BEAMS KPM

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

2. (b) Simplify the following.  (ii) x4 y7 6 

 (i) 2x3 5  (215 )( x35 )  (iv) 4 y9  8y7 7 

 25 x15
 32 x15

 (iii) w2  w12 3 

(v)  36 p9q 5 2   (vi) 2m3n2 3mn4 4 
9 p8q6


3. Simplify the following expressions: (b)  3 1 
4
(a) 25  1

25
1

32

(c)  x  4 (d) 2st 4 
3y2 6s 1t 5


(e)  m2n 1  3 (f)  8ab2c 3  2
2m3k 2 2a 3b 6
 

Curriculum Development Division 18
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

4. Find the value of each of the following. (b) 5
1002 
(a) 1
 643  3  64
 4

(c)  3 (d) 1 1
81 4 
32  272 

 (e) 1 1 (f) 3  1 4 
 27 
a10 5 (a3 )2 (am ) m 

Curriculum Development Division 19
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

ACTIVITY

Solve the questions to discover the WONDERWORD!
 You are given 11 multiple choice questions.
 Choose the correct answer for each of the question.

 Use the alphabets for each of the answer to form the WONDERWORD!

1. 410 
42  45

P 40 O 43 R 417 T 413

2. 107  102  53  52 

T 101455 O 10556 N 10555 B 101456

3. 22  32 
42

22 32 32 42
D E 22 N 42 O

4 3

4. 2 y9 x3  8y 2 x 

M y7x2 A 4 y11 y1x2 4y7
4 x4 L K x2

29  36 4

 5. 25  32 4 

A 220  38 N T 220  36 S 29  38

6. m5  m2  n2  n4 

T m7n8 U m10n8 L m7n6 E m10n6

Curriculum Development Division 20
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

7.  2 3  2 4   2 2  2 3 

5 5 5 5

F  2 12 A  2 2 V  2 6 E  2 5

5 5 5 5

8.  72 5 
43

Y  710  R  77  M  710  A  77 
415 48 48 415

9. 25a9b5 
5a 6b3

L 15a15b8 I 5a3b8 S 5a3b2 T 15a6b5

10.  1 2  1 3  2 2  2 5 

3 3 5 5

P  1 5  2 10 E  1 6  2 7 I  1 5  2 7 R  1 6  2 10
3 5 3 5
3 5 3 5

11. 12 p6q7 
3 p3q 2

p3q5 A 4 p3q5 1 D 3p9q9
Y3 R 3p9q9

Congratulations! You have completed this activity.
1 2 3 4 5 6 7 8 9 10 11

The WONDERWORD IS: ........................................................

Curriculum Development Division 21
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

TEST YOURSELF A: ANSWERS
1.
(b) 216
(a) 243 (d) 1
(c) 256
(e)  27 3125

64 (f)  4 21
(g) 2401
25
2.
(a) 12m5 (h) 32
(c) 18x9
243

(b) 15b7

(d) 14 p8

3. (b) 288
(a) 576
(c) 823543 (d) 16

(e) 250000 6075

(f)  256

83 349

Curriculum Development Division 22
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

4. (b) 54r5s2
(a) 12 f 4 g 2 (d) 144 h2k 5
(c) 64 827 w7v3
153125

TEST YOURSELF B: (b) 531 441
1. (d) 64

(a) 144 729
(c) 262 144 (f) 81
(e) 25
(b) 1 y 2
2.
(a) q 7 2
(c) 7 m2
3 (d) 64b3

3. (b) 16 c10d 6
(a) 9 m5n4 3
2
(c) 2 f 3g 6 (d) 14u7v3

Curriculum Development Division 23
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

TEST YOURSELF C: (b) 1
1.
(d)  3 6  729
(a) 32768  5  15625
(c) 64
(f) 224  16777216
2401
(e)  36   729 (ii) 224  56
(iv) 32
53 125
2(53 )
2. (a)
(vi) 36 (414)
(i) 2 2 4  8 52

3

(iii) 411

(v)  7(32 )

43

2. (b)

(i) 32x15 (ii) x 24 y 42

(iii) 1 (iv) y14
27
w30
(vi) 162m7n18
(v) 16 p  2
q

Curriculum Development Division 24
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
UNIT 5: Indices

3. (b) 4
(a) 1  1
3
25 32
(d) 1  s2 
(c) y8 3 t9

81 x4 (f) 1  a4c6 
16 b16
(e) 8k 6m3n3
(b) 100000
4.
(a) 4 (d) 9
(c) 1
(f) 1
27 81

(e) a 5

ACTIVITY:
The WONDERWORD is ONEMALAYSIA

Curriculum Development Division 25
Ministry of Education Malaysia

Basic Essential
Additional Mathematics Skills

UNIT 6

COORDINATES
AND

UGnRitA1P: HS OF FUNCTIONS
Negative Numbers

Curriculum Development Division
Ministry of Education Malaysia

TABLE OF CONTENTS

Module Overview 1

Part A: Coordinates 2
Part A1: State the Coordinates of the Given Points 4
Activity A1 8
Part A2: Plot the Point on the Cartesian Plane Given Its Coordinates 9
Activity A2 13

Part B: Graphs of Functions 14

Part B1: Mark Numbers on the x-Axis and y-Axis Based on the Scales Given 16

Part B2: Draw Graph of a Function Given a Table for Values of x and y 20

Activity B1 23

Part B3: State the Values of x and y on the Axes 24

Part B4: State the Value of y Given the Value x from the Graph and Vice Versa 28

Activity B2 34

Answers 35

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

MODULE OVERVIEW

1. The aim of this module is to reinforce pupils’ understanding of the concept of
coordinates and graphs.

2. It is hoped that this module will provide a solid foundation for the studies of
Additional Mathematics topics such as:
 Coordinate Geometry
 Linear Law
 Linear Programming
 Trigonometric Functions
 Statistics
 Vectors

3. Basically, this module is designed to enhance the pupils’ skills in:
 stating coordinates of points plotted on a Cartesian plane;
 plotting points on a Cartesian plane given the coordinates of the points;
 drawing graphs of functions on a Cartesian plane; and
 stating the y-coordinate given the x-coordinate of a point on a graph and
vice versa.

4. This module consists of two parts. Part A deals with coordinates in two sections
whereas Part B covers graphs of functions in four sections. Each section deals
with one particular skill. This format provides the teacher with the freedom of
choosing any section that is relevant to the skills to be reinforced.

5. Activities are also included to make the reinforcement of basic essential skills
more enjoyable and meaningful.

Curriculum Development Division 1
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A:

COORDINATES

LEARNING OBJECTIVES

Upon completion of Part A, pupils will be able to:
1. state the coordinates of points plotted on a Cartesian plane; and
2. plot points on the Cartesian plane, given the coordinates of the points.

TEACHING AND LEARNING STRATEGIES

Some pupils may find difficulty in stating the coordinates of a point. The
concept of negative coordinates is even more difficult for them to grasp.
The reverse process of plotting a point given its coordinates is yet another
problem area for some pupils.

Strategy:

Pupils at Form 4 level know what translation is. Capitalizing on this, the

teacher can use the translation = , where O is the origin and P

is a point on the Cartesian plane, to state the coordinates of P as (h, k).
Likewise, given the coordinates of P as ( h , k ), the pupils can carry out

the translation = to determine the position of P on the Cartesian

plane.

This common approach will definitely make the reinforcement of both the
basic skills mentioned above much easier for the pupils. This approach
of integrating coordinates with vectors will also give the pupils a head start
in the topic of Vectors.

Curriculum Development Division 2
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A:
COORDINATES

LESSON NOTES

1. y ●P
k units
Start from the
origin.

O h units x
Coordinates of P = (h, k)

2. The translation must start from the origin O horizontally [left or right] and then vertically
[up or down] to reach the point P.

3. The appropriate sign must be given to the components of the translation, h and k, as shown in the

following table.

Component Movement Sign
h left –
right
+

k up +
down –

4. If there is no horizontal movement, the x-coordinate is 0.
If there is no vertical movement, the y-coordinate is 0.

5. With this system, the coordinates of the Origin O are (0, 0).

Curriculum Development Division 3
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A1: State the coordinates of the given points.

EEXXAAMMPPLLEESS TTEESSTTYYOOUURRSESLEFLF

1. 1. y
4
Start from y
the origin, •3 A
move 2 units •4 A
to the right. 2
3 1
Next, move

2 3 units up.
1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2 –2
–3 –3
–4 –4

Coordinates of A = (2, 3) Coordinates of A =

2. 2.

Start from the y y
origin, move 3 units 4
3 •B 4
to the left. 2 3
1
B• 2

1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
-1 –1
–2 Next, move –2
–3 1 unit up. –3
–4 –4

Coordinates of B = (–3, 1) Coordinates of B =

3. 3.

Start from y y
the origin, 4 4
move 2 units 3 3
to the left. 2 2
1 1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1
Next, move 2 • –1
units down. • –2
C –2
–3 C –3
–4 –4

Coordinates of C = (–2, –2) Coordinates of C =

Curriculum Development Division 4
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A1: State the coordinates of the given points.

EEXXAAMMPLPELSES TTEESSTTYYOOUURRSSEELLFF

4. y 4. y
4 4
Start from 3 Next, move 3
the origin, 2 3 units 2
move 4 units 1 down. 1
to the right.

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2 D• –2 •D
–3 –3
–4 –4

Coordinates of D = (4, –3) Coordinates of D =

5. 5.

Start from the y y
origin, move 3 units 4 4
3
to the right. 3 2
1
2
–4 –3 –2 –1 0
1 •E –1 •E
–2
–4 –3 –2 –1 0 1 2 3 4x –3 1 2 3 4x
–1 –4
Do not move –2
along the y-axis –3
–4
since y = 0.

Coordinates of E = (3, 0) Coordinates of E =

6. 6.

Start from y y
the origin, 4 4
move 3 units
•3 F 3
up.
2 •2 F

1 1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2 Do not move
–3 along the x-axis –2
–4
since x = 0. –3

–4

Coordinates of F = (0, 3) Coordinates of F =

Curriculum Development Division 5
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A1: State the coordinates of the given points.

EEXXAAMMPLPELSES TTEESSTTYYOOUURRSSEELLFF

7. 7.

y y
4
Start from 4
3
the origin, 3
2
move 2 units 2
to the left. 1

1 1 2 3 4x •G 1 2 3 4x

•G –4 –3 –2 –1 0
–1
–4 –3 –2 –1 0 –2
–3
–1 –4

–2

–3

–4

Coordinates of G = (–2, 0) Coordinates of G =

8. 8.

Start from the y y
origin, move 2 units 4 4
3 3
down. 2 2
1 1

–4 –3 –2 –1 0 1 2 3 4 x •–4 –3 –2 –1 0 1 2 3 4x
–1 –1 H
–2
•–2 H –3
–4
–3

–4

Coordinates of H = (0, –2) Coordinates of H =

9. y 9. y
8 8
Start from J•
the origin, 6 •J
move 6 units Next, move
to the right. 4 8units up. 6

2 4

2

–8 –6 –4 –2 0 2 4 6 8x –8 –6 –4 –2 0 2 4 6 8x
–2 –2
–4 –4
–6 –6
–8 –8

Coordinates of J = (6, 8) Coordinates of J =

Curriculum Development Division 6
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A1: State the coordinates of the given points.

EXAMPLES TEST YOURSELF
EXAMPLES TEST YOURSELF

10. 10.

y Start from •y
the origin,
•K 8 move 6 units K8
6 to the left. 6
4
4 2

2

–8 –6 –4 –2 0 2 4 6 8x –8 –6 –4 –2 0 2 4 6 8x
–2 –2
–4
Next, move –4 –6
6 units up. –6 –8

–8

Coordinates of K = (– 6 , 6) Coordinates of K =

11. y 11.
20
Start from the 15 y
origin, move 15 units 10 20
5 15
to the left. 10
5

–20 –15 –10 –5 0 5 10 15 20 x –20 –15 –10 –5 0 5 10 15 20 x
–5 –5

Next, move L• –10 • –10
20 units –15 L –15
down. –20 –20

Coordinates of L = (–15, –20) Coordinates of L =

12. y Next, move 4 12.
4 units down.
Start from y
the origin, 2 4
move 3 units
to the right. 2

–4 –2 0 2 4x –4 –2 0 2 4x
–2
–2 •M
–4
•–4 M
Coordinates of M =
Coordinates of M = (3, – 4)

Curriculum Development Division 7
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

ACTIVITY A1

Write the step by step directions involving integer coordinates that
will get the mouse through the maze to the cheese.

y

7
6
5
4
3
2
1

–6 –5 –4 –3 –2 –1 0 x
–1 1234567

–2

–3

–4

–5

–6

Curriculum Development Division 8
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A2: Plot the point on the Cartesian plane given its coordinates.

. EXAMPLES TTEESSTTYYOOUURRSESELLF F
1. EXAMPLES

Plot point A (3, 4) 1. Plot point A (2, 3)

•y A y
4
4 3
3 2
2 1
1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2 –2
–3 –3
–4 –4

2. Plot point B (–2, 3) 2. Plot point B (–3, 4)

y y
4
•B 4 3
3 2
1
2

1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 -1 0 1 2 3 4x
–1 –1
–2 –2
–3 –3
–4 –4

3. Plot point C (–1, –3) 3. Plot point C (–1, –2)

y y
4 4
3 3
2 2
1 1

–4 –3 –2 –1 0 12 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2
•–2 –3
–4
C –3
–4

Curriculum Development Division 9
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A2: Plot the point on the Cartesian plane given the coordinates.

. EXAMPLES TETSTESYTOYUORSUERLSFELF
4. EXAMPLES

5. Plot point D (2, – 4) 4. Plot point D (1, –3)
5.
y y
4 4
3 3
2 2
1 1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2 •D –2
–3 –3
–4 –4

Plot point E (1, 0) Plot point E (2, 0)

y y
4 4
3
3 2
2 1

•1 E –4 –3 –2 –1 0 1 2 3 4x
–1
–4 –3 –2 –1 0 1 2 3 4x –2
–3
–1 –4

–2

–3

–4

6. Plot point F (0, 4) 6. Plot point F (0, 3)

•y F y
4
4 3
3 2
2 1
1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2
–3 –2
–4
–3

–4

Curriculum Development Division 10
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A2: Plot the point on the Cartesian plane given the coordinates.

EXAMPLES TTEESSTTYYOOUURRSESELLF F
EXAMPLES

7. Plot point G (–2, 0) 7. Plot point G (– 4,0)

yy
44

33

22

1 1

•G 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1
–4 –3 –2 –1 0
–1 –2

–2 –3

–3 –4

–4

8. Plot point H (0, – 4) 8. Plot point H (0, –2)

y y
4 4
3 3
2 2
1 1

–4 –3 –2 –1 0 1 2 3 4 x –4 –3 –2 –1 0 1 2 3 4x
–1 –1
–2
–2 –3
–4
•–3

–4 H

9. Plot point J (6, 4) 9. Plot point J (8, 6)
.
y y
8 8
6
6 4
2
•J

4

2

–8 –6 –4 –2 0 2 4 6 8x –8 –6 –4 –2 0 2 4 6 8x
–2 –2
–4 –4
–6 –6
–8 –8

Curriculum Development Division 11
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A2: Plot the point on the Cartesian plane given the coordinates.

EXAMPLES TTEESSTTYYOOUURRSSEELLFF
. EXAMPLES

10. Plot point K (– 4, 6) 10. Plot point K (– 6, 2)

y y
8 8

K• 4

4

–8 –4 0 4 8x -8 -4 0 4 8x
–4 –4
–8 –8

11. Plot point L (–15, –10) 11. Plot point L (–20, –5)

y y
29 20

10 10

–20 –10 0 10 20 x –20 –10 0 10 20 x
–10
•L –10 –20

–20

12. Plot point M (30, –15) 12. Plot point M (10, –25)

y y
20 20

10 10

–40 –20 0 20 40 x –40 –20 0 20 40 x
–10 –10
–20 •M –20

Curriculum Development Division 12
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

ACTIVITY A2

Exclusive News:

A group of robbers stole RM 1 million from a bank. They hid the money
somewhere near the Yakomi Islands. As an expert in treasure hunting, you
are required to locate the money! Carry out the following tasks to get the

clue to the location of the money.

Mark the location with the symbol.

1. Plot the following points on the CartesEinanjopylyaonue.rself !
P(3, 3) , Q(6, 3) , R(3, 1) , S(6, 1) , T(6, –2) , U(3, –2) ,
A(–3, 3) , B(–5, –1) , C(–2, –1) , D(–3, – 2) , E(1, 1) , F(2, 1).

2. Draw the following line segments:
AB, AD, BC, EF, PQ, PR, RS, UT, ST

YAKOMI ISLANDS

y

4
2

–4 –2 0 24 x

,

–2

–4

Curriculum Development Division 13
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B:

GRAPHS OF FUNCTIONS

LEARNING OBJECTIVES

Upon completion of Part B, pupils will be able to:
1. understand and use the concept of scales for the coordinate axes;
2. draw graphs of functions; and
3. state the y-coordinate given the x-coordinate of a point on a graph and

vice versa.

TEACHING AND LEARNING STRATEGIES

Drawing a graph on the graph paper is a challenge to some pupils. The concept
of scales used on both the x-axis and y-axis is equally difficult. Stating the
coordinates of points lying on a particular graph drawn is yet another
problematic area.

Strategy:

Before a proper graph can be drawn, pupils need to know how to mark numbers
on the number line, specifically both the axes, given the scales to be used.
Practice makes perfect. Thus, basic skill practices in this area are given in Part
B1. Combining this basic skills with the knowledge of plotting points
on the Cartesian plane, the skill of drawing graphs of functions, given the
values of x and y, is then further enhanced in Part B2.

Using a similar strategy, Stating the values of numbers on the axes is
done in Part B3 followed by Stating coordinates of points on a graph in
Part B4.

For both the skills mentioned above, only the common scales used in the
drawing of graphs are considered.

Curriculum Development Division 14
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B:
GRAPHS OF FUNCTIONS

LESSON NOTES

1. For a standard graph paper, 2 cm is represented by 10 small squares.

2 cm

2 cm

2. Some common scales used are as follows:

Scale Note
2 cm to 10 units
10 small squares represent 10 units
1 small square represents 1 unit

2 cm to 5 units 10 small squares represent 5 units
1 small square represents 0.5 unit

2 cm to 2 units 10 small squares represent 2 units
1 small square represents 0.2 unit

2 cm to 1 unit 10 small squares represent 1 unit
1 small square represents 0.1 unit

2 cm to 0.1 unit 10 small squares represent 0.1 unit
1 small square represents 0.01 unit

Curriculum Development Division 15
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B1: Mark numbers on the x-axis and y-axis based on the scales given.

EXAMPLES TEST YOURSELF

1. Mark – 4. 7, 16 and 27on the x-axis. 1. Mark – 6 4, 15 and 26 on the x-axis.
Scale: 2 cm to 10 units. Scale: 2 cm to 10 units.
[ 1 small square represents 1 unit ] [ 1 small square represents 1 unit ]

x x
27 30
–10 –4 0 7 10 16 20

2. Mark –7, –2, 3 and 8on the x-axis. 2. Mark –8, –3, 2 and 6, on the x-axis.
Scale: 2 cm to 5 units. Scale: 2 cm to 5 units.
[ 1 small square represents 0.5 unit ] [ 1 small square represents 0.5 unit ]

x x
8 10
–10 –7 –5 –2 0 35

3. Mark –3.4, – 0.8, 1 and 2.6, on the x-axis. 3. Mark –3.2, –1, 1.2 and 2.8 on the x-axis.
Scale: 2 cm to 2 units. Scale: 2 cm to 2 units.
[ 1 small square represents 0.2 unit ] [ 1 small square represents 0.2 unit ]

x x
4
–4 –3.4 –2 –0.8 0 1 2 2.6

4. Mark –1.3, – 0.6, 0.5 and 1.6 on the x-axis. 4. Mark –1.7, – 0.7, 0.7 and 1.5 on the x-axis.
Scale: 2 cm to 1 unit. Scale: 2 cm to 1 unit.
[ 1 small square represents 0.1 unit ] [ 1 small square represents 0.1 unit ]

x x

–2 –1.3 – 1 –0.6 0 0.5 1 1.6 2 16

Curriculum Development Division
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B1: Mark numbers on the x-axis and y-axis based on the scales given.

EXAMPLES TEST YOURSELF

5. Mark – 0.15, – 0.04, 0.03 and 0.17 on the 5. Mark – 0.17, – 0.06, 0.04 and 0.13 on the
x-axis. x-axis.

Scale: 2 cm to 0.1 unit Scale: 2 cm to 0.1 unit
[ 1 small square represents 0.01 unit ] [ 1 small square represents 0.01 unit ]

x x
–0.2 –0.15 –0.1 –0.04 0 0.03 0.1 0.17 0.2

6. Mark –13, –8, 2 and 14 on the y-axis. 6. Mark –16, – 4, 5 and 15 on the y-axis.

Scale: 2 cm to 10 units Scale: 2 cm to 10 units
[ 1 small square represents 1 unit ] [ 1 small square represents 1 unit ]

y y

20

14

10

2

0

–8
–10
–13

–20

Curriculum Development Division 17
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B1: Mark numbers on the x-axis and y-axis based on the scales given.

EXAMPLES TEST YOURSELF

7. Mark –9, –3, 1 and 7 on the y-axis. 7. Mark –7, – 4, 2 and 6 on the y-axis.

Scale: 2 cm to 5 units. Scale: 2 cm to 5 units.
[ 1 small square represents 0.5 unit ] [ 1 small square represents 0.5 unit ]

y y

10

7

5

1

0

–3
–5

–9 8. Mark –3.4, –1.4, 0.8 and 2.8 on the y-axis.
–10
Scale: 2 cm to 2 units.
8. Mark –3.2, – 0.6, 1.4 and 2.4 on the y-axis. [ 1 small square represents 0.2 unit ]

Scale: 2 cm to 2 units. y
[ 1 small square represents 0.2 unit ]

y

4

2.4

2

1.4

0

–0.6

–2

–3.2
–4

Curriculum Development Division 18
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B1: Mark numbers on the x-axis and y-axis based on the scales given.

EXAMPLES TEST YOURSELF

9. Mark –1.6, – 0.4, 0.4 and 1.5 on the y-axis. 9. Mark –1.5, – 0.8, 0.3 and 1.7 on the y-axis.
Scale: 2 cm to 1 unit.
Scale: 2 cm to 1 unit. [ 1 small square represents 0.1 unit ]
[ 1 small square represents 0.1 unit ] y

y 10. Mark – 0.18, – 0.03, 0.05 and 0.14 on the
y-axis.
2 Scale: 2 cm to 0.1 units.
[ 1 small square represents 0.01 unit ]
1.5 y

1

0.4

0

– 0.4

–1

–1.6
–2

10. Mark – 0.17, – 0.06, 0.08 and 0.16 on the
y-axis.

Scale: 2 cm to 0.1 unit.
[ 1 small square represents 0.01 unit ]

y

0.2
0.16

0.1

0.08

0

– 0.06
–0.1

– 0.17
–0.2

Curriculum Development Division 19
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B2: Draw graph of a function given a table for values of x and y.

EXAMPLES TEST YOURSELF

1. The table shows some values of two variables, x and y, 1. The table shows some values of two variables, x and y,

of a function. of a function.

x –2 –1 0 1 2 x –3 –2 –1 0 1
y –2 0 2 4 6 y –2 0 2 4 6
By using a scale of 2 cm to 1 unit on the x-axis and
2 cm to 2 units on the y-axis, draw the graph of the By using a scale of 2 cm to 1 unit on the x-axis and
function.
2 cm to 2 units on the y-axis, draw the graph of the
y
function.

6

4

2

 1 2x
–2 –1 0
 –2

2. The table shows some values of two variables, x and y, 2. The table shows some values of two variables, x and y,

of a function. of a function.

x –2 –1 0 1 2 x –2 –1 0 1 2
y 5 3 1 –1 –3 y 7 5 3 1 –1
By using a scale of 2 cm to 1 unit on the x-axis and
2 cm to 2 units on the y-axis, draw the graph of the By using a scale of 2 cm to 1 unit on the x-axis and
function. 2 cm to 2 units on the y-axis, draw the graph of the
function.
y

6


4


2


–2 –1 0 1 2 x
–2 

Curriculum Development Division 20
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B2: Draw graph of a function given a table for values of x and y.

EXAMPLES TEST YOURSELF

3. The table shows some values of two variables, x and y, 3. The table shows some values of two variables, x and y,

of a function. of a function.

x – 4 –3 –2 –1 0 1 2 x –1 0 1 2 3 4 5
y 15 5 –1 –3 –1 5 15 y 19 4 –5 –8 –5 4 19
By using a scale of 2 cm to 1 unit on the x-axis and
2 cm to 5 units on the y-axis, draw the graph of the By using a scale of 2 cm to 1 unit on the x-axis and
function. 2 cm to 5 units on the y-axis, draw the graph of the
function.
y

 15 

10
 5

–4 –3 –2 –1 0 1 2 x
–5

4. The table shows some values of two variables, x and y, 4. The table shows some values of two variables, x and y,

of a function. of a function.

x –2 –1 0 1 2 3 4 x –2 –1 0 1 2 3
y –7 –2 1 2 1 –2 –7 y –8 –4 –2 –2 – 4 –8
By using a scale of 2 cm to 1 unit on the x-axis and
2 cm to 2 units on the y-axis, draw the graph of the By using a scale of 2 cm to 1 unit on the x-axis and
function. 2 cm to 2 units on the y-axis, draw the graph of the
function.
y

2


–2 –1 0 1 2 3 4x
 –2 

–4

–6 


Curriculum Development Division 21
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B2: Draw graph of a function given a table for values of x and y.

EXAMPLES TEST YOURSELF

5. The table shows some values of two variables, x and y, 5. The table shows some values of two variables, x and y,

of a function. of a function.

x –2 –1 0 1 2 x –2 –1 0 1 2
y –7 –1 1 3 11 y –6 2 4 6 16
By using a scale of 2 cm to 1 unit on the x-axis and
2 cm to 5 units on the y-axis, draw the graph of the By using a scale of 2 cm to 1 unit on the x-axis and
function. 2 cm to 5 units on the y-axis, draw the graph of the
function.
y

15
10 

5 


–2 –1 –50
1 2x



6. The table shows some values of two variables, x and y, 6. The table shows some values of two variables, x and y,

of a function. of a function.

x –3 –2 –1 0 1 2 3 x –3 –2 –1 0 1 2 3

y 22 5 0 1 2 –3 –20 y 21 4 –1 0 1 – 4 –21

By using a scale of 2 cm to 1 unit on the x-axis and By using a scale of 2 cm to 1 unit on the x-axis and

2 cm to 10 units on the y-axis, draw the graph of the 2 cm to 10 units on the y-axis, draw the graph of the

function. function.

y

 20

10

 
1
–3 –2   2 3x
–1 0

–10

–20 

Curriculum Development Division 22
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

ACTIVITY B1

Each table below shows the values of x and y for a certain function.

FUNCTION 1 0 FUNCTION 2
x – 4 –3 –2 –1 x01234
y 20 19 18 17 16
y 16 17 18 19 20

FUNCTION 3

x –4 –3 –2 –1 0 12 3 4
y 16 9 14 9 16
41 0
x –3 –2 1 2 3
y9 14 FUNCTION 4 17 14 9
–1 0

17 18

x –3 FUNCTION 5 0
y9 –2 –1.5 –1 – 0.5 0

8 7.9 7 4.6

x0 FUNCTION 6 2 3
y0 0.5 1 1.5 8 9
4.6 7 7.9

The graphs of all these functions, when drawn on the same axes, form a beautiful logo. Draw the logo on

the graph paper provided by using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis.
y

0 x

Curriculum Development Division 23
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B3: State the values of x and y on the axes.

EXAMPLES TEST YOURSELF

1. State the values of a, b, c and d on the x-axis 1. State the values of a, b, c and d on the x-axis

below. below.

–20 d –10 c 0 a 10 b x –20 d –10 c 0 a x
20 10 b 20

Scale: 2 cm to 10 units.
[ 1 small square represents 1 unit ]

a = 7, b = 13, c = – 4, d = –14

2. State the values of a, b, c and d on the x-axis 2. State the values of a, b, c and d on the x-axis

below. below.

–10 d –5 c 0a 5b x –10 d –5 c 0 a5 b x
10 10

Scale: 2 cm to 5 units.
[ 1 small square represents 0.5 unit ]

a = 2, b = 7.5, c = –3, d = –8.5

3. State the values of a, b, c and d on the x-axis 3. State the values of a, b, c and d on the x-axis

below. below.

x x
–2 c 0 a 2 b 4
–4 d –2 c 0a 2 b4 – 4d

Scale: 2 cm to 2 units.
[ 1 small square represents 0.2 unit ]

a = 0.6, b = 3.4, c = –1.2, d = –2.6

Curriculum Development Division 24
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module TEST YOURSELF
Unit 6: Coordinates and Graphs of Functions

PART B3: State the values of x and y on the axes.

EXAMPLES

4. State the values of a, b, c and d on the x-axis 4. State the values of a, b, c and d on the x-axis

below. below.

–2 d –1 c0 a1 b x –2 d –1 c 0 a1 x
2 b2

Scale: 2 cm to 1 unit.

[ 1 small square represents 0.1 unit ]

a = 0.8, b = 1.4, c = – 0.3, d = –1.6

5. State the values of a, b, c and d on the x-axis 5. State the values of a, b, c and d on the x-axis

below. below.

xx

–0.2 d –0.1 c0 a 0.1 b 0.2 – 0.2 d –0.1 c0 a 0.1 b 0.2

Scale: 2 cm to 0.1 unit.

[ 1 small square represents 0.01 unit ]

a = 0.04, b = 0.14, c = – 0.03, d = – 0.16

6. State the values of a, b, c and d on the y-axis 6. State the values of a, b, c and d onythe y-axis
y below.
below.

Scale: 2 cm to 10 units. 20 20

[ 1 small square b

represents 1 unit ] b

a = 3, b = 17 10 10
c = – 6, d = –15
a a

0 0

c

c –10
–10

d
d

–20 –20

Curriculum Development Division 25
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B3: State the values of x and y on the axes.

EXAMPLES TEST YOURSELF

7. State the values of a, b, c and d on the y-axis 7. State the values of a, b, c and d on the y-axis

below. y below. y

Scale: 2 cm to 5 units. 10 10
[ 1 small square b
b
represents 0.5 unit ] 5
5
a = 4, b = 9.5 a

c = –2, d = –7.5 0 a

c 0

c

–5 –5

d
d

–10 –10

8. State the values of a, b, c and d on the y-axis 8. State the values of a, b, c and d on the y-axis

below. y below. y

Scale: 2 cm to 2 units. 4 4
[ 1 small square b b

represents 0.2 unit ] 2 2

a = 0.8, b = 3.2 a

c = –1.2, d = –2.6 a 0

0 c

c –2
–2
d
d –4

–4

Curriculum Development Division 26
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module TEST YOURSELF
Unit 6: Coordinates and Graphs of Functions

PART B3: State the values of x and y on the axes.

EXAMPLES

9. State the values of a, b, c and d on the y-axis 9. State the values of a, b, c and d on the y-axis

below. y below. y

Scale: 2 cm to 1 unit. 2 2
[ 1 small square
b b
represents 0.1 unit ]
1 1
a = 0.7, b = 1.2
a a

c = – 0.6, d = –1.4 0 0

c c
–1
–1
d
d
–2 –2

10. State the values of a, b, c and d on the y-axis 10. State the values of a, b, c and d on the y-axis

below. y below. y

Scale: 2 cm to 0.1 unit. 0.2 0.2
[ 1 small square b
b
represents 0.01 unit ]

0.1 0.1
a
a = 0.03, b = 0.07
c = – 0.04, d = – 0.18 a 0

0

c

–0.1 c
–0.1

d

d
–0.2 –0.2

Curriculum Development Division 27
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B4: State the value of y given the value x from the graph and vice versa.

EXAMPLES TEST YOURSELF

1. Based on the graph below, find the value of y 1. Based on the graph below, find the value of y

when (a) x = 1.5 when (a) x = 0.6
(b) x = –2.8 (b) x = –1.7

yy

7

66

44

2 2

– 2.8 –1 0 1 1.5 2 x –2 –1 0 1 2x
–2
–2

–2 – 1.6

(a) 7 (b) –1.6 (a) (b)

2. Based on the graph below, find the value of y 2. Based on the graph below, find the value of y

when ( a ) x = 0.14 when ( a ) x = 0.07
( b ) x = – 0.26 ( b ) x = – 0.18

y y

11.5 10

10

5 5

1.5 0.10.14 0.2 x –0. 2 –0.1 0 0.1 0.2 x
–5
– 0.2–6 0. 2 –0.1 0
–5 –10

–10

(a) 1.5 (b) 11.5 (a) (b)

Curriculum Development Division 28
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B4: State the value of y given the value x from the graph and vice versa.

EXAMPLES TEST YOURSELF

3. Based on the graph below, find the value of y 3. Based on the graph below, find the value of y

when ( a ) x = 0.6 when ( a ) x = 1.2
( b ) x = –2.7 ( b ) x = –1.8

yy

15 15

11

10 10

– 2.7 5 2x 5 1 2x
–1 0 0.6 1
– 4 –3 –2 – 4 –3 –2 –1 0
–5 – 3.5 –5

( a ) 11 ( b ) –3.5 (a) (b)

4. Based on the graph below, find the value of y 4. Based on the graph below, find the value of y

when (a) x = 1.4 when (a) x = 2.7
(b) x = –1.5 (b) x = –2.1

y y
2
3
1 1.4 2 3 4 x –2 –1 0 1 2 3 4x
2 –2

– 1.5 –4

–2 –1 0 –6
–2

–4
– 6 – 5.8

(a) 3 (b) –5.8 (a) (b)

Curriculum Development Division 29
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B4: State the value of y given the value x from the graph and vice versa.

EXAMPLES TEST YOURSELF

5. Based on the graph below, find the value of y 5. Based on the graph below, find the value of y

when (a) x = 1.7 when (a) x = 1.2
(b) x = –1.3 (b) x = –1.9

yy
15 15

10 10
5
5.5

5

– 1.3 1.72 x –2 –1 0 1 2x
–5
–2 –1 0 1
–5 – 3.5

(a) 5.5 (b) –3.5 (a) (b)

6. Based on the graph below, find the value of y 6. Based on the graph below, find the value of y

when (a) x = 1.6 when (a) x = 2.8
(b) x = –2.3 (b) x = –2.6

y y
20
25

20

10 1.6 3x 10 1 2 3x

–3 – 2.–3 2 –1 0 12 –3 –2 –1 0
–10– 9 –10
–20 –20

(a) –9 (b) 25 (a) (b)

Curriculum Development Division 30
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B4: State the value of y given the value x from the graph and vice versa.

EXAMPLES TEST YOURSELF

7. Based on the graph below, find the value of x 7. Based on the graph below, find the value of x

when (a) y = 5.4 when (a) y = 2.8
(b) y = –1.6 (b) y = –2.4

yy

66

5.4

44

2 2

– 2.8 –1 – 0 1 1.4 2 x –2 –1 0 1 2x
–2
–2 1.6

–2

(a) 1.4 (b) –2.8 (a) (b)

8. Based on the graph below, find the value of x 8. Based on the graph below, find the value of x

when ( a ) y = 4 when ( a ) y = 6.5
( b ) y = –7.5 ( b ) y = –7

yy

10 10

5 5

4 0.08 0.2 x –0. 2 –0.1 0 0.1 0.2 x
–5
–0. –20.0–70.1 0 0.1
–5 –10

– 7.5

–10

(a) – 0.07 (b) 0.08 (a) (b)

Curriculum Development Division 31
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B4: State the value of y given the value x from the graph and vice versa.

EXAMPLES TEST YOURSELF

9. Based on the graph below, find the values of x 9. Based on the graph below, find the values of x

when (a) y = 8.5 when (a) y = 3.5

(b) y = 0 (b) y = 0

yy
15 15

10 10

8.5

55

– 4 – 3–.13 –2 –1 0 1 22.1 x – 4 –3 –2 –1 0 1 2x
–5 –5

(a) –3.1 , 2.1 (b) –2 , 1 (a) (b)

10. Based on the graph below, find the values of x 10. Based on the graph below, find the values of x

when (a) y = 2.6 when (a) y = 1.2
(b) y = – 4.8 (b) y = – 4.4

y y
2
2.6
0.6 1 3.9 x –2 –1 0 1 2 3 4x
2 –2
22.1 3 4
– 1.2 –4

–2 –1 0 –6
–2

–4

– 4.8

–6

(a) 0.6 , 2.1 (b) –1.2 , 3.9 (a) (b)

Curriculum Development Division 32
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B4: State the value of y given the value x from the graph and vice versa.

EXAMPLES TEST YOURSELF

11. Based on the graph below, find the value of x 11. Based on the graph below, find the value of x

when (a) y = 14 when (a) y = 11
(b) y = –17 (b) y = –23

y y
20
20 10

14 –3 –2 –1 0
–10
10 –20

– 2.3 –1 0 1 2 2.6 3 x 1 2 3x

–3 –2 –10

– 17

–20

(a) 2.6 (b) –2.3 (a) (b)

12. Based on the graph below, find the value of x 12. Based on the graph below, find the value of x

when (a) y = 6.5 when (a) y = 7.5

(b) y = 0 (b ) y = 0
(c) y = –6 (c) y = –9

yy
15 15

10 1.3 2.3 10 1 2x
5
6.5 1 2x
–2 –1 0
5 –5

– 0.8

–2 –1 0
–5

–6

(a) – 0.8 (b) 1.3 (c) 2.3 (a) (b) (c)

Curriculum Development Division 33
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

ACTIVITY B2

There is smuggling at sea and you know two possible locations.
As a responsible citizen, you need to report to the marine police these two locations.

Task 1: Two points on the graph given are (6.5, k) and (h, 45).
Task 2: Find the values of h and k.
Smuggling takes place at the locations with coordinates (h, k).
State each location in terms of coordinates.

y

60 x
55
50 34
45
40
35
30
25
20
15
10
5
0

1 23 4 5 6 7 8 9

Curriculum Development Division
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

ANSWERS

PART A:

PART A1: 2. B (– 4, 3)
1. A (4, 2) 4. D (3, – 4)
2. 6. F (0, 2)
3. C (–3, –3) 8. H (0, –1)
10. K (– 4, 8)
5. E (2, 0) 12. M (4, –3)

7. G (–1, 0)

9. J (8, 6)

11. L (–10, –15)

ACTIVITY A1:

Start at (5, 3).

Then, move in order to (4, 3), (4, –3), (3, –3), (3, 2), (1, 2) , (1, –3) , (–3, –3) , (–3, 3),
(– 4, 3), (–
4, 5), (–3, 5) and (–3, 6).

Curriculum Development Division 35
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART A2:

1. 4.

y y
4 4
3
•A 2
1
3
–4 –3 –2 –1 0 1 2 3 4 x
2 –1

1 •–2 D

–4 –3 –2 –1 0 1 2 3 4x –3
–1 –4
–2
–3
–4

2. 5.

•B y y
4 4
3
2 3
1
2

–4 –3 –2 –1 0 1 2 3 4x 1 •E
–1
–2 –4 –3 –2 –1 0 1 2 3 4x
–3 –1
-–4 –2
–3
–4

3. 6.

y y
4
3 •4 F
2
1 3

2

1

–4 –3 –2 –1 0 1 2 3 4x –4 –3 –2 –1 0 1 2 3 4x
–1
• –1 –2
–3
C –2 –4
–3

–4

Curriculum Development Division 36
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

7. 10.

y y
4 8

3

2 •K 4
0
1 1 2 3 4x –8 –4 4 8x

•G –4

–4 –3 –2 –1 0 –8
–1
–2
–3
–4

8. 11.

y y
4 20
3
2 10
1
•–20 –10 0 10 20 x
–4 –3 –2 –1 0 1 2 3 4 x L
–10
–1– H
–20
•-2

–3
–4

9. 12.

y y
8 20

•J 10

6

4

2

–8 –6 –4 –2 0 2 4 6 8x –40 –20 0 20 40 x
–2
–4 –10
–6
–8 •–20 M

Curriculum Development Division 37
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

ACTIVITY A2:

YAKOMI ISLANDS

y

4 PQ
A

2

E R S
F x
–2 O
C 24
,–4

B

D –2 UT

–4  RM 1 million

Curriculum Development Division 38
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B1:

1 2.

–10 –6 04 10 15 20 x –10 –8 –5 –3 02 56 x
26 30 10
3.
4.

–4 –3.2 –2 –1 0 1.2 2 2.8 x –2 –1.7 –1 –0.7 0 0.7 1 x
4 1.5 2
5. y
6.
20

15

–0.2 –0.16 –0.1 –0.06 0 0.04 0.1 0.13 x 10
0.2

5

0

–4

–10

–16
–20

7. y 8. y 9. y 10. y

10 4 2 0.2
1.7
6 2.8 0.14
1 0.1
5 2 0.05
0.3
2 0.8 0
0
0 0 – 0.03
–0.8
–4 –1.4 –1 – 0.1
–5 –2
–7 –1.5 – 0.18
–3.4 –2 – 0.2
–10 –4

Curriculum Development Division 39
Ministry of Education Malaysia

Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 6: Coordinates and Graphs of Functions

PART B2:

1. y 2. y
6 

4 6

2
4


2


 1x –2 –1 0 1 2 x
–3 –2 –1 0 –2
 –2

3.  y  4. y

15 –2 –1 0 1 2 3 x
10 –2  

5   –4 
–6 
–1 0 1 2 3 4 5x
–5   –8



5. y 6. y

15   20

10 10

5   
 –3 –2 –1 0 1
2 3x

–2 –1 0 1 2x –10
 –5
–20 

Curriculum Development Division 40
Ministry of Education Malaysia