yearly lesson plan f5 2007

7/27/2019 Yearly Lesson Plan f5 2007

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YEARLY LESSON PLAN

MATHEMATICS FORM 5

2011

1. LEARNIG AREA: NUMBER BASES WEEK LEARNING OBJECTIVES LEARNING OUTCOMES REMARKS

1-2 1.1. Understand and use theconcept of number in basetwo, eight and five.

Students will be able to:i) State zero, one, two, three,..,as a

number in base:a) two

b) eightc) five

ii) State the value of a digit of a number in base:

a) two

b) eightc) fiveiii) Write a number in base:

a) two b) eightc) fivein expanded notation.

iv) Convert a number in base:a) two

b) eightc) fiveto a number in base ten and vice

versa.v) Convert a number in a certain base to anumber in another base.

vi) Perform computations involving:a) addition

b) subtractionof two numbers in base two.

2. LEARNIG AREA: GRAPHS OF FUNCTIONS II

3-5 2.1. Understand and use theconcept of graphs of

functions.

Students will be able to:i) Draw the graph of a:

a) linear function: ,bax y+=

where a and b are constants. b) quadratic function:

cbxax y ++= 2 where a , b andc are constants, .0a

c) cubic function:,23 d cxbxax y +++= where a,

b,c and d are constants, .0a

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d) reciprocal function: x

a y = ,

where a , is a constants, .0a ii) Find from a graph:

a) the value of y, given a value of x. b) the value(s) of x, given a value

of y.iii) Identify:

a) the shape of graph given a typeof function.

b) the type of function given agraph.

c) the graph given a function andvice versa.

iv) Sketch the graph of a given linear,quadratic, cubic or reciprocal function.

6 2.2. Understand and use theconcept of the solution of an equation by graphicalmethod.

Students will be able to: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.

7-8 2.3. Understand and use theconcept of the regionrepresenting inequalitiesin two variables.

Students will be able to:i) Determine whether a given point

satisfies:bax y += or

bax y + or

bax y+ii) Determine the position of a given point

relative to the equation bax y +=

iii) Identify the region satisfying

bax y + or .bax y+iv) Shade the regions representing the

inequalities:a) bax y + or

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bax y+ b) bax y + or bax y +

v) Determine the region which satisfiestwo or more simultaneous linear inequalities.

3. LEARNIG AREA: TRANSFORMATIONS III

9-11 3.1. Understand and use theconcept of combination of two transformations.

Students will be able to:i) Determine the image of an object

under combination of two isometrictransformations.

ii) Determine the image of an objectunder combination of:

a) two enlargements b) an enlargement and isometric

transformations.iii) Draw the image of an object under

combination of two transformation.iv) State the coordinates of the image of a

point under combined transformation.v) Determine whether combined

transformation AB is equivalent tocombined transformation BA .

vi) Specify two successive transformationsin a combined transformation given

the object and the image.vii) Specify a transformation which is

equivalent to the combination of twoisometric transformations.

viii) Solve problems involvingtransformation.

4. LEARNIG AREA: MATRICES

12 4.1. Understand and use theconcept of matrix.

Students will be able to: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.

13 4.2. Understand and use the Students will be able to:

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concept of equal matrices. i) Determine whether two matrices areequal.

ii) Solve problems involving equalmatrices.

14 4.3. Perform addition andsubtraction on matrices.

Students will be able to:i) Determine whether addition or

subtraction can be performed on twogiven matrices.

ii) Find the sum or the difference of twomatrices.

iii) Perform addition and subtraction on afew matrices.

iv) Solve matrix equations involvingaddition and subtraction.

15 4.4. Perform multiplication of a matrix by a number.

Students will be able to:i) Multiply a matrix by a number.ii) Express a given matrix as a

multiplication of another matrix by anumber.

iii) Perform calculation on matricesinvolving addition, subtraction andscalar multiplication.

iv) Solve matrix equations involvingaddition, subtraction and scalar multiplication.

16-17 4.5. Perform multiplication of two matrices.

Students will be able to:i) Determine whether two matrices can

be multiplied and state the order of the product when the two matrices can bemultiplied.

ii) Find the product of two matrices.iii) Solve matrix equations involving

multiplication of two matrices.

18 4.6. Understand and use theconcept of identify matrix.

Students will be able to:i) Determine whether a given matrix is an

identify matrix by multiplying it toanother matrix.

ii) Write identify matrix of any order.iii) Perform calculation involving identity

matrices.

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19-20 4.7. Understand and use theconcept of inverse matrix

Students will be able to:i) Determine whether a 22 matrix is

the inverse matrix of another 22 matrix.

ii) Find the inverse matrix of a 22 matrix using:

a) the method of solvingsimultaneous linear equations.

b) a formula

21 4.8. Solve simultaneous linear equations by usingmatrices.

Students will be able to:i) Write simultaneous linear equations in

matrix form.

ii) Find the matrix

q

pin

=

k

h

q

p

d c

bausing the inverse

matrix.iii) Solve simultaneous linear equations by

the matrix method.iv) Solve problems involving matrices.

5. LEARNIG AREA: VARIATIONS

22 5.1. Understand and use theconcept of direct variation.

Students will be able to:i) State the changes in a quantity with

respect to the changes in another quantity, in everyday life situationsinvolving direct variation.

ii) Determine from given informationwhether a quantity varies directly asanother quantity.

iii) Express a direct variation in the formof equation involving two variables.

iv) Find the value of a variable in a directvariation when sufficient informationis given.

v) Solve problems involving directvariation for the following cases:

21

32 ;;, x y x y x y x y

22 5.2. Understand and use theconcept of inversevariation.

Students will be able to:i) State the changes in a quantity with

respect to changes in another quantity,

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in everyday life situations involvinginverse variation.

ii) Determine from given informationwhether a quantity varies inversely asanother quantity.

iii) Express an inverse variation in theform of equation involving twovariables.

iv) Find the value of a variable in aninverse variation when sufficientinformation is given.

v) Solve problems involving directvariation for the following cases:

x

y1

, 21

x y ; 3

1

x y ;

2

1

1

x

y

23 5.3. Understand and use theconcept of joint variation.

Students will be able to:i) Represent a joint variation by using the

symbol for the following cases:a) two direct variations

b) two inverse variationsc) a direct variation and an inverse

variation.ii) Express a joint variation in the form of

equation.iii) Find the value of a variable in a joint

variation when sufficient informationis given.

iv) Solve problems involving jointvariation.

6. LEARNIG AREA: GRADIENT AND AREA UNDER A GRAPH

24-25 6.1. Understand and use theconcept of quantityrepresented by thegradient of a graph.

Students will be able to:i) State the quantity represented by the

gradient of a graph.ii) Draw the distance-time graph, given:

a) a table of distance-time values. b) a relationship between distance

and time.iii) Find and interpret the gradient of a

distance-time graph.iv) Find the speed for a period of time

from a distance-time graph.v) Draw a graph to show the relationship

between two variables representingcertain measurements and state themeaning of its gradient.

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26-27 6.2. Understand the concept of quantity represented bythe area under a graph.

Students will be able to:i) State the quantity represented by the

area under a graph.ii) Find the area under a graph.iii) Determine the distance by finding the

area under the following types of speed-time graphs:

a) k v = (uniform speed) b) kt v =c) hkt v +=d) a combination of the above.

iv) Solve problems involving gradient andarea under a graph.

7. LEARNIG AREA: PROBABILITY II

28 7.1. Understand and use theconcept of probability of an event.

Students will be able to:i) Determine the sample space of an

experiment with equally likelyoutcomes.

ii) Determine the probability of an eventwith equiprobable sample space.

iii) Solve problems involving probabilityof an event.

29 7.2. Understand and use theconcept of probability of complement of an event.

Students will be able to:i) State the complement of an event in:

a) words b) set notation

ii) Find the probability of the complementof an event.

30 7.3. Understand and use theconcept of probability of combined event.

Students will be able to:i) List the outcomes for events:

a) A or B as elements of set B A b) A and B as elements of set

B A ii) Find the probability by listing the

outcomes of the combined event:a) A or B

b) A and Biii) Solve problems involving probability

of combined event.

8. LEARNIG AREA: BEARING

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31-32 8.1. Understand and use theconcept of bearing.

Students will be able to:i) Draw and label the eight main compass

directions:a) north, south, east, west

b) north-east, north-west, south-east, south-west.

ii) State the compass angle of anycompass direction.

iii) Draw a diagram of a point whichshows the direction of B relative toanother point A given the bearing of B from A .

iv) State the bearing of point A from pointB based on given information.

v) Solve problems involving bearing.

9. LEARNIG AREA: EARTH AS A SPHERE

33 9.1. Understand and use theconcept of longitude.

Students will be able to:i) Sketch a great circle through the north

and south poles.ii) State the longitude of a given point.iii) Sketch and label a meridian with the

longitude given.iv) Find the difference between two

longitudes.

34 9.2. Understand and use theconcept of latitude.

Students will be able to:i) Sketch a circle parallel to the equator.ii) State the latitude of a given point.iii) Sketch and label a parallel of latitude.iv) Find the difference between two

latitudes.

35 9.3. Understand the concept of location of a place.

Students will be able to:i) State the latitude and longitude of a

given place.ii) Mark the location of a place.iii) Sketch and label the latitude and

longitude of a given place.

36-37 9.4. Understand and use theconcept of distance on thesurface of the earth tosolve problems.

Students will be able to:i) Find the length of an arc of a great

circle in nautical mile, given thesubtended angle at the centre of theearth and vice versa

ii) Find the distance between two point

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measured along a meridian, given thelatitudes of both points.

iii) Find the latitude of a point given thelatitude of another point and thedistance between the two points alongthe same meridian.

iv) Find the distance between two pointsmeasured along the equator, given thelongitudes of both points.

v) Find the longitude of a point given thelongitude of another point and thedistance between the two points alongthe equator.

vi) State the relation between the radius of the earth and the radius of a parallel of latitude.

vii) State the relation between the length of an arc on the equator between twomeridians and the length of thecorresponding arc on a parallel of latitude.

viii) Find the distance between two pointsmeasured along a parallel of latitude.

ix) Find the longitude of a point given thelongitude of another point and thedistance between the two points alonga parallel of latitude.

x) Find the shortest distance between two points on the surface of the earth.

xi) Solve problems involving:

a) distance between two points. b) traveling on the surface of the

earth.

10. LEARNIG AREA: PLANS AND ELEVATIONS

38 10.1. Understand and use theconcept of orthogonal

projection.

Students will be able to:i) Identify orthogonal projection.ii) Draw orthogonal projection, given an

object and a plane.iii) Determine the difference between an

object and its orthogonal projectionwith respect to edges and angles.

39 10.2. Understand and use theconcept of plan andelevation.

Students will be able to:i) Draw the plan of a solid object.ii) Draw

a) the front elevation b) side elevation

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of a solid object.iii) Draw

a) the plan b) the front elevationc) the side elevationof a solid object to scale.

iv) Solve problems involving plan andelevation.

40-44 REVISION FOR SPM 2010

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yearly lesson plan f5 2007

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