beams_unit 6 coordinates and graphs of functions

8/9/2019 BEAMS_Unit 6 Coordinates and Graphs of Functions

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Unit 1:Negative Numbers

UNIT 6

COORDINATES

AND

B a s i c E s s e n t i a l

A d d i t i o n a l M a t h e m a t i c s S k i l l s

Curriculum Development Division

Ministry of Education Malaysia


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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 thex-Axis andy-Axis Based on the Scales Given 16

Part B2: Draw Graph of a Function Given a Table for Values ofx andy 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


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Basic Essential Additional Mathematics Skills (BEAMS) Module

Unit 6: Coordinates and Graphs of Functions

1Curriculum Development DivisionMinistry of Education Malaysia

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 thex-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.


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LEARNING OBJECTIVES

Upon completion ofPart A, pupils will be able to:

1. state the coordinates of points plotted on a Cartesian plane; and2. plot points on the Cartesian plane, given the coordinates of the points.

PART A:

COORDINATES

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 ofP as (h, k).

Likewise, given the coordinates of P as ( h , k), the pupils can carry out

the translation = to determine the position ofP 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.


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PART A:

COORDINATES

1.

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 +

kup +

down

4. If there is no horizontal movement, thex-coordinate is 0.

If there is no vertical movement, they-coordinate is 0.

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

Coordinates ofP = (h, k)

Start from the

origin.

x

y

O

P

h units

kunits

LESSON NOTES


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PART A1: State the coordinates of the given points.

1.

Coordinates ofA = (2, 3)

1.

Coordinates ofA =

2.

Coordinates ofB = (3, 1)

2.

Coordinates ofB =

3.

Coordinates ofC= (2,2)

3.

Coordinates ofC=

EXAMPLES TEST YOURSELF

A

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

Start from

the origin,

move 2 units

to the right.

Next, move

3 units up. A

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

-1

2

3

4

y

4

3

2

1 0 1 2 3 4 x

Next, move

1 unit up.

B

Start from the

origin, move 3 units

to the left.

4

3

2

1

1

2

3

4

y

4

3

2

1 0 1 2 3 4 x

B

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

C

Start from

the origin,

move 2 unitsto the left.

Next, move 2

units down.

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

C

EXAMPLESTEST YOURSELF


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4.

Coordinates ofD = (4,3)

4.

Coordinates ofD =

5.

Coordinates ofE= (3, 0)

5.

Coordinates ofE=

6.

Coordinates ofF= (0, 3)

6.

Coordinates ofF=


4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

Start from

the origin,

move 4 units

to the right.

Next, move

3 units

down.

D

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 xE

Start from the


to the right.

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

Start from

the origin,

move 3 unitsup.

F

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

D

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 xE

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

F


Do not move

along they-axis

sincey = 0.

Do not move

along thex-axis

sincex = 0.


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7.

Coordinates ofG = (2, 0)

7.

Coordinates ofG =

8.

Coordinates ofH= (0,2)

8.

Coordinates ofH=

9.

Coordinates ofJ= (6, 8)

9.

Coordinates ofJ=


4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

Start from

the origin,

move 2 units

to the left.

G

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 xG

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

H

Start from the


down.

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

H

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

J

Start from

the origin,

move 6 unitsto the right.

Next, move

8units up.

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

J



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10.

Coordinates ofK= (6 , 6)

10.

Coordinates ofK=

11.

Coordinates ofL = (15,20)

11.

Coordinates ofL =

12.

Coordinates ofM= (3,4)

12.

Coordinates ofM=

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

Start from

the origin,

move 6 units

to the left.

K

Next, move

6 units up.

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

K

20

15

10

5

5

10

15

20

y

20

15

10

5 0 5 10 15 20x

L

Next, move

20 units

down.

Start from the


to the left.

20

15

10

5

5

10

15

20

y

20

15

10

5 0 5 10 15 20 x

L

M

4

2

2

4

y

4 2 0 2 4 x

Start from

the origin,

move 3 units

to the right.

Next, move 4

units down.

4

2

2

4

y

4 2 0 2 4 x

M




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

6 5 4 3 2 1

7

6

5

4

3

2

1

1

2

3

4

5

6

0

y

1 2 3 4 5 6 7

x

ACTIVITY A1


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

.

1. Plot pointA (3, 4) 1. Plot pointA (2, 3)

2. Plot pointB (2, 3) 2. Plot pointB (3, 4)

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

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 -1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x


4

3

2

1

1

2

3

4

A

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

B

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

C



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

.

4. Plot pointD (2,4) 4. Plot pointD (1,3)

5. Plot pointE(1, 0) 5. Plot pointE(2, 0)

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

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x


4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

D

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 xE

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

F



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.

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

8. Plot pointH(0,4) 8. Plot pointH(0,2)

9. Plot pointJ(6, 4) 9. Plot pointJ(8, 6)


4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 xG

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

J

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

H



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.

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

11. Plot pointL (15,10) 11. Plot pointL (20,5)

12. Plot pointM(30,15) 12. Plot pointM(10,25)

29

10

10

20

y

20 10 0 10 20 x

L


8

4

4

8

y

8 4 0 4 8 x

K

8

4

4

8

y

-8 -4 0 4 8 x

20 10 0 10 20

20

10

10

20

y

x

20

10

10

20

y

40 20 0 20 40 x

20

10

10

20

y

40 20 0 20 40 x

M



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1. Plot the following points on the Cartesian plane.

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

2 424x

2

4

2

y

0

4

,

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.

ACTIVITY A2


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LEARNING OBJECTIVES

Upon completion ofPart B, pupils will be able to:

1. understand and use the concept of scales for the coordinate axes;2. draw graphs of functions; and3. state the y-coordinate given the x-coordinate of a point on a graph and

vice versa.

PART B:

GRAPHS OF FUNCTIONS

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 thecoordinates 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 pointson the Cartesian plane, the skill of drawing graphs of functions, given the

values ofx 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.


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PART B:

GRAPHS OF FUNCTIONS

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

2. Some common scales used are as follows:

Scale Note

2 cm to 10 units10 small squares represent 10 units

1 small square represents 1 unit

2 cm to 5 units 10 small squares represent 5 units1 small square represents 0.5 unit

2 cm to 2 units10 small squares represent 2 units

1 small square represents 0.2 unit

2 cm to 1 unit10 small squares represent 1 unit


2 cm to 0.1 unit10 small squares represent 0.1 unit


2 cm

2 cm

LESSON NOTES


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PART B1: Mark numbers on thex-axis andy-axis based on the scales given.

1. Mark4. 7, 16 and 27on thex-axis.Scale: 2 cm to 10 units.

[ 1 small square represents 1 unit ]

1. Mark6 4, 15 and 26 on thex-axis.Scale: 2 cm to 10 units.


2. Mark7,2, 3 and 8on thex-axis.

Scale: 2 cm to 5 units.

[ 1 small square represents 0.5 unit ]

2. Mark8,3, 2 and 6, on thex-axis.



3. Mark3.4,0.8, 1 and 2.6, on thex-axis.

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

3. Mark3.2,1, 1.2 and 2.8 on thex-axis.


4. Mark1.3,0.6, 0.5 and 1.6 on thex-axis.Scale: 2 cm to 1 unit.


4. Mark1.7,0.7, 0.7 and 1.5 on thex-axis.Scale: 2 cm to 1 unit.


010 10 20 30

x

7 16 27

4

x

x510 0 5 10x

2 3 87

x24 2 4

x13.4 00.8 2.6

x

12 1 2

x

0.5

1.3 0

0.6 1.6



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5. Mark0.15, 0.04, 0.03 and 0.17 on the

x-axis.

Scale: 2 cm to 0.1 unit


5. Mark0.17,0.06, 0.04 and 0.13 on the

x-axis.

Scale: 2 cm to 0.1 unit


6. Mark13,8, 2 and 14 on they-axis.

Scale: 2 cm to 10 units



Scale: 2 cm to 10 units


x

00.10.2 0.1 0.20.03 0.170.040.15

x

yy

0

10

20

20

10

13

8

2

14



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8. Mark3.2,0.6, 1.4 and 2.4 on they-axis.




y

y

y

0

5

10

10

9

3

1

7

5

y

0

4

4

2

3.2

0.6

21.4

2.4



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


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

10. Mark0.17, 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 ]

10. Mark0.18, 0.03, 0.05 and 0.14 on the

y-axis.

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

y

y

y

0

1

2

2

1

0.4

1.5

0.4

1.6

y

0

0.2

0.17

0.1

0.06

0.1

0.08

0.16

0.2



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PART B2: Draw graph of a function given a table for values ofx andy.

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

x 2 1 0 1 2

y 2 0 2 4 6

By using a scale of 2 cm to 1 unit on the x-axis and2 cm to 2 units on they-axis, draw the graph of thefunction.

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

x 3 2 1 0 1

y 2 0 2 4 6



x 2 1 0 1 2

y 5 3 1 1 3

By using a scale of 2 cm to 1 unit on the x-axis and2 cm to 2 units on they-axis, draw the graph of the

function.


x 2 1 0 1 2

y 7 5 3 1 1


function.

1 1 x2 2

2

6

4

2

y

0

1 1 x2 2

2

6

4

2

y

0



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x 4 3 2 1 0 1 2

y 15 5 1 3 1 5 15


function.


x 1 0 1 2 3 4 5

y 19 4 5 8 5 4 19


function.


x 2 1 0 1 2 3 4

y 7 2 1 2 1 2 7



x 2 1 0 1 2 3

y 8 4 2 2 4 8


y

10

5

15

5

x3 14 2012

0

y

2

6

2

4

x3 42112



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x 2 1 0 1 2

y 7 1 1 3 11


function.


x 2 1 0 1 2

y 6 2 4 6 16


function.


x 3 2 1 0 1 2 3

y 22 5 0 1 2 3 20



x 3 2 1 0 1 2 3

y 21 4 1 0 1 4 21


x2 3123 1 0

y

20

20

10

10

y

10

5

15

5

x

2 1 21

0



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Each table below shows the values ofx andy for a certain function.

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 they-axis.

FUNCTION 1 FUNCTION 2

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

y 16 17 18 19 20 y 20 19 18 17 16

FUNCTION 3

x 4 3 2 1 0 1 2 3 4

y 16 9 4 1 0 1 4 9 16

FUNCTION 4

x 3 2 1 0 1 2 3

y 9 14 17 18 17 14 9

FUNCTION 5

x 3 2 1.5 1 0.5 0

y 9 8 7.9 7 4.6 0

FUNCTION 6

x 0 0.5 1 1.5 2 3

y 0 4.6 7 7.9 8 9

x

y

0

ACTIVITY B1


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PART B3: State the values ofx andy on the axes.

1. State the values ofa, b, c and don thex-axis

below.



a = 7, b = 13, c =4, d=14


below.


below.


a = 2, b = 7.5, c =3, d=8.5


below.


below.



a = 0.6, b = 3.4, c =1.2, d=2.6


below.

20 10 20

x

cd 010 a b 20 10 20

x

cd 010 a b

510 0 5 10

x

c a bd 510 0 5 10

x

c a bd

c24 2 4

x

ad 0 b c24 2 4

x

ad 0 b



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4. State the values ofa, b, c and don thex-axisbelow.

Scale: 2 cm to 1 unit.


a = 0.8, b = 1.4, c =0.3, d=1.6

4. State the values ofa, b, c and don thex-axisbelow.


below.

Scale: 2 cm to 0.1 unit.


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


below.

6. State the values ofa, b, c and don the y-axis

below.


[ 1 small square

represents 1 unit ]

a = 3, b = 17

c =6, d =15


below.

12 1 2

x

ad 0c b 12 1 2

x

ad 0c b

c

x

00.10.2 0.1 0.2a bd c

x

00.10.2 0.1 0.2a bd

y

0

10

20

20

10

d

c

a

b

y

0

10

20

20

10

d

c

a

b



28/44






below.


[ 1 small square

represents 0.5 unit ]

a = 4, b = 9.5

c =2, d =7.5


below.

8. State the values ofa, b, c and don the y-axisbelow.


[ 1 small squarerepresents 0.2 unit ]

a = 0.8, b = 3.2

c =1.2, d =2.6


y

0

5

10

10

d

c

a

b

5

y

0

5

10

10

d

c

a

b

5

y

0

4

4

2

d

c

2

a

b

y

0

4

4

2

d

c

2

a

b



29/44






below.

Scale: 2 cm to 1 unit.

[ 1 small square

represents 0.1 unit ]

a = 0.7, b = 1.2

c =0.6, d =1.4


below.


Scale: 2 cm to 0.1 unit.

[ 1 small squarerepresents 0.01 unit ]

a = 0.03, b = 0.07

c =0.04, d =0.18


y

0

1

2

2

1

a

b

c

d

y

0

1

2

2

1

a

b

c

d

y

0

d

0.1

c

a

0.2

0.2

b

0.1

y

0

d

c

a

0.2

0.2

b

0.1

0.1



30/44




PART B4: State the value ofy given the valuex from the graph and vice versa.

1. Based on the graph below, find the value ofywhen (a) x = 1.5

(b) x = 2.8

(a) 7 (b) 1.6


(b) x = 1.7

(a) (b)

2. Based on the graph below, find the value ofy

when ( a ) x = 0.14

( b ) x = 0.26

(a) 1.5 (b) 11.5


when ( a ) x = 0.07

( b ) x = 0.18

(a) (b)

1 1 x2 2

2

6

4

2

y

0

2.8

1.5

7

1.6

1 1 x2 2

2

6

4

2

y

0

0.26

1.5

0.14

11.5

x0.10. 2 0.1 0.2

y

10

10

5

5

0 x0.10. 2 0.1 0.2

y

10

10

5

5

0



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when ( a ) x = 0.6

( b ) x = 2.7

( a ) 11 ( b ) 3.5


when ( a ) x = 1.2

( b ) x = 1.8

( a ) ( b )


(b) x = 1.5

(a) 3 (b) 5.8


(b) x = 2.1

(a) (b)

y

10

5

15

5

x3 14 2012

11

0.6

2.7

3.5

y

10

5

15

5

x3 14 2012

x3 421

1

2 0

y

2

6

2

4

1.4

3

1.5

5.8

x3 421

1

2 0

y

2

6

2

4



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when (a) x = 1.7

(b) x = 1.3

(a) 5.5 (b) 3.5


when (a) x = 1.2

(b) x = 1.9

(a) (b)


when (a) x = 1.6(b) x = 2.3

(a) 9 (b) 25


when (a) x = 2.8(b) x = 2.6

(a) (b)

y

10

5

15

5

2 x1 21 0

5.5

1.7

1.3

3.5

y

10

5

15

5

2 x1 21 0

x2 3123 1 0

y

20

20

10

10

1.6

9

2.3

25

x2 3123 1 0

y

20

20

10

10



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7. Based on the graph below, find the value ofx

when (a) y = 5.4

(b) y = 1.6

(a) 1.4 (b) 2.8


when (a) y = 2.8

(b) y = 2.4

(a) (b)

8. Based on the graph below, find the value ofxwhen ( a ) y = 4

( b ) y = 7.5

(a) 0.07 (b) 0.08

8. Based on the graph below, find the value ofxwhen ( a ) y = 6.5

( b ) y = 7

(a) (b)

1 1 x2 2

2

6

4

2

y

0

x0.10. 2 0.1 0.2

y

10

10

5

5

0

1 1 x2 2

2

6

4

2

y

0

2.8

1.4

5.4

1.6

0.07

4

0.08

7.5

x0.10. 2 0.1 0.2

y

10

10

5

5

0



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9. Based on the graph below, find the values ofx

when (a) y = 8.5

(b) y = 0

(a) 3.1 , 2.1 (b) 2 , 1

9. Based on the graph below, find the values ofx

when (a) y = 3.5

(b) y = 0

(a) (b)

10. Based on the graph below, find the values ofxwhen (a) y = 2.6

(b) y = 4.8

(a) 0.6 , 2.1 (b) 1.2 , 3.9

10. Based on the graph below, find the values ofxwhen (a) y = 1.2

(b) y = 4.4

(a) (b)

x3 421

1

2 0

y

2

6

2

4

x3 14 212

2.13.1

8.5

0

y

10

5

15

5

x3 421

1

2 0

y

2

6

2

4

0.6 2.1

1.2 3.9

2.6

4.8

x3 14 212 0

y

10

5

15

5



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when (a) y = 14

(b) y = 17

(a) 2.6 (b) 2.3


when (a) y = 11

(b) y = 23

(a) (b)


when (a) y = 6.5(b) y = 0

(c) y = 6

(a) 0.8 (b) 1.3 (c) 2.3


when (a) y = 7.5(b ) y = 0

(c) y = 9

(a) (b) (c)

x2 3123 1 0

y

20

20

10

10

2.6

2.3

17

14

x2 3123 1 0

y

20

20

10

10

y

10

5

15

5

2 x1 21 0

y

10

5

15

5

2 x1 21 0

6.5

6

1.30.8 2.3



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Task 1: Two points on the graph given are (6.5, k) and (h, 45).

Find the values ofh and k.

Task 2: Smuggling takes place at the locations with coordinates (h, k).

State each location in terms of coordinates.

0

5

10

15

20

25

30

35

40

45

50

55

60

y

12

3 4 5 6 7 8 9x

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.

ACTIVITY B2


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PART A:

PART A1:

1. A (4, 2) 2. B (4, 3)2.3. C(3,3) 4. D (3,4)

5. E(2, 0) 6. F(0, 2)

7. G (1, 0) 8. H(0,1)

9. J(8, 6) 10. K(4, 8)

11. L (10,15) 12. M(4,3)

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).

ANSWERS


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PART A2:

1. 4.

2. 5.

3. 6.

4

3

2

1

1

23

-4

4 3 2 1 0 1 2 3 4

y

x

B

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

A

4

3

2

1

1

2

3

4

4 3 2 1 0 1 2 3 4

y

x

D

4

3

2

1

1

23

4

4 3 2 1 0 1 2 3 4

y

xE

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

C

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 x

F


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7. 10.

8. 11.

9. 12.

4

3

2

1

1

2

3

4

y

4 3 2 1 0 1 2 3 4 xG

K

8

4

4

8

y

8 4 0 4 8 x

4

3

2

1

1

-2

3

4

y

4 3 2 1 0 1 2 3 4 x

H

20 10 0 10 20

20

10

10

20

y

x

L

8

6

4

2

2

4

6

8

y

8 6 4 2 0 2 4 6 8 x

J

M

20

10

10

20

y

40 20 0 20 40 x


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ACTIVITY A2:

YAKOMI ISLANDS

2

4

2

y

O

4RM 1 million

U

A

B C

D

E F

P Q

R S

T

2 424x

,


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PART B1:

1 2.

3. 4.

5. 6.

7. 8. 9. 10.

010 10 20 30

x

4 15 266 510 0 5 10

x

3 2 68

24 2 4

x

3.2 01 2.81.2 12 1 2

x

0.71.7 00.7 1.5

x

00.10.2 0.1 0.20.04 0.130.060.16

y

0

10

20

20

10

16

4

5

15

y

0

5

10

10

7

4

2

6

5

y

0

1

2

2

1

0.3

1.7

0.8

1.5

y

0

0.2

0.18

0.1

0.03

0.1

0.05

0.14

0.2

y

0

4

4

2

3.4

1.4

2

0.8

2.8


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PART B2:

1. 2.

3. 4.

5. 6.

2

6

4

2

y

0 x3 112 1 1 x2 2

2

6

4

2

y

0

x4

1 510

y

10

5

15

5

2 3

y

4

8

2

6

0 x32112

y

10

5

15

5

2 x1 21 0

x2 3123 1 0

y

20

20

10

10


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ACTIVITY B1:

4 3 2 1 0 1 2 3 4x

2

4

6

8

10

12

14

16

18

20

y


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PART B3:

1. a = 3, b = 16, c = 3, d = 18

2. a = 3.5, b = 7, c = 2.5, d = 8

3. a = 1.4, b = 2.4, c = 1.6, d = 3.8

4. a = 0.7, b = 1.8, c = 0.5, d = 1.4

5. a = 0.08, b = 0.16, c = 0.02, d = 0.17

6. a = 6, b = 15, c = 3, d = 17

7. a = 2, b = 8, c = 0.5, d = 8.5

8. a = 1.4, b = 3.6, c = 0.8, d = 3.4

9. a = 0.5, b = 1.7, c = 0.4, d = 1.6

10. a = 0.06, b = 0.16, c = 0.07, d = 0.15

PART B4:

1. (a) 6.4 (b) 2.8

2. (a) 12 (b) 13

3. (a) 2.5 (b) 9

4. (a) 0.6 (b) 5.4

5. (a) 8 (b) 6.5

6. (a) 16 (b) 22

7. (a) 0.7 (b) 1.3

8. (a) 0.08 (b) 0.12

9. (a) 3.5, 1.5 (b) 3 , 1

10. (a) 1.6, 0.6 (b) 2.7, 1.7

11. (a) 2.2 (b) 3.5

12. (a) 2.3 (b) 0.6 (c) 1.4

ACTIVITY B2:

k=15, h = 1.1, 8.9

beams_unit 6 coordinates and graphs of functions

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