form 5 _ maths - chapter 2

8/20/2019 Form 5 _ Maths - Chapter 2

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Graphs of Functions 1

CHAPTER 11 : GRAPHS OF FUNCTIONS II

Steps involved in solving an equation graphically:

1. Find the y value by substituting x value into the given function.

2. Draw the graph by using the given scale for x-axis and y- axis.

3. Find the value of y or x when given value of x or y from the graph.

4. On the same axes, draw a suitable straight line which satisfies the equation.

5. Determine the solutions by reading off the x-coordinates of the point of

intersection of the two graphs.




Example 2

Complete the following table for theequation 32 += x y

-1 0 3 y 1 3 9

By using scientific calculator, substituteeach of the x value in equation above.

3)(2 += x y -1 2(-1) + 3 = 1

0 2(0) + 3 = 33 2(3) + 3 = 9

Example 3

Complete the following table for the

equation 12

−= x

y

2 4 8 y 0 1 3


12

−= x

y

201

22

=−

411

2

4=−

831

28

=−

Exercise 2


-1 0 3


1)(3 += x y -1

03

Exercise 3


equation 23

−= x

y

2 4 8


x

2

4

8




Example 4

Complete the following table for theequation x y 23 −=

-1 0 1 y 5 3 1


)(23 x y −= -1 5)1(23 =−−

0 3)0(23 =− 1 1)1(23 =−

Exercise 4

Complete the following table for theequation x y 35 −=

-1 0 1


)(35 x y −=

-1

01




11.2: Quadratic FunctionComplete the following table below

Example:1. Complete the following table for

the equation y = 2x 2

x 1 2 3y 2 8 18


x y1 2(1) 2 = 22 2(2) 2 = 83 2(3) 2 = 18

Exercise:Complete the following table for theequations:

1. y = - 2x 2 x -1 0 1y

By using scientific calculator, substitute eachof the x value in equation above.

x y=- 2(x) 2 -101

2. y =21

x 2

x -1 0 1y


xy =

21

(x) 2

-101

3. y = 3x 2

x -1 0 1y


x y = 3(x) 2 -101




4. y = -25

x 2

x -1 0 1y


xy = -

25

(x) 2

-10

1

5. y = 5x 2 x -1 0 1y


x y = 5(x) 2 -101




11.3: Cubic Function

Complete the following table below

Example 1

Complete the following table for theequation 33 x y =

x 1 2 3 y 3 24 81

By using scientific calculator, substitute

each of the x value in equation above.

x 3)(3 x y = 1 3)1(3 3 = 2 24)2(3 3 = 3 81)3(3 3 =

Exercise 1

Complete the following table for theequations:

i. 35 x y =

x 1 2 3 y


3)(5 x y = 123

ii. 32 x y −=

x 1 2 3 y


3)(2 x y −= 123




Example 2

Complete the following table for theequation 52 3 += x y

x -2 0 2 y -11 5 21


x 5)(2 3 += x y -2 115)2(2 3 −=+− 0

55)0(23 =+

2 215)2(2 3 =+

Example 3

Complete the following table for theequation 43 +−= x y

x -1 -2 3 y 5 12 -23


x 4)( 3 +−= x y -1 54)1( 3 =+−− -2 124)2( 3 =+−− 3 234)3( 3 −=+−

Exercise 2


-2 0 2


x 5)( 3 += x y

-20

2

Exercise 3

Complete the following table for theequation

i. 33 +−= x y x -1 -2 3


3)( 3 +−= x y

-1-23

ii. 12 3 −= x y x -1 -2 3


1)(2 3 −= x y -1-23




Example 4

Complete the following table for theequation 943 −−= x x y

-3 0 2-24 -9 -9


x 9)(4)( 3 −−= x x y -3 249)3(4)3( 3 −=−−−− 0 99)0(4)0( 3 −=−− 2 99)2(4)2( 3 −=−−

Exercise 4


i. 733 +−= x x y

x -3 0 2 y


7)(3)( 3 +−= x x y

-30

2

ii. 3612 x x y −−=

x 1 0 2 y


x 3)()(612 x x y −−= 10

2




11.4: Reciprocal Function

Complete the following table below

Example 1:


equation y = x1

x -2 -1 1 2y -1/2 -1 1 1/2


x y-2 - ½-1 - 1/1 = -11 1/1 = 12 ½

Exercise:


1. y = - x2

x -2 -1 1 2

y


xy = -

x2

-2-112

2. y =3

x -2 -1 1 2y


xy =

3

-2-112




3. y = -

x2

1

x -2 -1 1 2y


xy = -

x21

-2-112

4. y =16

x -2 -1 1 2y


xy =

x16

-2-112




5. y = - x5

x -2 -1 1 2y


xy = -

x5

-2-112




11.21 : Quadratic Graph

Example :

a) Complete the following table for the equation 542 2 −−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 542 2 −−= x x y for 52 ≤≤− x

c) From your graph, find

i) the value of y, when x = -1.5ii) the values of x, when y= 0

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 0382 2 =+− x x for 52 ≤≤− x . State the values of x.

Answer For Example :

a) x = -1, y = 1x = 2, y = -5x = 4, y = 11

b) Refer graph on the next page

c) i) y = 5.5ii) x = -0.9, 2.9

d)

Therefore, the appropriate graph that should be drawn is

x 0 1y − 8 − 4

From the graph, the solutions of the equation are

x = 0.4, 3.65

x -2 -1 0 1 2 3 4 5 y 11 -5 -7 1 25

0382 2 =+− x x

382 2 −= x x

5438542 2 −−−=−− x x x x

84 −= x y

Rearrange the equationso that one side of theequation is 2 x2 − 4 x − 5

84 −= x y

0382 2 =+− x x




Graph for Example Quadratic Graph

-2 -1 0 1 2 3 4 5

-5

--10

5

10

15

20

25

y

x

x

x

x

x

x

x

x

x

x

x

y = 4x - 8




Exercise 1 :

a) Complete the following table for the equation 592 2 +−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 592 2 +−= x x y for 70 ≤≤ x

c) From your graph, findi) the value of y, when x = 1.7ii) the value of x, when y = 15

d) Draw a suitable straight line on your graph to find the values of x which satisfy the

equation 041022

=+− x x for 70 ≤≤ x . State the values of x.

Exercise 2 :

a) Complete the following table for the equation 752 2 −−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw the

graph of 7522

−−= x x y for 53 ≤≤− x c) From your graph, find

i) the value of y, when x = -2.5ii) the value of x, when y = 15

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 0472 2 =+− x x for 53 ≤≤− x . State the values of x.

Exercise 3:

a) Complete the following table for the equation ( ) 952 −−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of ( ) 952 −−= x x y for 53 ≤≤− x

c) Draw a suitable straight line on your graph to find the values of x which satisfy theequation ( ) x x x 24952 −=−− for 53 ≤≤− x . State the values of x.

x 0 1 2 3 4 5 6 75 -2 -5 1 10 40

x -3 -2 -1 0 1 2 3 4 526 0 -7 -10 -9 5 18

x -3 -2 -1 0 1 2 3 4 524 -2 -9 -12 -11 3 6




Exercise 4 :

a) Complete the following table for the equation 523 2 ++−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 523 2 ++−= x x y for 43 ≤≤− x

c) From your graph, findi) the value of y, when x = -0.5ii) the value of x, that satisfy the equation of 523 2 =− x x

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 02523 2 =−+ x x for 43 ≤≤− x . State the values of x.

Exercise 5 :

a) Complete the following table for the equation ( ) x x y −= 821


graph of ( ) x x y −= 821

for 70 ≤≤ x

c) Draw a suitable straight line on your graph to find the values of x which satisfy theequation ( ) 108 =− x x for 70 ≤≤ x . State the values of x.

Exercise 6 :

a) Complete the following table for the equation 2238 x x y −+=

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 2238 x x y −+= for 43 ≤≤− x

c) From your graph, findi) the value of y, when x = 1.35ii) the values of x, when y = -10

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 02632 2 =+−− x x for 43 ≤≤− x . State the values of x.

x -3 -2 -1 0 1 2 3 4-11 0 4 -16 -35

x 0 0.5 1 2 3 4 5 6 70 1.88 6 7.5 7.5 3.5

x -3 -2 -1 0 1 2 3 4-19 3 8 9 6 -12




Exercise 7 :




d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 01132 2 =−− x x for 53 ≤≤− x . State the values of x.

Exercise 8 :




d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 01332 2 =−− x x for 53 ≤≤− x . State the values of x.

x -3 -2 -1 0 1 2 3 4 5 y -34 -4 5 11 8 -10

x -3 -2 -1 0 1 2 3 4 5-36 -6 3 9 6 -12




11.31 : Cubic Graph

Example 1:

a) Complete the following table for the equation 583 +−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 583 +−= x x y for 43 ≤≤− x

c) From your graph, findi) the value of y, when x = -1.4

ii) the value of x, when y= 25d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 01123 =−− x x for 43 ≤≤− x . State the values of x.


a) x = -2, y = 13x = 1, y = -2x = 3, y = 8


c) i) y = 13. 5ii) x = 3.7

d)

Therefore, the appropriate graph that should be drawn is

x 0 1y 6 10

From the graph, the solutions of the equation are

x = − 0.1, 3.5

x -3 -2 -1 0 1 2 3 3.5 42 12 5 -3 19.9 37

01123 =−− x x

1123 += x x

58112583 +−+=+− x x x x64 += x y

Rearrange the equationso that one side of theequation is x3 − 8 x + 5

64 += x y

01123 =−− x x




Graph for Example Cubic Graph

-3 -2 -1 0 1 2 3 4

-5

5

10

15

20

25

30

35

40

y

x

x

x

x

xx

x

x

x

x

x

= y 64 + x




Exercise 1:


b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 5103 +−= x x y for 5.35.3 ≤≤− x

c) From your graph, find the value of y, when x = -2.5

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 6103 =− x x for 5.35.3 ≤≤− x . State the values of x.

Exercise 2:



c) From your graph, find the value of y, when x = -0.5

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 010103 =−− x x for 4.3 ≤≤− x . State the values of x.

Exercise 3:



c) From your graph, findi) the value of y, when x = 2.5ii) the values of negative x that satisfy the equation 7123 −= x x

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 02153 =+− x x for 44 ≤≤− x . State the values of x.

x -3.5 -3 -2 -1 0 1 2 3 3.5-2.9 8 14 5 -7 12.9

x -3 -2 -1 0 1 2 3 3.5 421 27 18 6 25.88 42

x -4 -3 -2 -1 0 1 2 3 4-9 16 18 7 -4 -9 23




Exercise 4:


b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 10 unit on the y-axis, drawthe graph of 6123 +−= x x y for 45 ≤≤− x

c) From your graph, findi) the value of y, when x = -2.5ii) the values of positive x, when y = 0

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 12123 =− x x for 44 ≤≤− x . State the values of x.

Exercise 5:

a) Complete the following table for the equation 1253 −−= x x y

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw thegraph of 1253 −−= x x y for 5.33 ≤≤− x

c) From your graph, findi) the value of y, when x = 0.8ii) the value of x which satisfies the equation 1253 =− x x

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 493 =− x x for 5.33 ≤≤− x . State the values of x.

x -5 -4 -3 -2 -1 0 1 2 3 4 y -59 -10 22 17 6 -5 -3 22

x -3 -2 -1.5 -1 0 1 2 3 3.5-10 -7.9 -8 -12 -16 0 13.4




11.41 : Reciprocal Graph

Example 1:

a) Complete the following table for the equation x

y 8=


graph of y8

= for 55 ≤≤− x

c) From your graph, findi) the value of y, when x = -3.2

ii) the value of x, when y = 4.4d) From the graph, state the values of x when x and y have a same value.


a) x = -5, y = -1.6x = -2.5, y = -3.2x = 1.6, y = 5


c) i) y = -2.6ii) x = 1.8

d) x = -2.7, 2.73

x -5 -4 -2.5 -1.6 -1 1 1.6 2.5 4 5-2 -5 -8 8 3.2 2 1.6




x

x

55

Graph for Example Reciprocal Graph

-2

-4

-6

-8

0

2

4

6

8

10

y

-1-2-3-4 1 2 3 4

x

x

x

x

x

x

x

x

x

x

x

y = x




Exercise 1:


y1

=


graph of y1

= for 44 ≤≤− x

c) From your graph, find the value of y, when x = -2.4d) Draw a suitable straight line on your graph to find the values of x which satisfy the

equation ( )0,11

≠=− x x for 44 ≤≤− x . State the values of x.

Exercise 2:

a) Complete the following table for the equation y6

−=


graph of y6

−= for 44 ≤≤− x

c) From your graph,i) find the value of y, when x = 1.3ii) find the value of x, when y = 3.5


equation x=+ 13

for 44 ≤≤− x . State the values of x.

Exercise 3:


y2

=


graph of y 2= for 44 ≤≤− x

c) From your graph,i) find the value of y, when x = 1.5ii) find the value of x, when y = -1.8


equation x

x4

12 =+ for 44 ≤≤− x . State the values of x.

x -4 -3 -2 -1 -0.5 0.5 1 2 3 4-0.25 -0.33 -1 -2 1 0.5 0.25

x -4 -2.5 -1 -0.6 0.6 1 2 3 41.5 6 10 -10 -6 -3 -1.5

x -4 -3 -2 -1 -0.5 0.5 1 2 3 4-0.5 -0.7 -1 -2 4 1 0.7 0.5




Exercise 4:


y4

=

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 2unit on the y-axis, draw the

graph of y4

= for 55 ≤≤− x

c) From your graph,i) find the value of y, when x = -1.4ii) find the value of x, when y = 4.4

d) Draw a suitable straight line on your graph to find the values of x which satisfy theequation 0

23

=− x x

for 45.0 ≤≤ x . State the values of x.

Exercise 5:

a) Complete the following table for the equation 123

+= y

b) By using a scale of 2 cm to 0.5 unit on the x-axis and 2cm to 0.5unit on the y-axis, draw

the graph of 123 += x

y for 45.0 ≤≤ x

c) From your graph,i) find the value of y, when x = 1.3ii) find the value of x, when y = 2.8


equation 023

=− x x

for 45.0 ≤≤ x . State the values of x.

x -5 -4 -2 -1 -0.5 0.5 0.8 1.5 2.5 5-1 -4 -8 8 5 1.6

x 0.5 1 1.5 2 2.5 3 3.5 44 2.5 1.75 1.6 1.43 1.38




PAST YEAR EXAMINATION QUESTIONS

1. Nov 2003, Q12

(a) Complete the following table for the equation y 4−= .

(b)

x -4 -2.5 -1 -0.5 0.5 1 2 3.2 4y 1 1.6 8 -8 -4 -1.25 -1

[2 marks ]

For this part of the question, use the graph paper. You may use a flexible curve.

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 x

y 4−= for -4 ≤ x ≤ 4.

[5 marks ](c) From your graph, find

(i) the value of y when x = 1.8,(ii) the value of x when y = 3.4.

[2 marks ](d)

(e) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation 324

+= x x

for -4 ≤ x ≤ 4.

State these values of x.[3 marks ]

2. July 2004, Q12

(a) Table 2 shows values of x and y which satisfy the equation 1053 +−= x x y .

x -3.4 -3 -2 -1 0 1 2 3 3.4y -12.3 k 12 14 10 6 m 22 32.3

TABLE 2 Calculate the value of k and of m. [2 marks ]

(b) For this part of the question, use the graph paper on page 33. You may use a flexible curve rule. 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 1053 +−= x x y for -3.4 ≤ x ≤ 3.4.


(i) the value of y when x = 0.7 ,(ii) the value of x when 01053 =+− x x .

[2 marks ]




(d) Draw a suitable straight line on your graph to find all the values of x whichsatisfy the equation 0263 =−− x x for -3.4 ≤ x ≤ 3.4.State these values of x.

[4 marks ]

Answer :

(a) k = ………………..

m = ……………….

(b) Refer graph on page 33

(c) (i) y = ………………..

(ii) x = ……………….

(d) x = ………………………………………………………………………………..

3. Nov 2004, Q12

(a) Table 1 shows values of x and y which satisfy the equation 342 2 −−= x x y .

x -2 -1 0 1 2 3 4 4.5 5y k 3 -3 -5 -3 m 13 19.5 27

Table 1Calculate the value of k and of m. [2 marks ]

(b) For this part of the question, use the graph paper. You may use a flexible curve. 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 342 2 −−= x x y for -2 ≤ x ≤ 5.


i. the value of y when x = -1.5,ii. the value of x when y = 0.

[2 marks ](d) Draw a suitable straight line on your graph to find a value of x which satisfies the

equation 0232 2 =−+ x x for -2 ≤ x ≤ 5.State this value of x.

[3 marks ]




4. Nov 2005, Q12

(a) Complete Table 2 for equation 32 2 −−= x x y .

x -2 -1 0.5 1 2 3 4 4.5 5y 7 -2 -2 3 12 33 42

Table 2[2 marks ]

(b) For this part of the question, use the graph paper. You may use a flexible curve. 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 32 2 −−= x x y for -2 ≤ x ≤ 5.


i. the value of y when x = 3.6,ii. the value of x when y = 37.

[2 marks ](d) Draw a suitable straight line on your graph to find all value of x which satisfy the

equation 1032 2 =− x x for -2 ≤ x ≤ 5.State these values of x.

5. July 2005, Q12

(a) Complete Table 1 in the answer space for the equation 223 x x y −−= .

[2 mark ] Answer :

(a)x -3 -2 -1 0 1 2 3 3.5 4y -12 -3 3 0 -7 -25 -33

TABLE 1

(b) For this part of the question, use the graph paper provided on page 33.

You may use a flexible curve rule.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 223 x x y −−= for -3 ≤ x ≤ 4.

[4 marks ] Answer :

(b) Refer graph on page 33 .

(c) From your graph, find(i) the value of y when x = 1.7 ,




(ii) the value of x when y = − 26 .

Answer :

(c) (i) y = ……………………….

(ii) x = ………………………

(d) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation 0221

18 2 =−+ x x for -3 ≤ x ≤ 4.

State these values of x.[4 marks ]

Answer :

(d) x = ………………………… , ……………………………

6. July 2006, Q12

(a) Complete Table 2 in the answer space for the equation 383 +−= x x y by writing down the values of y when x = -2 and 2 .

[2 marks ]

(b) For this part of the question, use the graph paper provided on page 35.

You may use a flexible curve rule.

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 383 +−= x x y for -3.5 ≤ x ≤ 3.5 .


(i) the value of y when x = − 0.7 ,(ii) the value of x when y = − 9 .

[2 marks ]

(d) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation 8133 −=

x x for -3.5 ≤ x ≤ 3.5 .State these values of x.[4 marks ]

Answer :

(a)x -3 -2 -1 0 1 2 3 3.5 4y -12 -3 3 0 -7 -25 -33

TABLE 1





(c) (i) y = ……………………….

(ii) x = ………………………

(d) x = ………………………… , ……………………………

7. Nov 2006, Q13

(a) Complete Table 1 in the answer space for the equation y = x24

by writing down

the value of y when x = -3 and x = 1.5. [2 marks ]

(b) For this part of the question, use the graph paper provided on page 35. You mayuse a flexible curve rule .

By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis,

draw the graph of y =24

for 44 ≤≤− x . [5 marks ]

(c) From your graph, findi. the value of y when x = 2.9

ii. the value of x when y = -13.

[ 2 marks ](d) Draw a suitable line on your graph to find a value of x which satisfies the

equation 2x 2 + 5x = 24 for 44 ≤≤− x .State this value of x.

[ 3 marks ]Answer :

(a)

x -4 -3 -2 -1 1 1.5 2 3 4y -6 -12 -24 24 12 8 6

TABLE 1

(b) Refer graph on page 35 (c) (i) y = ………………………………………..

(ii) x = ………………………………………..

(d) x = ……………………………..




8 Jun 2007 Q 16

(a) Complete Table 3 in the answer space for the equation 132 2 −+= x x y by writing down the values of y when x = –3 and x = 1 .

(b) For this part of the question, use the graph paper provided on page 37.You may use a flexible curve rule .

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 unitson the y-axis, draw the graph of 132 2 −+= x x y for 5.34 ≤≤− x .

(c) From your graph, find

(i) the value of y when x = – 3.6 ,

(ii) the value of x when y = 24 .

(d) Draw a suitable straight line on your graph to find the values of x which satisfiy the equation 072 2 =−+ x x for 5.34 ≤≤− x .State these values of x .

Answer :

(a)

x – 4 –3 –2 –1 0 1 2 2.6 3.5 y 19 1 –2 –1 13 20.3 34


(c) (i) y = …………………………………….

(ii) x = …………………………………….

(d) x = …………………………. , …………………………….

[2 marks ]

[4 marks ]

[2 marks ]

[4 marks ]




9 November 2007 Q 12

(a) Complete Table 1 in the answer space for the equation 36 x y −= by writing down the values of y when x = –1 and x = 2 .

(b) For this part of the question, use the graph paper provided on page 23.You may use a flexible curve rule .

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 unitson the y-axis, draw the graph of 36 x y −= for 5.23 ≤≤− x .

(c) From your graph, find

(i) the value of y when x = 1.5 ,

(ii) the value of x when y = 10 .

(d) Draw a suitable straight line on your graph to find the values of x which satisfiy the equation 36 x y −= for 5.23 ≤≤− x .State these values of x .

Answer :

(a)

x – 3 –2.5 –2 –1 0 1 2 2.5 y 33 21.63 14 6 5


(c) (i) y = …………………………………….

(ii) x = …………………………………….

(d) x = …………………………. , …………………………….

[2 marks ]

[4 marks ]

[2 marks ]

[4 marks ]




10 Jun 2008 Q 12

(a) Complete Table 12 in the answer space for the quation 343 +−= x x y by writing down the values of y when x = –1 and x = 2 .

(b) For this part of the question, use the graph paper provided on page 25You may use a flexible curve rule .

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 unitson the y-axis, draw the graph of 343 +−= x x y for 45.3 ≤≤− x .

(c) From your graph in 12( b), find

(i) the value of y when x = – 0.7 ,

(ii) the value of x when y = 25 ,

(d) Draw a suitable straight line on the graph in 12( b) to find the values of x which satisfiy the equation 017163 =−− x x for .45.3 ≤≤− x State these values of x .

Answer :

(a) x –3.5 –3 –2 –1 0 1 2 3 4

y –25.9 –12 3 3 0 18 51


(c) (i) y = …………………………………….

(ii) x = …………………………………….

(d) x = …………………………. , …………………………….

[2 marks ]

[4 marks ]

[2 marks ]

[4 marks ]




11 Nov 2008 Q 12

(a) Complete Table 12 in the answer space for the quation y36

= by writing down the values of y when x = 6 and x = 10 .

(b) For this part of the question, use the graph paper provided on page 23 . You may use a flexible curve rule .

Using a scale of 1 cm to 1 unit on the x-axis and 1 cm to 1 unit

on the y-axis, draw the graph of y36

= for 142 ≤≤ x .

(c) From your graph in 12( b), find

(i) the value of y when x = 2.8 ,

(ii) the value of x when y = 5 ,

(d) Draw a suitable straight line on the graph in 12( b) to find the values of x

which satisfiy the equation 01436

=−+ x x

for .142 ≤≤ x

State these values of x .

Answer :

(a) x 2 2.4 3 4 6 8 10 12 14

y 18 15 12 9 4.5 3 2.6


(c) (i) y = …………………………………….

(ii) x = …………………………………….

(d) x = …………………………. , …………………………….

[2 marks ]

[4 marks ]

[2 marks ]

[4 marks ]




ANSWERS

1 SPM 2003(N)

(a) 4 , – 2

(b) Graph

(c) (i) y = – 2.2 (ii) x = – 1.2

(d) 32 −−= x y , x = – 2.3 , 0.85

2 SPM 2004(J)

a) k = – 2 , m = 8

(b) Graph

(c) (i) y = 6.8 (ii) x = – 2.9

(d) 122 += x y , x = – 2.25 , – 0.32 , 2.6

3 SPM 2004(N)

(a) k = 13 , m = 3

(b) Graph

(c) (i) y = 7 (ii) x = 2.6 , – 0.5

(d) 205 +−= x y , 3.1 ≤ x ≤ 3.2

4 SPM 2005(J)

(a) 2 , – 18

(b) Graph(c) (i) y = – 4.7 (ii) x = 3.55

(d) 723

−−= x y , x = – 2.85 , 3.1




5 SPM 2005(N)

(a) 0 , 25

(b) Graph

(c) (i) y = 19 (ii) x = 4.7

(d) 72 += x y , x = – 1.6 , 3.1

6 SPM 2006(J)

(a) y = 11 , y = – 5

(b) Graph

(c) (i) y = 8 (ii) x = – 3.4

(d) 55 −= x y , x = 0.64 , x = 3.24 ,

7 SPM 2006(N)

(a) y = – 8 , y = 16

(b) Graph

(c) (i) y = 8 (ii) x = – 1.85

(d) 52 += x y , x = 2.45

8 SPM 2007(J)

(a) y = 8 , y = 4

(b) Graph

(c) (i) y = 14 (ii) x = 2.85

(d) 62 += x y , x = – 2.14 , x = 1.64 ,



9 SPM 2007(N)

(a) y = 7 , y = – 2

(b) Graph

(c) (i) y = 2.5 (ii) x = – 1.65

(d) x y 8−= , x = – 0.8 , x = – 2.4 ,

10 SPM 2008(J)

(a) y = 7 , y = – 2

(b) Graph

(c) (i) y = 2.5 (ii) x = – 1.65

(d) x y 8−= , x = – 0.8 , x = – 2.4 ,

11 SPM 2008(N)

(a) y = 6 , y = 3

(b) Graph

(c) (i) y = 5.5 (ii) x = 3.75

(d) 2012 += x y , x = – 3.3

form 5 _ maths - chapter 2

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