Post on 04-Jun-2018
8/13/2019 Math Yearly Plan f4 2012
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MATHEMATICS YEARLY PLAN F4 2014
Week No. Learning Objective Learning Outcome
Students should be able to:
Suggested teaching and learning activity
2
6/1-10/1
Standard Form [1 week]
1.1 Understand and use the
concept of significant figure
(i) round off positive numbers to a given number ofsignificant 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 numbersand state the answer in specific significant figures;
(iii) solve problems involving significant figures;
Discuss the significance of zero in anumber.
Discuss the use of significant figures ineveryday life and other areas.
1.2 Understand and use the
concept of standard form to
solve problems.
(i) state positive numbers in standard form when thenumbers 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 numbersand state the answers in standard form;
(iv) solve problems involving numbers in standard 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.
3
13/1-17/1
Sets [2 weeks]
2.1 Understand the concept of
set(i) sort given objects into groups;(ii) define sets by:
a) descriptions;b) using set notation;
(iii) identify whether a given object is an element of a setand use the symbol or ;
(iv) represent 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;
Use everyday life examples to introduce
the concept of set.
Discuss the difference between the
representation of elements and the
number of elements in Venn diagrams.
Discuss why { 0 } and { } are not emptysets.
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MATHEMATICS YEARLY PLAN F4 2014
3
13/1-17/1
2.2 Understand and use the
concept of subset, universal
set and the complement of a
set;
(i) determine whether a given set is a subset of a specificset 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 of a set;
Begin with everyday life situations.
Discuss the relationship between sets
and universal sets.
4
20/1-24/1
2.3 perform operations on sets:
the intersection of sets; the union of sets.
(i) determine the intersection of:a) two sets;
b) three sets; and use the symbol;(ii) represent the intersection of sets using Venn diagram;(iii) state the relationship between
a) ABand A;b) ABand 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) ABand A;
b) ABand 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.
Discuss cases when:
AB= AB
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MATHEMATICS YEARLY PLAN F4 2014
5
27/1-29/1
Statistics [4 weeks]
3.1 Understand the concept of
class interval
(i) complete the class interval for a set of data given one ofthe class intervals;
(ii) determine:a) the upper limit and lower limit;
b) the upper boundary and lower boundaryof 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 ofdata;
(vi) construct a frequency table for a given set of data.
Use data obtained from activities and
other sources such as research studies
to introduce the concept of class
interval.
Discuss criteria for suitable class
intervals.
3.2 Understand and use theconcept of mode and mean
of grouped data
(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 theaccuracy of the mean for a specific set of grouped data..
7
10/2-14/2
3.3 Represent and interpret data
in histograms with class
intervals of the same size to
solve problems
(i) draw a histogram based on the frequency table of agrouped data;
(ii) 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.
3.4 Represent and interpret data
in frequency polygons to
solve problems
(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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3.5 Understand the concept of
cumulative frequency
(i) construct the cumulative frequency table for:a) ungrouped data;
b) grouped data;(ii) draw the ogive for:
a) ungrouped data;b) grouped data;
3.6 Understand and use the
concept of measures of
dispersion to solve problems
(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 an ogive;(iv) solve problems involving data representations and
measures of dispersion.
Discuss the meaning of dispersion by
comparing a few sets of data. Graphing
calculator can be used for this purpose.
Carry out a project/research and analyse
as well as interpret the data. Present the
findings of the project/research.
Emphasise the importance of honestyand accuracy in managing statistical
research.
Week 9 &
1024/2-7/3
Mathematical
Reasoning[2weeks]
4.1 Understand the concept of
statement
(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;
4.2 Understand the concept of
quantifiers all and some
(i) construct statements using the quantifier:a) all b )some
(ii) determine whether a statement that contains thequantifier all is true or false;
(iii) determine whether a statement can be generalised tocover all cases by using the quantifier all;
(iv) construct a true statement using the quantifier all orsome, given an object and a property.
Start with everyday life situations.
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Week 9 &
10
24/2-7/3
4.3 Perform operations
involving the words not or
no, and and or on
statements
(i) change the truth value of a given statement by placingthe word not into the original statement;
(ii) identify two statements from a compound statementthat contains the word and;
(iii) form a compound statement by combining two givenstatements using the word and;
(iv) identify two statement from a compound statement thatcontains the word or ;
(v) form a compound statement by combining two givenstatements using the word or;
(vi) determine the truth value of a compound statementwhich is the combination of two statements with the
word and;
(vii) determine the truth value of a compound statementwhich is the combination of two statements with theword or.
Begin with everyday life situations.
4.4 Understand the concept of
implication
(i) identify the antecedent and consequent of animplication ifp, then q;
(ii) write two implications from a compound statementcontaining if and only if;
(iii) construct mathematical statements in the form ofimplication:
a) Ifp, then q; b)pif and only if q;(iv) determine the converse of a given implication;(v) determine whether the converse of an implication is
true or false.
Start with everyday life situations
4.5 Understand the concept of
argument
(i) identify the premise and conclusion of a given simpleargument;
(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 theconclusion.
Start with everyday life situations.
Encourage students to produce
arguments based on previous
knowledge.
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Week 9 &
10
24/2-7/3
4.6 Understand and use the
concept of deduction and
induction to solve problems
(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 anumerical sequence, by induction;
(iv) use deduction and induction in problem solving.
Use specific examples/activities to
introduce the concept.
Week 14
& 15
31/3-11/4
Quadratic Expression and
Equation [2 weeks]
5.1 Understand the concept of
quadratic expression
(i) identify quadratic expressions;(ii) form quadratic expressions by multiplying any two
linear expressions;
(iii) form quadratic expressions based on specific situations;
Discuss the characteristics of quadratic
expressions of the form
02 cbxax , where a, band care
constants, a0 andxis an unknown.
5.2 Factorise quadratic
expression
(i) factorise quadratic expressions of the formcbxax 2 , where b= 0 or c= 0;
(ii) factorise quadratic expressions of the formpx2q,pand qare perfect squares;
(iii) factorise quadratic expressions of the formcbxax 2 , where a, band cnot equal to zero;
(iv) factorise quadratic expressions containing coefficientswith common factors;
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.
5.3 Understand the concept of
quadratic equation
(i) identify quadratic equations with one unknown;(ii) write quadratic equations in general form i.e.
02 cbxax ;
(iii) form quadratic equations based on specific situations;
Discuss the characteristics of quadratic
equations.
5.4 Understand and use the
concept of roots of quadratic
equations to solve problems
(i) determine whether a given value is a root of a specificquadratic equation;
(ii) determine the solutions for quadratic equations by:a) trial and error method;
b) factorisation;(iii) solve problems involving quadratic equations.
Discuss the number of roots of a
quadratic equation.
Use everyday life situations.
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MATHEMATICS YEARLY PLAN F4 2014
Week 16,17 & 18
14/4-2/5
Graph of Functions II [3 weeks]
6.1 Understand and use the
concept of graphs of
functions
(i) Draw the graph of a:a) linear function :y = ax+ b, where a and b are
constant;
b) quadratic function cbxaxy 2 , where a, b andc are constans, 0a
c) cubic function : dcxbxaxy 23 ,
where a, b, c and d are constants, 0a
d) reciprocal functionx
ay , where a is a constants,
0a (ii) Find from the graph
a) the value ofy, given a value ofx
b) the value(s) ofx, given a value ofy(iii) Identify:
a) the shape of graph given a type of functionb) the type of function given a graphc) the graph given a function and vice versa
(iv) Sketch the graph of a given linear, quadratic, cubic orreciprocal function.
Explore graphs of functions usinggraphing calculator or the GSP
Compare the characteristic of graphsof functions with different values ofconstants.
Play a game or quiz
6.2 Understand and use the
concept of the solution of an
equation by graphical method
(i) Find the point(s) of intersection of two graphs(ii) Obtain the solution of an equation by finding the
point(s) of intersection of two graphs(iii) Solve problems involving solution of an equation by
graphical method.
Explore using graphing calculator ofGST to relate thex-coordinate of a
point of intersection of twoappropriate graphs to the solution of a
given equation.
6.3 Understand and use the
concept of the region
representing inequalities in
two variables
(i) Determine whether a given point satisfies
a) baxy or baxy or baxy (ii) Determine the position of a given point relative to the
equation baxy (iii) Identify the region satisfying baxy or baxy (iv) Shade the regions representing the inequalities
(v) Determine the region which satisfy two or more
simultaneous linear inequalities.
Include situations involving ax ,ax , ax , ax or ax .
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MATHEMATICS YEARLY PLAN F4 2014
Week 25
& 26
16/6-27/6
Plan and Elevations [2 weeks]
7.1 Understand and use the
concept of orthogonal
projection
(i) Identify orthogonal projections.(ii) Draw orthogonal projections, given an object and a
plane.
(iii)Determine the difference between an object and itsorthogonal projections with respect to edges and angles
Use models, blocks or plan and elevationkit.
7.2 Understand and use the
concept of plan and
elevation.
(i) Draw the plan of a solid object.(ii) Draw
- the front elevation- side elevation
of a solid object
(iii)Draw the plan of a solid object.(iv)Draw
- the front elevation- side elevation of a solid object
Carry out activities in groups where
students combine two or more different
shapes of simple solid objects into
interesting models and draw plans and
elevation for the models.
Use models to show that it is important
to have a plan and at least two side
elevation to construct a solid object.
Week 27,
28 & 29
30/6-18/7
Matrices [3 weeks]
8.1 Understand and use the
concept of matrix
(i) Form a matrix from given information.(ii) Determine:a. the number of rows
b. the number of columnsc. the order of a matrix(iii) Identify a specific element in a matrix
Understanding the concept of matrices
through daily examples:
Introduce the order (mxn) of a matrix
Class activitystudents are requested to
identify the students seating position in
class
8.2 Understand and use theconcept of equal matrices
(i) Determine whether two matrices are equal.(ii) Solve problems involving equal matrices Teacher gives examples of two equalmatrices and discusses equal matrices in
terms of the corresponding elements.
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8.3 Perform addition and
subtraction on matrices
(i) Relate to real life situations such as keeping score ofmedal tally or points in sports.
(ii) Find the sum or the difference of two matrices.(iii) Perform addition and subtraction on a few matrices.(iv) Solve matrix equations involving addition and
subtraction.
Teacher shows the examples from the
textbook to determine how addition or
subtraction can be performed on 2 given
matrices.
Week 30,
31 & 32
21/7-8/8
8.4 Perform Multiplication of a
matrix by a number.
(i) Multiply a matrix by a number.(ii) Express a given matrix as a multiplication of another
matrix by a number.
(iii) Perform calculation on matrices involving addition,subtraction and scalar multiplication.
(v) Solve matrix equations involving addition, subtractionand scalar multiplication.
Teacher shows examples on scalar
multiplication of matrix:
examples given on the calculation of
matrices involving addition, subtraction,
and scalar multiplication.
Examples given on problem solving
questions.
To include finding values of unknown
elements8.5 Perform multiplication of
two matrices
(i) determine whether two matrices can be multiplied andstate the order of the product when the two matricescan be multiplied.
(ii) Find the product of two matrices.(iii) Solve matrix equations involving multiplication of
two matrices
Teacher gives real life situations.
8.6 Understand and use the
concept of identify matrix
(i) determine whether a given matrix is an identity matrixby multiplying it to another matrix.
(ii) Write identity matrix of any order.(iii) Perform calculation involving identity matrices
Teacher introduce identity matrix
Discuss the properties:
- AI=A- IA=A
8.7 Understand and use the
concept of inverse matrix
(i) Determine whether a 2 X 2 matrix is the inversematrix of another 2 X 2 matrix.
(ii) Find the inverse matrix of a 2 X 2 matrix using:---- the method of solving simultaneous linear equations
---- a formula
teacher introduces the concept of inverse
matrix and its denotion
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8.8 Solve simultaneous linear
equations by using matrices
(i) Write simultaneous linear equations in matrix form.(ii) Find the matrix p
q
ina b p h
c d q k
using
the inverse matrix.(iii) solve simultaneous linear equations by the matrix
method.
(iv) Solve problems involving matrices.
Teacher shows examples how to write
simultaneous linear equations in matrix
form
To solve simultaneous linear equationsby using inverse matrix
Week 33
& 34
11/8-22/8
Circles III [2 weeks]
9.1 Understand and use the
concept of tangents to a
circle.
(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) 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.
Develop concepts and abilities through
activities using technology such as the
Geometers Sketchpad and graphing
calculator.
9.2 Understand and use the
properties of angle between
tangent and chord to solve
problems
(i) identify the angle in the alternate segment which issubtended by the chord through the contact point of thetangent;
(ii) verify the relationship between the angle formed by thetangent and the chord with the angle in the alternate
segment which is subtended by the chord;(iii) perform calculations involving the angle in alternate
segment;
(iv) solve problems involving tangent to a circle and anglein alternate segment.
Explore the property of angle in
alternate segment using Geometers
Sketchpad or other teaching aids
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MATHEMATICS YEARLY PLAN F4 2014
9.3 Understand and use the
properties of common
tangents to solve problems
(i) determine the number of common tangents which canbe drawn to two circles which:a) intersect at two points;
b) intersect only at one point;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 point;c) do not intersect;
(iii) solve problems involving common tangents to twocircles;
(iv) solve problems involving tangents and commontangents.
Discuss the maximum number of
common tangents for the three cases.
Include daily situations.
Week 35
25/8-29/8
Trigonometry II [3 weeks]
10.1 Understand and use theconcept of the values of
sin , cos and tan (0
360) to solve problems
(i)
identify the quadrants and angles in the unit circle(ii) determine:a) the value ofy-coordinate;
b) the value ofx-coordinate;c) the ratio ofy-coordinate tox-coordinate;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 =y-coordinate ;
b) cos=x-coordinate;c) coordinate
coordinate
tan
xy
(iv) determine the values ofa) sine;
b) cosine;c) tangent; of an angle in quadrant I of the unit circle
(v) determine the values ofa) sin ;
Explain the meaning of unit circle.
Begin with definitions of sine, cosine
and tangent of an acute angle.
yy
OP
PQ
1sin
xx
OP
OQ
1cos
x
y
OQ
PQtan
0
y
x
P (x,y)
y1
x Q
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Week 36
1/9-5/9
b) cos ;c) tan ; for 90360;
(vi) determine whether the values of:a) sine;
b) cosine;c) tangent,
of an angle in a specific quadrant is positive ornegative;
(vii) determine the values of sine, cosine and tangent forspecial angles;
(viii) determine the values of the angles in quadrant I whichcorrespond to the values of the angles in otherquadrants
(ix) state the relationships between the values of:a) sine;
b) cosine; andc) tangent;of angles 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 90and 360
(xi) find the angles between 0and 360, given the values of
sine, cosine or tangent
(xii) solve problems involving sine, cosine and tangent
Explain that the concept
sin = y-coordinate ;
cos=x-coordinate;
coordinate
coordinatetan
x
y
can be extended to angles in
quadrant II, III and IV
Use the above triangles to find the
values of sine, cosine and tangent for
30, 45, 60.
Teaching can be expanded through
activities such as reflection.
221
330
o
45o 60
o
1 1
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Week 38
15/9-19/9
10.2 Draw and use the graphs of
sine, cosine and tangent.
(i) draw the graphs of sine, cosine and tangent for anglesbetween 0and 360;
(ii) compare the graphs of sine, cosine and tangent forangles between 0and 360;
(iii) solve problems involving graphs of sine, cosine andtangent.
Use the graphing calculator and
Geometers Sketchpad to explore the
feature of the graphs of
y= sin , y= cos , y= tan .
Discuss the feature of the graphs ofy= sin , y= cos , y= tan .
Discuss the examples of these graphs in
other area.
Week 39
22/9-26/9
Angles of Elevation and
Depression [1 week]
11.1 Understand and use the
concept of angle of
elevation and angle of
depression to solveproblems
(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.
Use daily situations to introduce the
concept
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Week 40
& 41
29/9-
10/10
Line and Planes in 3-
Dimensions [2 weeks]
12.1 Understand and use the
concept of angle between
lines and planes to solve
problems
(i) identify planes;(ii) identify horizontal planes, vertical planes and inclined
planes;
(iii) sketch a three dimensional shape and identify thespecific 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 name the orthogonal projection of a line on aplane;(viii)determine the angle between a line and a plane;(ix) solve problems involving the angle between a line and a
plane.
Carry out activities using daily situations
and 3-dimensional models.
Differentiate between 2-dimensionaland 3-dimensional shapes. Involve
planes found in natural surroundings.
Begin with 3-dimensional models.
Use 3-dimensional models to give
clearer pictures.
12.2 Understand and use the
concept of angle between
two planes to solve
problems.
(i) identify the line of 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 theline of intersection;
(iii) determine the angle between two planes on a model anda given diagram;
(iv) solve problems involving lines and planes in 3-dimensional shapes.
Use 3-dimensional models to give
clearer pictures.