THE STRAIGHT
LINE
W13 ( 25/3 - 29/3 ) MID TERM BREAK
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line which equation is of the form :
(a) y = mx + c (b) ax + by = c
v. 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 two given points
vi. Find the point of intersection of two straight lines by :
(a) drawing the two straight lines
(b) solving simultaneous equations
i. Verify that two parallel lines have the same gradient
and vice versa
ii. Determine from the given equations whether two
straight lines are parallel
iii. Find the equations of the straight line which passes
through a given point and is parallel to another straight line
iv. Solve problems involving equation of straight line
i. Determine whether the outcome is a possible
outcome of an experiment
ii. List all the possible outcomes of an experiment :
W 17, 18 (a) from activities (b) by reasoning
22/5 - 3/6 iii. Determine the sample space of an experiment
5.5 Understand
anduse the
concept of
parallel lines
7.1 Understand
the concept of
Sample space
CHAPTER 7 :
PROBABILITY
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iv. Write the sample space by using set notations
i. Identify the elements of a sample space which satisfy
given conditions
ii. List all the elements of a sample space which satisfy
certain conditions using set notations
iii. Determine whether an event is possible for a
sample space
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 event and number of trials
iv. Solve problems involving probability
v. Predict the occurrence of an outcome and make a
decision based on known information
CHAPTER 4 : i. Determine whether the given sentence is a statement
ii. Determine whether the given statement is true or false
iii. Construct true or false statement using given
W 24, 25, 26 numbers and mathematical symbols
10/6 - 28/6 i. Construct statement using the quantifier: (a) all (b) some
MID YEAR HOLIDAYS
MID YEAR EXAMINATIONS
REVISION WEEK
7.2 Understand
the concept of
events
W 19 ( 6/5 - 10/5)
W 20, 21 ( 13/5 - 24/5 )
W 22, 23 ( 27/5 - 7/6 )
7.3 Understand
and use the
concept of
probability of an
event to solve
problems
4.1 Understand
the concept of
statement
4.2 Understand
the concept of
quantifier “all”
or “some”
MATHEMATICAL
REASONING
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ii. Determine whether a statement that contains the
quantifier “all” true or false
iii. Determine whether a statement can be generalized
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
i. Change the truth value of a given statement by
placing the words “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 using the words “and ”
iv. Identify two statements from a compound that
contains the word “or ”
v. Form a compound statement by combining two
given statements using the words “or ”
vi. Determine the truth value of a compound
statement which is the combination of two statements
using the words “and ”
vii. Determine the truth value of a compound
statement which is the combination of two
statements using the words “or ”
i. Identify the antecedent and consequent of an
implication “ if p, then q “
4.4 Understand
the concept of
implication
4.2 Understand
the concept of
quantifier “all”
or “some”
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ii. Write two implications from a compound statement
that containing “if and only if”
iii. Construct mathematical statement in the form of
implication :
(a) “ if p, then q“ (b) “ p if and only if q”
iv. Determine the converse of a given implication
v. Determine whether the converse of an implication is
true or false
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
conclusion
i. Determine whether the 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
numerical sequence, by induction
iv. Use deduction and induction in problem solving
4.5 Understand
the concept of
argument
4.6 Understand
and use the
concept of
deduction and
induction to
solve problems
4.4 Understand
the concept of
implication
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i. Identify tangents to a circle
ii. Make inference that the tangent to a circle is a straight
line perpendicular to the radius that passes through the
W 27, 28, 29 contact point
1/7 - 19/7 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 properties related to two tangents to a
circle from a given point outside the circle
v. Solve problems involving tangents to a circle
i. Identify the angle in the alternate segment which is
subtended by the chord through the contact point of
the tangent
ii. Verify the relationship between the angle formed the
tangent and the chord with angle in the alternate
segment which is subtended by the chord
iii. Perform calculations involving the angle in alternate
segment
iv. Solve problems involving tangents to a circle and angle
in alternate segment
i. Determine the number of common tangents which can
be drawn to two circles which :
(a) intersect at two points
8.2 Understand
and use the
properties of an
angle between
tangent and
chord to solve
problems
CHAPTER 8 :
CIRCLES III
8.1 Understand
anduse the
concept of
tangents to a
circle
8.3 Understand
and use the
properties of
common tangent
to solve
problems
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(b) intersect only at one points
(c) do not intersect
ii. Determine the properties related to the common
tangent to two circles which :
(a) intersect at two points
(b) intersect only at one points
(c) do not intersect
iii. Solve problems involving common tangent to two
circles
iv. Solve problems involving tangent and common tangent
i. Identify the quadrant and angle in the unit circle
ii. Determine :
(a) the value of y-coordinate
(b) the value of x-coordinate
W 34, 35, 36 (c) the ratio of y-coordinate to x-coordinate
19/8 - 6/9 of several points on the circumference of the unit circle
iii. Verify that, for an angle in quadrant I of the unit circle :
(a) sin θ = y-coordinate
(b) cos θ = x-coordinate
(c) tan θ = y-coordinate
x-coordinate
9.1 Understand
and use the
concept of
values of sin θ ,
cos θ and tan θ
for 0° ≤ θ ≤ 360°
to solve
problems
REVISION WEEK
CHAPTER 9 : TRIGONOMETRY II
8.3 Understand
and use the
properties of
common tangent
to solve
problems
MID TERM BREAK
UP2
W30 ( 22/7 - 26/7 )
W 31, 32 ( 29/3 - 9/8 )
W33 ( 12/8 - 16/8 )
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iv. Determine the values of :
(a) sine (b) cosine (c) tangent
of an angle in quadrant I of the unit circle
v. Determine the values of :
(a) sin θ (b) cos θ (c) tan θ, for 90° ≤ θ ≤ 360°
vi. Determine whether the values of :
(a) sin θ (b) cos θ (c) tan θ,
of an angle in specific quadrant is positive or negative
vii. Determine the values of sine, cosine, and tangent for
special angles
viii. Determine the values of the angles in quadrant I which
correspond to the values of the angles in other quadrants
ix. State the relationships between the values of :
(a) sine (b) cosine (c) tangent
of an angle in quadrant II, III and IV with their
respective values of the corresponding angle in
quadrant I
x. Find the values of sine, cosine and tangent of the
angles between 90° and 360°
xi. Find the angles between 0° and 360°, given the values
of sine, cosine or tangent
xii. Solve problems involving sine, cosine and tangent.
i. Draw the graphs of sine, cosine and tangent for angles
between 0° and 360°
9.1 Understand
and use the
concept of
values of sin θ ,
cos θ and tan θ
for 0° ≤ θ ≤ 360°
to solve
problems
9.2 Draw and
use the Graphs
of sine, cosine
and tangentn_wati/jan2013
ii. Compare the graphs of sine, cosine and tangent for
angles between 0° and 360°
iii. Solve problems involving graphs of sine, cosine and
tangent
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 :
W 37, 38 (a) the angle of elevation (b) the angle of depression
9/9 - 20/9 using diagrams
iii. Solve problems involving the angle of elevation and
the angle of depression
i. Identify planes
ii. Identify horizontal planes, vertical planes and inclined
planes
iii. Sketch a three dimensional shape and identify the
specific planes
W 39, 40 iv. Identify : (a) lines that lies on a plane
23/9 - 4/10 (b) lines that intersect with a plane
v. Identify normal to a given plane
vi. Determine the orthogonal projection of a line on a plane
vii. Draw and name the orthogonal projection of a line on a
plane
viii. Determine the angle between a line and a plane
CHAPTER 10 :
ANGLES OF
ELEVATION &
DEPRESSION
9.2 Draw and
use the Graphs
of sine, cosine
and tangent
10.1 Understand
and use the
concept of angle
of elevation and
angle of
depression to
solve problems
CHAPTER 11
LINES AND
PLANES IN 3-
DIMENSIONS
11.1 Understand
and use the
concept of angle
between lines
and planes to
solve problems
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ix. Solve problems involving the angle between a line
and a plane
i. Identify the line of intersection between two planes
ii. Draw a line in 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
11.2 Understand
and use the
concept of angle
between two
planes to solve
problems
REVISION
W 44, 45 ( 28/10 - 8/11 )
W 41, 42, 43 ( 7/10 - 25/10 )
W 47 - W 53 ( 18/11/13 - 1/1/14 )
W 46 ( 11/11 - 15/11 )
END OF YEAR HOLIDAY
DISCUSSIONS
END OF YEAR EXAMINATIONS
n_wati/jan2013
