Math Yearly Plan f4 2012

8/13/2019 Math Yearly Plan f4 2012

1/14

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.


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.


2/14


3

13/1-17/1


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


3/14


5

27/1-29/1

Statistics [4 weeks]


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.


4/14


8

17/2-21/2


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;


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]


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;


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.


5/14


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.


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


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.


6/14


Week 9 &

10

24/2-7/3


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]


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.


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.


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.


7/14


Week 16,17 & 18

14/4-2/5

Graph of Functions II [3 weeks]


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


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.


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 .


8/14


Week 25

& 26

16/6-27/6

Plan and Elevations [2 weeks]


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.


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]


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.


9/14


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.


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


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


10/14


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]


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.


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


11/14



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


12/14


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


13/14


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]


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


14/14


Week 40

& 41

29/9-

10/10

Line and Planes in 3-

Dimensions [2 weeks]


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.


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.

Math Yearly Plan f4 2012

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