YEARLY PLAN FOR MATHEMATICSFORM 5 2014

SEKOLAH MENENGAH KEBANGSAAN VICTORIAJALAN HANG TUAH, 55200 KUALA LUMPUR

SUBJECT COORDINATOR: PN RAFIDAH BT RAMLI

MATHEMATICS PANEL: PUAN NURUL IZZAH AB HALIM

HEAD OF MATHEMATICS AND SCIENCE DEPARTMENT: PN ZURAIDAH BT MAT PA

PRINCIPAL:EN MAZLAN BIN BUNIRAN

SEKOLAH MENENGAH KEBANGSAAN VICTORIAJALAN HANG TUAH, 55200 KUALA LUMPUR

WEEK TOPICS / SUBTOPICS

LEARNING OBJECTIVESStudents will be taught to:

LEARNING OUTCOMES CCTS VALUES VOCAB/NOTES

2 weeks

12 – 23 Jan

1. Number Bases

1. Understand and use the concept of number in base two, eight and five..

1. State the value of a digit of a number in base:a) twob) eightc) five

2. State the value of a digit of a number in base:a) twob) eightc) five

3. Write a number in base:a) twob) eightc) five - in expanded notation

Conceptual

Compare and contrast

Systematic

Rational

Accurate

Emphasise the ways to read numbers in various bases.Examples : 1012 is read as “one zero

one base two” 72058 is read as “seven two

zero five base eight” 43255 is read as “ four three

two five base five”

Numbers in base two are also known as binary numbers.

4 weeks

26 Jan – 27 Feb

2. Graphs Of Functions II

2.1 Understand and use the concept of graphs of functions

1. Draw the graph of a ;

a) linear function; y=ax+b, where a and b are constants

b) quadratic function; y=ax2+bx+c , where a, b and c are constants, a ≠ 0

c) cubic function : y=ax3+bx2+cx+d , where a,b,c and d are constants, a≠0

d) reciprocal function,y=a

x,where a is a

constants,a≠0.3. Find from a graph :

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

4. Identify:a) 2the shape of graph given a type of functionb) the type of function given a graphc) the graph given a function and vice versa.

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

Conceptconstructivim

Compare and contrast

Analising

Mental visualization

Relationship

Punctuality

Awareness

Systematic

Neatness

Limit cubic functions to the following forms:

y=ax3

y=ax3+by=ax3+bx+c

2.2 Understand and use the concept of the solution of an

1. Find the point(s) of intersection of two graphs.2. Obtain the solution of an equation by finding the

point(s) of intersection of two graphs.

- Identifying relation- Identifying

SystematicNeatness Precise

To sketch a graphTo draw a graphUse the traditional graph plotting

equation by graphical methods

3. Solve problems involving solution of an equation by graphical method.

patterns.- Recognizing and representing.-Representing and interpreting data.

Rationale Diligence SystematicAccuracy

exercise if the graphing calculator or the Sketchpad is unavailable.

Involve everyday problems.

2.3 Understand and use the concept of the region representing in inequalities in two variables

1. Determine whether a given point satisfies :

baxy or y >ax+b or y <ax+b2. Determine the position of a given point relative to the

equation y=ax+b3. Identify the region satisfying y>ax+b or y<ax+b4. Shade the regions representing the inequalities

a) y>ax+b ory<ax+b

b) y≥ax+b or y≤ax+b5. Determine the region which satisfies two or more

simultaneous linear inequalities

Identifying patterns SystematicDeterminationMaking inferences

Emphasise that:For the region representing y>ax+b or y<ax+b ,the line y=ax+b is drawn as a dashed line to indicate that all points on the line are not in the region.For the region representing y≥ax+b or y≤ax+b , the line y=ax+bis drawn as a solid line to indicate that all points on the line y=ax+b are in the region.

2 – 6 Mac 2015

UJIAN INTERVENSI SPM

3 weeks

9 Mac – 3 April 2015

3. Transforma-tions III

3.1 Understand and use the concep of combination of two transformations

1. Determine the image of an object under combination of two isometric transformations

IdentifyingrelationsCharacterizing

SystematicDeterminationAccuracy

Begin with a point, followed by a line and a object

2. Determine the image of an object under combination of a. two enlargements.

b. an enlargement and an isometric transformation

Comparing and DifferentiatingInterpretingIdentifying Relation

Rules and RegulationsSelf ConfidenceNeatness

Limit isometric transformations to translations, reflections and rotations.

3. Draw the image of and object under combination of two transformations.

Drawing diagramsIdentifying relation

Systematic

4. State the coordinates of the image of a point under combined transformation

Identifying RelationArranging Sequentially

DiligenceAccuracyConsistent

Combined transformation.

5. Determine whether combined transformation AB is equivalent to combined transformation BA

Comparing and DifferentiatingIdentifying Relation

RationalCautious

Equivalent

6. Specify two successive transformation in a combined transformation given the object and the image

Identifying patternsIdentifying RelationLogical ReasoningRepresenting and Interpreting Data

Systematic

Hardworking

Specify

7. Specify a transformation which is equivalent to the combination of two isometric transformations

Using AnalogiesWorking Out Mentally

HonestyCooperation

Limit the equivalent

8. Solve problems involving transformation Find all possible solutionUsing AnalogiesDrawing DiagramWorking out Mentally

Sharing

Rational

Diligence

2 weeks

6 – 17 April

4. Matrices 4.1 Understand and use the concept of matrix

1. Form a matrix from given information.2. Determine :

a) the number of rowsb) the number of columnsc) the order of a matrix

3. Identify a specific element in a matrix.

Arranging sequentiallyCollecting and handling dataIdentifying patternsIdentifying patterns

Neatness and systematic

Accurate

Systematic

Emphasize that matrices are written in bracket.Matrix, row matrix, column matrix, square matrixEmphasize that a matrix of order m x n is read as ‘an m by n matrix’Use row number and column number to specify the position of an element.

4.2 Understand and use the concept of equal matrices

1. Determine whether two matrices are equal.2. Solve problems involving equal matrices

Using algorithm and relationshipComparing and differentiating

SystematicAccurate

Equal matricesIncluding finding values of unknown elements.

4.3 Perform addition and subtraction on matrices

1. Determine whether addition or subtraction can be performed on two given matrices.

2. Find the sum or the difference of two matrices.3. Perform addition and subtraction on a few matrices.4. Solve matrix equation involving addition and

subtractions

Comparing and differentiating

Using algorithm and relationship

Problem solving

Cooperation

Rationale

Confidence

Systematic

Limit to matrices with not more than three rows and three columns.Include finding values of unknown elements/matrix equation

4.4 Perform multiplication of a matrix by a number

1. Multiply a matrix by a number.2. Express a given matrix as a multiplication of another

matrix by a number.3. Perform calculation on matrices involving addition,

subtraction and scalar multiplication.4. Solve matrix equations involving addition, subtraction

and scalar multiplication.

EvaluatingConceptualize and finding all possible solutionsEvaluating and problems solving

systematic Multiplying a matrix by a number is known as scalar multiplication

Include finding the values of unknown elements

4.5 Perform multiplication of two matrices

1. Determine whether two matrices can be multiplied and state the order of the product when the two matrices can be multiplied.

2. Find the product of two matrices3. Solve matrix equations involving multiplication of

two matrices.

Identifyingpatterns

Arrangingsequentially

Recognizingandrepresenting

Makinggeneralization

classifying

DeterminationSystematicConsistentDiligenceNeatness

The number of columns of first matrix must be same with the number of rows of second matrix.The order of the matrices : (m x n) x (n x s) = (m x s)Limit to matrices with not more than three rows and three columns.Limit to two unknown elements.

4.6 Understand and use the concept of identity matrix

1. Determine whether a given matrix is an identity matrix by multiplying it to another matrix.

2. Write identity matrix of any order.3. Perform calculation involving identity matrices.

Making generalizationIdentifying patternsSolving problems

RationalSystematicNeatness

Identity matrix is usually denoted by I and is also known as unit matrix.Identity matrix unit matrix.Limit to matrices with no more than three rows and three columns.

4.7 Understand and 1. Determine whether a 2 x 2 matrix is the inverse matrix Comparing Cooperation The inverse of matrix A is

use the concept of inverse matrix.

of another 2 x 2 matrix.2. Find the inverse matrix of a 2 x 2 matrix using :

a) the method of solving simultaneous linear equations

b) a formula.

Identifying patterns and relationsComparingIdentifying patterns and relations

NeatnessSystematicCooperationNeatnessSystematic

denoted by A−1

.Emphasize that:

If matrix B is the inverse of matrix A, then matrix A is also the inverse of matrix B, AB = BA = IInverse matrices can only exist for square matrices, but not all square matrices have inverse matrices.

Prior to use the formula, carry out operations leading to the formula.

4.8 Solve simultaneous linear equations by using matrices

1. Write simultaneous linear equations in matrix form.

2. Find the matrix ( p

q ) in

(a bc d )( p

q )=(hk )

Using the inverse matrix.3. Solve simultaneous linear equations by the matrix

method.4. Solve problems involving matrices

Identifying PatternsIdentifying relationsRepresenting & Interpreting data

RationalSystematicNeatnessRationalSystematicNeatnessRationalSystematicNeatness

Limit to two unknowns.Simultaneous linear equationsap + bq = hcp + dq = kin matrix form is

(a bc d )( p

q )=(hk )

Where a, b, c, d, h and k are constants, p ad q are constants, p and q are unknowns.

A−1 (a bc d )( p

q )=A−1(hk )

Where

A = (a bc d ).

The matrix method uses inverse matrix to solve simultaneous linear equations.

1 weeks

20 – 24 April

5. Variations

5.1 Understand and use the concept of direct variation

1. State the changes in a quantity with respect to the changes in another quantity, in everyday life situations involving direct variation.

2. Determine from given information whether a quantity varies directly as another quantity.

3. Express a direct variation in the form of equation involving two variables.

4. Find the value of a variable in a direct variation when sufficient information is given.

5. Solve problems involving direct variations for the following cases:

y∝ x ; y∝ x2; y∝ x3

;y∝ x12

Identifyingrelations

Making generalization

Estimating

Rationale

Systematic

Tolerance

Hardworking

Y varies directly as y∝ 1x if and only

if

yx is a constant.

If y varies directly as x , the

relation is written as y∝ x .

If y∝ x , then y=kx where k is constant of variation.

Using y=kx ; ory1

x1=

y2

x2 to get the solutions5.2 Understand and

use the concept of inverse variations

1. State the changes in a quantity with respect to changes in another quantity, in everyday life situations involving inverse variation.

2. Determine from given information whether a quantity varies inversely as another quantity.

Making inferences

Representing and interpreting data

RationalSystematic

y varies inversely as x if and only if xy is a constant.If y varies inversely as x, the

relation is written asy∝ 1

x

3. Express a inverse variation in the form of equation involving two variables.

4. Find the value of a variable in an inverse variation when sufficient information is given.

5. Solve problems involving inverse variation for the following cases:

y∝ 1

x ; y∝ 1

x2;y∝ 1

x3;y∝ 1

x12

Identifying relations

ProblemSolving

Rational

Systematic

Accuracy

.If y∝ 1

x , then y= k

xwhere k is the constant of variation.

Using:y= k

x or x1 y1 = x2 y2

to get the solution.5.3 Understand and

use the concept of joint variation.

1. Represent a joint variation by using the symbol for the following cases: a) two direct variations. b) two inverse variations. c) a direct variation and an inverse variation.2. Express a joint variation in the form of equation.3. Find the value of a variable in a joint variation when

sufficient information is given.4. Solve problems involving joint variation.

Identifying relations

comparing and differentiating

collecting and handling data

using analogies

finding all possible solutions

Cooperation

Punctuality

Systematic

Rational

For the cases

y∝ xn zn , y∝ 1xn zn

and y∝ xn

zn , limit n to 2, 3,

12 .

Joint variation

30 April – 18 Mei

PEPERIKSAAN DIAGNOSTIK SPM7 – 26 Mei 2010

1 weeks

15 – 19 Jun

6. Gradient And Area Under A Graph

6.1 Understand and use the concept of quantity represented by the gradient of a graph

1. State the quantity represented by the gradient of a graph.

2. Draw the distance-time graph, given ;a. a table of distance-time values.b. a relationship between distance and time.

3. Find and interpret the gradient of a distance-time graph.4. Find the speed for a period of time from a distance-time

graph.5. Draw a graph to show the relationship between two

variables representing certain measurements and state the meaning of its gradient

Recognizing and representing

Comparing and differentiating

Interpreting data

Rationality

Respect

Limit to graph a straight line.

The gradient of a graph represents the rate of change of a quantity on the vertical axis with respect to the change of another quantity on the horizontal axis. The rate of change may have a specific name for example “speed” for a distance time graph.

Emphasis that: Gradient

= change of distancechange of time =speed

6.2 Understand the concept of quantity represented by the area under a graph

1. State the quantity represented the area under a graph.2. Find the area under a graph.3. Determine the distance by finding the area under the

following types of speed-time graph:(a) v = k (uniformspeed)(b) v = kt(c) v = kt + h(d) a combinationof the above.

4. Solve problems involving gradient and area under a graph.

Recognising and representing

Respect Include speed-time and acceleration-time graphs.Limit to graph of a straight line of a combination of a few straight lines.v represents speed,t represents time,h and k are constants.For example:Speed, v

2 weeks

22 Jun – 3

7. Probability II

7.1 Understand and use the concept of probability of an

1. Determine the sample space of an experiment with equally likely outcomes

2. Determine the probability of an event with equiprobable

Making inference

Working out

DeterminationCooperation

Limit to sample space with equally likely outcomes.Equally likely

Julai 2015 event. sample space.3. Solve problems involving probability of an event.

mentally

Finding all possible solutions.

Finding all possible solutions.

Rational A sample space in which each outcome is equally likely is called equiprobable sample space.The probability of an outcome A, with equiprobable sample spaceS, is P(A)= n(A) n(S)Use tree diagram where appropriate.

Include everyday problems and making predictions.

7.2 Understand and use the oncept of probability of the complement of an event.

1. State the complement of an event in :a. words

b. set notation

2. Find the probability of the complement of an event

Identifying relationsFinding all possible solutionsMaking inferencesDrawing diagrams

CooperationEquity

Rationale

Precise

The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A.

7.3 Understand and use the concept of probability of combined event

1. List the outcomes for events : a) A or B as elements of set A ¿ B

2. Find the probability by listing the outcomes of the combined event : a) A or B

3. List the outcomes for events A and B as elements of set A ∩ B

EstimatingIdentifyingPatternsIdentifyingRelationsFindingall possiblesolutionsDrawing diagram

Tolerance

Determination

Consistent

Event

Combined event

Consecutively

Toss

1 weeks

6 – 10 Julai

8. Bearing 8.1 Understand and use the concept of bearing

1. Draw and label the eight main compass directions:

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

2 State the compass angle of any compass direction3 Draw a diagram of a point which shows the direction of

B relative to another point A given the bearing of B from A

4 State the bearing of point A from point b based on given information.

5 Solve problems involving bearing

Making connectionsVisualize mentallyMaking connectionsVisualize mentallyComparing and differentiatingInterpretDraw diagramsRecognizing relationshipProblem solving

CooperationAccuracyNeatnessCarefulnessRationalAccuracySystematicCarefulnessAccuracyRationalResponsibilityAppreciation

North–eastSouth–eastNorth-westSouth-west

Compass angle bearing

Compass angle and bearing are written in three-digit form, 000o to 360o. They are measured in a clockwise direction from north. Due north is considered as bearing 000o. For cases involving degrees and minutes, state in degrees up to one decimal point.

3 weeks

13 – 31 Julai

9. Earth As A Sphere

9.1 Understand and use the concept of longitude.

1. Sketch a great circle through the north and south poles.2. State the longitude of a given point.3. Sketch and label a meridian with the longitude given.4. Find the difference between two longitudes

Identifying patterns

Identifying relations

Understanding Great circle

Meridian

Longitude

9.2 Understand and use the concept of

1. Sketch a circle parallel to the equator.2. State the latitude of a given point.3. Sketch and label a parallel of latitude.

Drawing diagramsFinding all possible solutions

RationalCooperationSharing

Equator, Latitude,Emphasize that* the latitude of the equator is 0

latitude 4. Find the difference between two latitudes.Logicalreasoning Recognizing & interpreting data

SystematicTolerance

* latitude ranges from 0 to 90N/SParallel of latitudeInvolve actual places on the earthExpress the difference between two latitudes with an angle in the range of 0x180.

9.3 Understand he concept of location of a place.

1. State the latitude and longitude f a given place.2. Mark the location of a place.3. Sketch and label the latitude and longitude of a given

place.

Logical Reasoning,Identifying Relation,Recognizing and Representing.

Systematic,Neatness,Public Spiritedness.

A place on the surface of the earth is represented by a point.The location of a place A at latitude x◦N and longitude y◦E is written as A(x◦N, y◦E).

9.4 Understand and use the concept of distance on the surface of the earth to solve problems

1. Find the length of an arc of a great circle in nautical mile, given the subtended angle at the centre of the earth and vice versa

2. Find the distance between two points measured along a meridian, given the latitudes of both points.

3. Find the latitude of a point given the latitude of another point and the distance between the two points along the same meridian.

4. Find the distance between two points measured along the equator, given the longitudes of both points.

5. Find the longitudes of a point given the longitude of another point and the distance between the two points along the equator.

6. State the relations between the radius of the earth and the radius of a parallel of latitude.

7. State the relation between the length of an arc on the equator between two meridians and the length of the corresponding arc on a parallel of latitude.

8. Find the distance between two points measured along a parallel of a latitude.

9. Find the latitude of a point given the longitude of another point and the distance between the points along a parallel of latitude.

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

11. Solve problems involving :-(a) distance between two points traveling on a

surface of the earth

Identifying relationsRepresenting and interpreting dataDrawing diagramsIdentifying relationsIdentifying relationsDrawing diagramsComparing & differentiatingMaking inferences

SystematicRationalNeatnessSystematicRationalCooperationToleranceSharing

2 weeks

4 – 14 Ogos

10. Plans And Elevations

10.1 Understand and use the concept of orthogonal projection

10.1.1 Identify orthogonal projection10.1.2 Draw orthogonal projection ,given an object and a

plane10.1.3 Determine the difference between an object and

Comparing and Differentiating

Visualization

Identifying relationship

Accuracy

Creative thinking

Systematic

Emphasize the different uses of dashed lines and solid lines

Begin with simple solid objects such as cubic, cuboids, cylinder, cone, prism and right pyramid

VocabOrthogonal projection

10.2 Understand and use the concept of

10.2.1 Draw the plan of a solid Object10.2.2 Draw

Analyzing

Synthesizing

AccuracyCreative thinking

Limit to full scale drawings only

plan and elevation

a) the front elevationb) side elevation of a solid object

10.2.3 Draw a) the plan b) the front elevation c) the side elevation of a solid object to scale

10.2.3 Solve problems involving plans and elevation

Identifying Relationship

SystematicSelf ConfidentNeatnessDedicationDetermination

Include drawing plan and elevation in one diagram showing projections lines

17 – 26 Ogos

SESI ULANGKAJI1. Teknik Menjawab

2. Drilling – modules consisting of clones and past year SPM Questions.19 – 27

SeptPEPERIKSAAN PERCUBAAN SPM 2011

18 – 26 Ogos

CUTI PERTENGAHAN PENGGAL

28 Ogos – 31 Oktober

SESI ULANGKAJI1. Jadual Anjal

2. Teknik Menjawab3. Drilling – modules consisting of clones and past year SPM Questions.