Topics Opsme t4
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WEEK TOPICS LEARNING
OBJECTIVES
LEARNING OUTCOMES VALUES TEACHING
AIDS/ CCTS
2-3 OPSME T4
4, 5, 6
Standard Form 1.1 Understand and
use the concept of
significant figure.
1.2 Understand and
use the concept of
standard form to
solve problems.
i. round off positive numbers to a
given number of significant figures
when the numbers are :a) greater then 1b) less then 1
ii. perform operations of addition,subtraction, multiplication and division,
involving a few numbers and state theanswer in specific 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 instandard form;
iv. solve problems involving numbers in
standard form.
CorporationWorking outmentally
Identifyingrelations
Textbook,worksheets
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7, 8, 9
CHAPTER 2 :
QUADRATIC
EXPRESSIONS
AND
EQUATIONS
2.1 Understand the
concept Of
quadratic
expressions;
2.2 Factorisequadratic
expression;
2.3 understand theconcept of
quadratic
equations.
2.4 understand and
use the concept ofroots of quadratic
equations to solve
problems.
Student will be able to:i. identify quadratic expressions;
ii. form quadratic expressions by
multiplying any two linear expressions;
iii. form quadratic expressions base onspecific situations.
i. factorise quadratic expressions of theform ax2 + bx + c , whereb=0 or c=0
ii. factorise quadratic expressions of the form
px2
q , p and q are 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 common factors.
i. identify quadratic equations with one unknown;
ii. write quadratic equations in general formi.e;
ax2
+ bx + c = 0iii. form quadratic equations base on specific
situations;
i. determine whether a given value is a root ofa specific quadratic equations;ii. determine the solutions for quadratic equations by
a) trial and error method;b) factorisations;
iii. solve problems involving quadratic equations.
CorporationWorking out
mentally
Comparing
and
contrasting
Translating,
Interpreting
Find allpossible
solutions
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10, 11,
12
CHAPTER 3 :
SETS
3.1 Understand theconcept Of
set
3.2 Understand the
concept Of
subset and the
compliment of a set
3.3 Perform operationof set;
the intersectionset
the union of set
Student will be able to:i. sort given objects into groups;ii. define sets by :
a) descriptions ;b) using set notation;
iii. identify whether the given object is an element of
a set and use the symbol or
iv. represents sets by using Venn diagrams;
v. list the elements and state the number of elementsof a set;
vi. determine whether a set is an empty set;.vii. determine whether two sets are equal
Student will be able to: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. ilustrate 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;
Student 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 using Venn
diagrams;
CorporationWorking out
mentally
Drawingdiagrams,
Translating,
InterpretingFind all
possible
solutions
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13 CHAPTER 3 :SETS
3.3 Perform operationof set;
the intersectionset
the union of set
Student will be able to: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 ofset ;
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
c) A B and A ;d) A B 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
on sets;
xii. solve problems involving combined operations
on sets;
Corporation
Working out
mentally
Translating,
Interpreting
Find all
possiblesolutions
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AIDS/ CCT
14CHAPTER 4 :
MATHEMATICAL
REASONING
4.1 Understand theconcept of
statement;
4.2 Understand theconcept of
quantifier
all or some ;
4.3 Perform
operations involving
the words not or
no,and and or
on statements ;
Student will be able to:i. determine whether the given sentence is a
statement ;
ii. determine whether the given statement is true or
false;
iii. Contruct true or false statement using givennumbers and mathematical symbols ;
i. contruct statement using the quantifier :a) all ;
b) some ;
ii. determine whether a statement that contains thequantifier all true or false;
iii. determine whether a statement can be
generalized to cover all cases by using the
quantifier all ;iv. contruct 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 twogiven statements using the words and ;
Corporation
Working out
mentally
Translating,
Interpreting
Find all
possiblesolutions
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AIDS/ CCT
15MATHEMATICALREASONING 4.3 Perform
operations involving
the words not or
no,and and or
on statements ;
4.4 Understand the
concept of
implication ;
Student will be able to: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 compoundstatement which is the combination of two
statements using the words and ;
vii. determine the truth value of a compoundstatement which is the combination of two
statements using the words or ;
i. identify the antecedent and consequent of an
implication if p, then q
ii. write two implications from a compound
statement that containing if and only if ;iii. contruct 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 animplication is true or false.
CorporationWorking out
mentally
Translating,
Interpreting
Find allpossible
solutions
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16
CHAPTER 4 :
MATHEMATICAL
REASONING
4.5 Understand the
concept of
argument ;
4.6 Understand and
use the concept of
deduction and
induction to solve
problems ;
Student will be able to:i. identify thepremise andconclusion of a given
simple argument ;
ii. make a conclusion based on two given premises
for;
a) Argument Form Ib) Argument Form II
c) Argument Form III
iii. Complete an argument given apremise andconclusion ;
i. determine whether the conclusion is madethrough :
a) reasoning by deduction ;
b) reasoning by induction ;
ii. make a cloncusion for a specific case based on agiven 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
Corporation
Working out
mentally
Translating,
Interpreting
Find allpossible
solutions
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AIDS/ CCT
17
18
CHAPTER 5 :
THE STRAIGHT
LINE
5.1 understand the
concept of gradient
of a straight line ;
5.2 understand the
concept of gradient
of a straight line inCartesian
coordinates;
5.3 Understand the
Concept of
Intercept ;
Student will be able to: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.
i. derive the formula for the gradient of a straight
line ;
ii. calculate the gradient of a straight line passingthrough 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-intersept and the y-intercept of a
straight line ;
ii. derive the formula for the gradient of a straightline in terms of the x-intersept and the
y-intercept;
iii. perform calculations involving gradient,x-intersept and the y-intercept
CorporationWorking out
mentally Translating,
Interpreting
Find allpossible
solutions
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LEARNING OUTCOMES VALUES TEACHING
AIDS/ CCT
19CHAPTER 5 :
THE STRAIGHT
LINE
5.4 understand and
use equation
of a straight line ;
5.5 Understand and
use the Concept of
Parallel lines
Student will be able to: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 thegradient and y-intercept ;
iv. determine the gradient and y-intercept of the
straight line which equation is of the form :a) y = mx + cb) 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 samegradient 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
Corporation
Working out
mentally
Translating,
Interpreting
Find allpossible
solutions
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AIDS/ CCT
20, 21CHAPTER 6 :STATISTICS 6.1 understand the
Concept of class
Interval ;
6.2 Understand and
use the Concept of
Mode and mean ofgrouped data ;
6.3represent and
interpret data in
histograms with class
intervals of the same
size to solve problems;
Student will be able to:i. complete the class interval for a set of data given
one of the class interval ;
ii. determine
a) the upper limit and the lower limit ;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 dataand the number of classes ;
v. determine the suitable class interval for a given
set of data ;vi. Contruct 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 ofgrouped data ;
v. discuss the effect of the size of class interval on
the accuracy of the mean for a specific sets ofgrouped data.
i. draw a histogram based on the frequency table ofgrouped data ;
ii. interpret information from a given histogram ;
iii. solve problems involving histogram.
Corporation
Working out
mentally Translating,
InterpretingFind all
possible
solutions
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22, 23 CHAPTER 6 :STATISTICS
6.4 represent and
interpret data in
frequency polygons
to solve problems;
6.5 Understand theconcept of
cumulative
frequency
6.6 Understand and
use the Concept ofmeasures of
dispersion to solve
problems;
Student will be able to:i. draw the frequency polygon based on :
a) a histogramb) a frequency table ;
ii. interpret information from a given frequency
polygons ;
iii. solve problems involving frequency polygons ;
i. construc the cumulative frequency table for :a) ungrouped data
b) grouped data ;
ii. draw the ogive for :a) unrouped 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.
Corporation
Working out
mentally
Translating,
Interpreting
Find all
possiblesolutions
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AIDS/ CCT
24,25,26
CHAPTER 7 :
PROBABILITY
7.1 Understand the
concept of
Sample space
7.2 Understand the
concept of events
7.3 Understand anduse the concept of
Probability of an
event to solve
problems.
Student will be able to:i. determine whether the 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 thesample space of an experiment ;iv. write the sample space by using set notations.
i. identify the elements of asample space which
satisfy given condisions ;
ii. list all the elements of asample space whichsatisfy certain condisions using set notations ;
iii. determine whether an event is possible for a
sample space.
i. find the ratio of the number of times an eventoccurs to the number of trials ;
ii. find the probability of an event from a big enoughnumber of trials ;
iii. calculate the expected number of times an event
will occur, given the probability of the event andnumber of trials ;
iv. solve problems involving probability ;
v. predict the occurrence of an outcome and make adecision based on known information.
CorporationWorking out
mentally
Translating,
Interpreting
Find all
possiblesolutions
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27,28 CHAPTER 8 :
CIRCLES III
8.1 Understand and
use the concept of
tangents to a
circle
8.2 Understand and
use the properties of
an angle between
tangent and chord to
solve problems
Student will be able to: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 contact point ;
iii. construc the tangent to a circle passing through apoint :
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 ;
vi. solve problems involving tangents to a circle
i. identify the angle in the alternate segment which
is sustended by the chord through the contact
point of the tangent ;
ii. verify the relationship between the angle formedthe tangent and the chord with angle in the
alternate segment which is sustended by thechord ;
iii. perform calculations involving the angle in
alternate segment ;iv. solve problems involving tangents to a circle and
angle in alternate segment ;
Corporation
Working out
mentally
Translating,
Interpreting
Find allpossible
solutions
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LEARNING OUTCOMES VALUES TEACHINGAIDS/ CCT
29 CHAPTER 8 :
CIRCLES III
8.3 Understand and
use the properties of
common tangent to
solve problems
Student 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 points ;c) do not intersect ;
ii. determine the properties related to the commontangent 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 commontangent.
Corporation
Working out
mentally
Translating,Interpreting
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possiblesolutions
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30,31 CHAPTER 9 :
TRIGONOMETRY
II
9.1 Understand and
use the concept of
values of sin ,cos , and tan (0
0 3600)to solve problems.
Student will be able to:i. identify the quadrant and angle in the unit circleii. determine :
a) the value of y-coordinate ;b) the value of x-coordinate ;c) the ratio of y-coordinate to x-coordinate;of several points on the circumference of the unit
circle.
iii. verify that, for an angle in quadrant I of the unitcircle :
a) sin = y-coordinate
b) cos = x-coordinate
c) tan = y-coordinatex-coordinate
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 ;
b) cos ;
c) tan ;
for 900
3600
vi. determine whether the values of :
a) sin ;
b) cos ;
c) tan ;of an angle in specific quadrant is positive or
negative.
Corporation
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Translating,
Interpreting
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solutions
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32,33 CHAPTER 9 :
TRIGONOMETRY
II
9.1 Understand and
use the concept of
values of sin ,cos , and tan (0
0 3600)to solve problems.
9.2 Draw and use the
Graphs of sine,
cosine and tangent.
Student will be able to: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 inquadrant I ;
x. find the values of sine, cosine and tangent of the
angles between900 and3600
xi. find the angles between 00 and3600 ,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 00 and3600
ii. compare the graphs of sine, cosine and tangentfor angles between 00 and3600
iii. solve problems involving graphs of sine, cosine
and tangent .
Corporation
Working outmentally
Translating,
InterpretingFind all
possible
solutions
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34, 35 CHAPTER 10 :
ANGLES OF
ELEVATION
AND
DEPRESSION
10.1 Understand and
use the concept of
angle of elevation
and angle of
depression to solve
problems.
Student 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 of elevation ;b) the angle of depression ;using diagrams ;
iii. solve problems involving the angle of elevation
and the angle of depression.
Corporation
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InterpretingFind all
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36
37, 38
CHAPTER 10 :
ANGLES OF
ELEVATION
AND
DEPRESSION
CHAPTER 11 :
LINES AND
PLANES IN
3-DIMENSIONS
10.1 Understand and
use the concept of
angle of elevation
and angle of
depression to solve
problems.
11.1 Understand anduse the concept of
angle between lines
and planes to solve
problems.
Student 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 :c) the angle of elevation ;d) the angle of depression ;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 ;iv. identify :
a) lines that lies on a plane ;b) lines that intersect with a plane ;
v. identify normals to a given plane ;
vi. determine the orthogonal projection of a line on
a plane ;vii. draw and neme the orthogonal projection of a
line on a plane ;
viii. determine the angle between a line and a plane ;
ix. solve problems involving the angle between aline and a plane ;
Corporation
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39, 40 CHAPTER 11 :
LINES AND
PLANES IN
3-DIMENSIONS
11.2 Understand and
use the concept of
angle between two
planes to solve
problems.
Student will be able to:i. identify the line of intersection between two
planes ;
ii. draw a line in each plane which is perpendicular
to the lilne of intersection of the two planes at apoint 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.
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