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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
1. STANDARD FORM 1.1 Understand and use theconcept if significant
figure.
i. Round off positive numbers to agiven number of significant figures
when the numbers are:a) Greater than 1
b) Less than 1
Discuss the significance if zero
in a number.
Rounded numbers are onlyapproximates.
Limit to positive numbers only.
Teaching aids
Mahjong paper
Pictures
Ccts
Working out mentallyDecision making
Identifying relationship
ii. Perform operations of addition,substraction , multiplication and
division, involving a few numbersand state the answer in specific
significant figures.
Discuss the use of significant
figures in everyday life and other
areas.Generally, rounding is done on
the final answer.
Moral values
Cooperation rational
Being systematicConscientious
iii. Solve problems involvingsignificant figures.
Vocabulary
Significance
Significant figureRelevant
Round off
Accuracy
1.2 Understand and use theconcept of standard
form to solve problems
i. State positive numbers in standardform when the numbers are:
a) Greater than or equal to 10b) Less than 1
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.Another term for standard formis scientific notation.
Teaching aids
Flash card
Scientific calculator
Ccts
Working out mentally
Identifying relationship
ii. Convert numbers in standard formto single numbers.
Moral values
Cooperation, rational,
being systematic
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AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
iii. Perform operations of addition,subtraction, multiplication and
division, involving any twonumbers and state the answers in
standard form.
Include two numbers in standard
form.
Vocabulary
Standard form
Single numberScientific notation
iv. solve problems involving numbersin standard form.
2. QUADRATICEXPRESSIONS
AND EQUATIONS
2.1 understand the conceptof quadratic expression;
i. identify quadratic expressions; Discuss the characteristics ofquadratic expressions of the
form 02 ! cbxax , where a,b and c are constants, a{ 0 andxis an unknown.
Include the case when b = 0
and/orc = 0.
Vocabulary
Quadratic expression
ConstantConstant factor
Unknown
Highest power
Expand
Coefficient
Term
ii. form quadratic expressions bymultiplying any two linearexpressions;
Emphasise that for the terms x2
and x, the coefficients areunderstood to be 1.
iii. form quadratic expressions basedon specific situations;
Include everyday life situations.
2.2 factorise quadraticexpression;
i. factorise quadratic expressions ofthe form cbxax
2, where b =
0 orc = 0;
Discuss the various methods to
obtain the desired product.
Vocabulary
Factorise
Common factor
Perfect square
Cross methodInspection
Common factor
Complete factorisation
ii. factorise quadratic expressions ofthe form px2q, p and q are
perfect squares;
1 is also a perfect square.
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AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
iii. factorise quadratic expressions ofthe form cbxax
2
, where a, band c not equal to zero;
factorise quadratic expressions
of the form cbxax
2
,where a, b and c not equal tozero;
Factorisation methods that can
be used are:
y cross method;y inspection.
iv. factorise quadratic expressionscontaining coefficients with
common factors
2.3 understand the conceptof quadratic equation;
i. identify quadratic equation withone unknown;
Discuss the characteristics of
quadratic equations.
Vocabulary
Quadratic equationGeneral form
Substitute
Root
Trial and error methodSolution
ii. write quadratic equations ingeneral form i.e. 0
2! cbxax
;
Moral values
Diligence
Rationality
Justice
iii. form quadratic equations based onspecific situations;
Include everyday life situations. CctsIdentifying relationship
Classifying
CatogerisingDrawing diagramsIdentify patterns
Problem solving
2.4 understand and use theconcept of roots of
quadratic equations to
solve problems.
i. determine whether a given value isa root of a specific quadratic
equation;
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
ii. determine the solutions forquadratic equations by:
a) trial and error method;b) factorisation;
Discuss the number of roots of a
quadratic equation.
There are quadratic equationsthat cannot be solved by
factorisation.
Teaching aids
Cd courseware
iii. solve problems involving quadraticequations.
Use everyday life situations.
Check the rationality of the
solution.
3. SETS 3.1 understand the conceptof set;
i. sort given objects into groups; Use everyday life examples tointroduce the concept of set.The word set refers to any
collection or group of objects.
Teaching aids
Flash cards
ii. define sets by:a) descriptions;
b) using set notation;The notation used for sets is
braces, { }.
The same elements in a set need
not be repeated.Sets are usually denoted by
capital letters.The definition of sets has to be
clear and precise so that the
elements can be identified.
Vocabulary
Set
Element
DescriptionLabel
Set NotationDenote
Venn diagram
Empty set
Equal set
iii. identify whether a given object isan element of a set and use the
symbol or;
The symbol (epsilon) is readis an element of or is a
member of.
The symbol is read is not anelement of or is not a member
of.
Ccts
Classifying
Translating
Identifying
relationships
iv. represent sets by using Venndiagrams;
Discuss the difference between
the representation of elements
and the number of elements in
Venn diagrams.
Moral values
Paying attention
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
v. list the elements and state thenumber of elements of a set;
Discuss why { 0 } and { } arenot empty sets.
The notation n(A) denotes thenumber of elements in set A.
vi. determine whether a set is anempty set;
The symbol (phi) or { }denotes an empty set.
vii. determine whether two sets areequal;
An empty set is also called a nullset.
3.2 understand and use theconcept of subset,
universal set and thecomplement of a set;
i. determine whether a given set is asubset of a specific set and use the
symbol or ;
Begin with everyday life
situations.
An empty set is a subset of anyset.
Every set is a subset of itself.
Vocabulary
Subset
Universal setComplement of a set
ii. represent subset using Venndiagram;
Teaching aids
Laptop
Diagramsiii. list the subsets for a specific set;iv. illustrate the relationship between
set and universal set using Venn
diagram;
Discuss the relationship between
sets and universal sets.
The symbol \ denotes auniversal set.
Ccts
Translating
Categorizing
v. determine the complement of agiven set;
The symbol Ad denotes thecomplement of set A.
Moral values
Being hard-workingBeing honest
vi. determine the relationship betweenset, subset, universal set and the
complement of a set;
Include everyday life situations.
3.3perform operations onsets:
y the intersection of sets;y the union of sets.
i. determine the intersection of:a) two sets;
b) three sets;and use the symbol ;
Include everyday life situations. Moral values
Paying attentionCooperation
Concentration
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
ii. represent the intersection of setsusing Venn diagram;
Discuss cases when:
y AB =y AB
Teaching aids
Laptop
DiagramsText book
iii. state the relationship betweena) AB and A ;
b) AB and B ;VocabularyIntersection
Union
Operation
iv. determine the complement of theintersection of sets;
v. solve problems involving theintersection of sets;
Include everyday life situations.
vi. determine the union of:c) two sets;d) three sets;and use the symbol ;
Teaching aidsLaptop
Diagrams
Text book
vii. represent the union of sets usingVenn diagram;
viii.state the relationship betweena) AB and A ;
b) AB and B ;ix. determine the complement of the
union of sets;
x. solve problems involving the unionof sets;
Include everyday life situations.
xi. determine the outcome ofcombined operations on sets;
xii. solve problems involvingcombined operations on sets.
Include everyday life situations.
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
4. MATHEMATICALREASONING
4.1 understand the conceptof statement
i. determine whether a givensentence is a statement;
Introduce this topic using
everyday life situations.
Statements consisting of:
Ccts
Making general
statement
ii. determine whether a givenstatement is true or false;
Focus on mathematical
sentences.
y words only, e.g. Five isgreater than two.;
y numbers and words, e.g. 5 isgreater than 2.;
y numbers and symbols, e.g. 5 >2.
Moral values
Cooperation
Teaching aids
Multimedia
iii. construct true or false statementusing given numbers andmathematical symbols;
Discuss sentences consisting of:
y words only;y numbers and words;y numbers and mathematical
symbols;The following are not
statements:
y Is the place value of digit 9in 1928 hundreds?;
y 4n 5m + 2s;y Add the two numbers.;y x + 2 = 8.
Vocabulary
StatementTrue
False
Mathematical sentence
Mathematical statement
Mathematical symbol
4.2 understand the conceptof quantifiers all and
some;
i. construct statements using thequantifier:
a) all;b) some;
Start with everyday life
situations.
Quantifiers such as every and
any can be introduced basedon context.
Ccts
Categorizing
Moral valuesSocial interaction
ii. determine whether a statement thatcontains the quantifier all is true
or false;
Examples:
y All squares are four sidedfigures.
y Every square is a four sidedfigure.
y Any square is a four sidedfigure.
Vocabulary
Quantifier
AllEvery
Any
Some
Several
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
iii. determine whether a statement canbe generalised to cover all cases by
using the quantifier all;
Other quantifiers such as
several, one of and part of
can be used based on context.
One of
Part of
NegateContrary
Object
iv. construct a true statement using thequantifier all or some, given
an object and a property.
Example:
Object: Trapezium.
Property: Two sides are parallel
to each other.
Statement: All trapeziums have
two parallel sides.Object: Even numbers.
Property: Divisible by 4.
Statement: Some even numbers
are divisible by 4.
Teaching aids
Multimedia
4.4perform operationsinvolving the words
not or no, andand or on statements;
i. change the truth value of a givenstatement by placing the word
not into the original statement;
Begin with everyday lifesituations.
The negation no can be usedwhere appropriate.
The symbol ~ (tilde) denotes
negation.
~p denotes negation ofp
which means not p or no p.
The truth table forp and ~p are
as follows:
p ~p
True
False
False
True
VocabularyNegation
Not pNo p
Truth table
Truth value
And
Compound statement
Or
Teaching Aids
Multimedia
ii. identify two statements from acompound statement that contains
the word and;
The truth values for p and qare as follows:
p q p and q
True True True
True False False
False True False
False False False
CctsReasoning
Moral values
Confidence
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
iii. form a compound statement bycombining two given statements
using the word and;
iv. identify two statement from acompound statement that containsthe word or ;
The truth values for p orq are
as follows:
v. form a compound statement bycombining two given statements
using the word or;
p q p orq
True True True
True False True
False True TrueFalse False False
vi. determine the truth value of acompound statement which is the
combination of two statements
with the word and;
vii. determine the truth value of acompound statement which is the
combination of two statements
with the word or.
4.4 understand the conceptof implication;
i. identify the antecedent andconsequent of an implication ifp,
then q;
Start with everyday life
situations.
Implication ifp, then q can be
written aspq, and p if andonly ifq can be written as pq, which means pq and qp.
Ccts
Identifying information
Moral values
Cooperation
ii. write two implications from acompound statement containing if
and only if;
Teaching aids
Multimedia
iii. construct mathematical statementsin the form of implication:
a) Ifp, then q;b) p if and only ifq;
Vocabulary
Implication
Antecedent
Consequent
Converse
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AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
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STRATEGIES
iv. determine the converse of a givenimplication;
The converse of an implication
is not necessarily true.
v. determine whether the converse ofan implication is true or false.
Example 1:
Ifx < 3, then
x < 5 (true).Conversely:
Ifx < 5, then
x < 3 (false).
Example 2:
IfPQR is a triangle, then the
sum of the interior angles ofPQR is 180r.(true)
Conversely:
If the sum of the interior angles
ofPQR is 180r, thenPQR is atriangle.
(true)
4.5understand the conceptof argument; i.
identify the premise andconclusion of a given simple
argument;
Start with everyday lifesituations.Limit to arguments with true
premises.
CctsMaking justificationMaking conclusion
ii. make a conclusion based on twogiven premises for:a) Argument Form I;
b) Argument Form II;c) Argument Form III;
Names for argument forms, i.e.
syllogism (Form I), modus
ponens (Form II) and modus
tollens (Form III), need not be
introduced.
Moral values
Cooperation
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AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
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STRATEGIES
iii. complete an argument given apremise and the conclusion.
Specify that these three forms of
arguments are deductions based
on two premises only.Argument Form I
Premise 1: All A areB.
Premise 2: C isA.Conclusion: C is B.
Argument Form II:
Premise 1: Ifp, then q.
Premise 2: p is true.
Conclusion: q is true.
Argument Form III:Premise 1: Ifp, then q.
Premise 2: Not q is true.
Conclusion: Not p is true.
Vocabulary
Argument
PremiseConclusion
Teaching AidsMultimedia
understand and use the
concept of deduction and
induction to solve problems.
i. determine whether a conclusion ismade through:
a) reasoning by deduction;b) reasoning by induction;
Ccts
Justifying
Making conclusion
Moral valuesCooperation
ii. make a conclusion for a specificcase based on a given general
statement, by deduction;
iii. make a generalization based on thepattern of a numerical sequence, by
induction;
Limit to cases where formulae
can be induced.
Teaching aids
Multimedia
iv. use deduction and induction inproblem solving.
Specify that:y making conclusion by
deduction is definite;
y making conclusion byinduction is not necessarily
definite.
VocabularyReasoning
DeductionInduction
Pattern
Special conclusion
General statement
General conclusion
Specific case
Numerical sequence
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AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
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STRATEGIES
5. THE STRAIGHTLINE
5.1 understand the conceptof gradient of a straight
line;
i. determine the vertical andhorizontal distances between two
given points on a straight line.
Use technology such as the
Geometers Sketchpad, graphing
calculators, graph boards,magnetic boards, topo maps as
teaching aids where appropriate.
ii. determine the ratio of verticaldistance to horizontal distance.
Begin with concrete
examples/daily situations to
introduce the concept of
gradient.
Discuss:
y the relationship betweengradient and tan
U.
y the steepness of the straightline with different values ofgradient.
Carry out activities to find the
ratio of vertical distance tohorizontal distance for several
pairs of points on a straight line
to conclude that the ratio is
constant.
Vertical
distance
Horizontal distance
U
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LEARNING
AREA/WEEKS
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LEARNING OUTCOMEStudents will be able to:
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STRATEGIES
5.2 understand the conceptof gradient of a straight
line in Cartesiancoordinates;
i. derive the formula for the gradientof a straight line;
Discuss the value of gradient if
yPis chosen as (x1,y1) and Q is(x2,y2);
yPis chosen as (x2,y2) and Q is(x1,y1).
The gradient of a straight line
passing through P(x1,y1) and
Q(x2,y2) is:
12
12
xx
yym
!
ii. calculate the gradient of a straightline passing through two points;
determine the relationship
between the value of the gradient
and the:
a) steepness,b) direction of
inclination,
of a straight line;
5.3 understand the conceptof intercept;
i. determine thex-intercept and they-intercept of a straight line;
Emphasise that thex-intercept
and they-intercept are not
written in the form of
coordinates.
ii. derive the formula for the gradientof a straight line in terms of thex-
intercept and they-intercept;
iii. perform calculations involvinggradient,x-intercept andy-intercept;
5.4 understand and useequation of a straightline;
i. draw the graph given an equationof the formy = mx + c;
Discuss the change in the form
of the straight line if the valuesofm and c are changed.
Emphasise that the graph
obtained is a straight line.
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
ii. determine whether a given pointlies on a specific straight line;
Carry out activities using the
graphing calculator, Geometers
Sketchpad or other teaching aids.If a point lies on a straight line,
then the coordinates of the point
satisfy the equation of thestraight line.
iii. write the equation of the straightline given the gradient andy-
intercept;
Verify that m is the gradient and
c is they-intercept of a straight
line with equationy=mx + c .
iv. determine the gradient andy-intercept of the straight line whichequation is of the form:
a. y = mx + c;b. ax + by = c;
The equation
ax + by = c can be written in theform
y = mx + c.
v. find the equation of the straightline which:
a) is parallel to thex-axis;b) is parallel to they-axis;c) passes through a given point
and has a specific gradient;
d) passes through two givenpoints;
vi. find the point of intersection of twostraight lines by:a) drawing the two straight lines;
b) solving simultaneousequations.
Discuss and conclude that the
point of intersection is the onlypoint that satisfies both
equations.Use the graphing calculator and
Geometers Sketchpad or other
teaching aids to find the point of
intersection.
5.5 understand and use theconcept of parallel lines
i. verify that two parallel lines havethe same gradient and vice versa;
Explore properties of parallel
lines using the graphing
calculator and Geometers
Sketchpad or other teaching aids.
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
ii. determine from the given equationswhether two straight lines are
parallel;
iii. find the equation of the straightline which passes through a given
point and is parallel to another
straight line;
iv. solve problems involvingequations of straight lines.
6. STATISTICS 6.1 understand the conceptof class interval;
i. complete the class interval for a setof data given one of the class
intervals;
Use data obtained from activities
and other sources such as
research studies to introduce the
concept of class interval.
ii. determine:a) the upper limit and lower
limit;
b) the upper boundary and lowerboundary of a class in agrouped data;
iii. calculate the size of a classinterval;
Size of class interval
=[upper boundarylower
boundary]
iv. determine the class interval, givena set of data and the number of
classes;
v. determine a suitable class intervalfor a given set of data;
vi. construct a frequency table for agiven set of data.
Discuss criteria for suitable class
intervals.
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
6.2 understand and use theconcept of mode and
mean of grouped data;
i. determine the modal class from thefrequency table of grouped data;
ii. calculate the midpoint of a class; Midpoint of class=
21 (lower limit + upper limit)
iii. verify the formula for the mean ofgrouped data;
iv. calculate the mean from thefrequency table of grouped data;
v. discuss the effect of the size ofclass interval on the accuracy of
the mean for a specific set of
grouped data..
6.3 represent and interpretdata in histograms with
class intervals of thesame size to solve
problems;
i. draw a histogram based on thefrequency table of a grouped data;
Discuss the difference between
histogram and bar chart.
ii. interpret information from a givenhistogram;
Use graphing calculator to
explore the effect of different
class interval on histogram.
iii. solve problems involvinghistograms.
Include everyday life situations.
6.4 represent and interpretdata in frequency
polygons to solveproblems.
i. draw the frequency polygon basedon:
a) a histogram;b) a frequency table;
When drawing a frequencypolygon add a class with 0
frequency before the first class andafter the last class.
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LEARNING
AREA/WEEKS
LEARNING
OBJECTIVES
LEARNING OUTCOMEStudents will be able to:
TEACHING AND
LEARNING ACTIVITIES
STRATEGIES
6.5 ii.
interpret information from a given frequency polygon;
solve problems involving frequency polygon.Include everyday life situations.
understand the concept of cumulative frequency;construct the cumulative frequency table for:
ungrouped data;grouped data;
draw the ogive for:ungrouped data;
grouped data;When drawing ogive:use the upper boundaries;
add a class with zero frequency before the first class.understand and use the concept of measures of dispersion to solve problems.determine the range of a set of data.For grouped data:
Range = [midpoint of the last class midpoint of the first class]Discuss the meaning of dispersion by comparing a few sets of data. Graphing calculator can be used for this purpose.
CctsInterpreting
DescribingIdentifying information
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determine:the median;
the first quartile;
the third quartile;the interquartile range;from the ogive.Moral values
CooperationDevelop social skills
Mental & physical cleanlinessRationality
Systematicinterpret information from an ogive;
solve problems involving data representations and measures of dispersion.Carry out a project/research and analyse as well as interpret the data. Present the findings of the project/research.Emphasise the importance of honesty and accuracy in managing statistical researchTeaching aids Courseware
Graphing calculatorStatistical data
PROBABILITY
understand the concept of sample space;determine whether an outcome is a possible outcome of an experiment;Use concrete examples
such as throwing a die and tossing a coin.list all the possible outcomes of an experiment:from activities;
by reasoning;determine the sample space of an experiment;
write the sample space by using set notationsunderstand the concept of events.identify the elements of a sample space which satisfy given conditions;An impossible event is an
empty set.
Discuss that an event is a subset of the sample space.Discuss also impossible events for a sample space.list all the elements of a sample space which satisfy certain conditions using set notations;
determine whether an event is possible for a sample space.Discuss that the sample space itself is an event.understand and use the concept of probability of an event to solve problems.find the
ratio of the number of times an event occurs to the number of trials;Probability is obtained from activities and appropriate data.Carry out activities to introduce the concept of probability. The graphing calculator can be used to simulate such activities.
find the probability of an event from a big enough number of trials;calculate the expected number of times an event will occur, given the probability of the event and number of trials;Discuss situation
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which results in:probability of event = 1.
probability of event = 0.
solve problems involving probabilityEmphasise that the value of probability is between 0 and 1.predict the occurrence of an outcome and make a decision based on known information.Predict possible events which might occur indaily situations.
CIRCLES III
understand and use the concept of tangents to a circle.identify tangents to a circle;Develop concepts and abilities through activitiesusing technology such as the Geometers Sketchpad and graphing calculator.
Teaching aids
CompassGeometry setGspmake inference that the tangent to a circle is a straight line perpendicular to the radius that passes through the contact point;
construct the tangent to a circle passing through a point:on the circumference of the circle;
outside the circle;Ccts
Making inference
Drawing diagramdetermine the properties related to two tangents to a circle from a given point outside the circle;Properties of angle insemicircles can be used. Examples of properties of two tangents to a circle:AC = BC
(ACO = (BCO(AOC = (BOC
(AOC and (BOC are congruent.VocabularyTangent to a circle
Circle
PerpendicularRadiusCircumference
Semi circleCongruent
solve problems involving tangents to a circle.Relate to Pythagoras theorem.
O
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understand and use the properties of angle between tangent and chord to solve problems.identify the angle in the alternate segmentwhich is subtended by the chord through the contact point of the tangent;
Explore the property of angle in alternate segment using Geometers Sketchpad or other teaching aids.
VocabularyChordsAlternate segment
Major sectorSubtended
Moral values
Diligence
CooperationCourageverify 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;( ABE = ( BDE
( CBD = ( BEDCctsIdentifying information
Justify relationships
Problem solvingperform calculations involving the angle in alternate segmentsolve problems involving tangent to a circle and angle in alternate segment.understand and use the properties of common tangents to solve problems.determine the number of common tangents which can be
drawn to two circles which:intersect at two points;
intersect only at one point;do not intersect;Emphasise that the lengths of common tangents are equal.
Discuss the maximum number of common tangents for the three cases.VocabularyCommon tangent
E
D
A B
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verify that, for an angle in quadrant I of the unit circle :
sin ( = y-coordinate ;cos( = x-coordinate.
EMBED Equation.3 ;Begin with definitions of sine, cosine and tangent of an acute angle.
EMBED Equation.3EMBED Equation.3
EMBED Equation.3
determine the values ofsine;
cosine;tangent;
of an angle in quadrant I of the unit circle;determine the values of
sin (;cos (;tan (;
for 90( ( ( ( 360(;Explain that the conceptsin ( = y-coordinate ;
cos( = x-coordinate;EMBED Equation.3
can be extended to angles inquadrant II, III and IV.
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VocabularyQuadrant
Sine (Cosine (
Tan (determine whether the values of:
sine;cosine;
tangent,of an angle in a specific quadrant is positive or negative;Consider special angles such as 0(, 30(, 45(, 60(, 90(, 180(, 270(, 360(.
determine the values of sine, cosine and tangent for special angles;Use the above triangles to find the values of sine, cosine and
tangent for 30(, 45(, 60(.determine the values of the angles in quadrant I which correspond to the values of the angles in otherquadrants;Teaching can be expanded through activities such as reflection.
state the relationships between the values of:sine;
cosine; andtangent;
of angles in quadrant II, III and IV with their respective values of the corresponding angle in quadrant I;
Use the Geometers Sketchpad to explore the change in the values of sine, cosine and tangent relative to the change in angles.
find the values of sine, cosine and tangent of the angles between 90( and 360(;
Teaching aids
Gsp
12
45o
1
60o
30o
1
2
3
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Graph paperGraphmatica
Geometry set
find the angles between 0( and 360(, given the values of sine, cosine or tangent;
solve problems involving sine, cosine and tangent.
Relate to daily situations.
i. 9.2 draw and usethe graphs of sine,cosine and
tangent.draw the
graphs of sine,cosine and tangentfor angles between
0( and 360(;Use
the graphingcalculator andGeometers
Sketchpad toexplore the feature
of the graphs of
y = sin (, y = cos(, y = tan
(.CctsProblem
solve problems involving
graphs of sine, cosine and
tangent.
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solvingCompare
andcontrastDrawing
graphscompare
the graphs of sine,cosine and tangentfor angles between
0( and
360(;Discuss thefeature of the
graphs of y =sin(, y = cos(, y =
tan(.MoralvaluesCooperati
onHonestyDiligenceIntegritysolve problems
involving graphs
of sine, cosine andtangent.
10. ANGLES OFELEVATIONSAND
DEPRESSION
10.1 understand and use the
concept of angle ofelevation and angle of
depression to solve
problems.
i. identify:a) the horizontal line;b) the angle of elevation;c) the angle of depression,
for a particular situation;
Use daily situations to introduce
the concept.
Ccts
Working out mentallyCompare and contrast
Identifying
relationship
Decision making
Problem solving
ii. Represent a particular situationinvolving:
a)
the angle of elevation;b) the angle of depression, usingdiagrams;
Include two observations on the
same horizontal plane.
Vocabulary
Angle of elevation
Angle of depressionHorizontal line
Moral values
Rationality
Cooperation
iii. Solve problems involving theangle of elevation and the angle of
depression.
Involve activities outside the
classroom.
Teaching aids:
Models
Cd courseware
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11.LINES ANDPLANES IN 3-
DIMENSIONS
11.1 understand and use the
concept of angle
between lines and
planes to solveproblems
i. identify planes; Carry out activities using dailysituations and 3-dimensional
models.
Ccts
Describing
Interpreting
Drawing diagramsProblem solving
ii. identify horizontal planes, verticalplanes and inclined planes;
Differentiate between 2-
dimensional and 3-dimensional
shapes. Involve planes found innatural surroundings.
Moral values
Respect
Cooperation
iii. sketch a three dimensional shapeand identify the specific planes;
Approaches
Constructivism
Exploratory
Cooperative learning
iv. identify:A) lines that lies on a
plane;
B) lines that intersectwith a plane;
Vocabulary
Horizontal plane
Vertical plane
3-dimensional
Normal to a planeOrthogonal projectionSpace diagonal
Angle between twoplanes
v. identify normals to a given plane;vi. determine the orthogonal
projection of a line on a plane;
Begin with 3-dimensional
models.
vii. draw and name the orthogonalprojection of a line on a plane;
Include lines in 3-dimensional
shapes.
viii.determine the angle between a lineand a plane;
ix. solve problems involving the anglebetween a line and a plane.
Use 3-dimensional models to
give clearer pictures.
11.2 understand and use the
concept of angle
i. identify the line of intersectionbetween two planes;
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between two planes to
solve problems.
ii. draw a line on each plane which isperpendicular to the line ofintersection of the two planes at a
point on the line of intersection;
iii. determine the angle between twoplanes on a model and a given
diagram;
Use 3-dimensional models to
give clearer pictures.
iv. solve problems involving lines andplanes in 3-dimensional shapes.