The table shows experimental values of variables x and y. x 2 2.5 3 3.5

y 18.8 29.6 46.9 74.1

By plotting a suitable straight-line graph on a grid, show that x and y are related by the equation y=ab^x, where a and b are constants.

(4 marks) B) Find the value of a and b.

1 (CIE 2012, s, paper 11, question 7)

The table shows values of variables

x

and

y

.

x

1

3

6

10

14

y

2.5

4.5

0

–

20

–

56

(i) By plotting a suitable straight line graph, show that

y

and

x

are related by the equation

y

=

A

x

+

B

x

2

,

where

A

and

B

are constants. [4]

(ii) Use your graph to find the value of

A

and of

B

.

[4]

2 (CIE 2012, s, paper 22, question 7)

The table shows experimental values of variables

x

and

y

.

x

5

30

150

400

y

8.9

21.9

48.9

80.6

(i) By plotting a suitable straight line graph, show that

y

and

x

are related by the equation

y

=

a

x

b

,

where

a

and

b

are constants. [4]

(ii) Use your graph to estimate the value of

a

and of

b

.

[4]

3 (CIE 2012, w, paper 11, question 10)

The table shows values of the variables

x

and

y

.

x

∘

10

30

45

60

80

y

11.2

16

19.5

22.4

24.7

(i) Using the graph paper below, plot a suitable straight line graph to show that, for 10°

≤

x

≤

80°,

√

y

=

A

sin

x

+

B

,

where

A

and

B

are positive constants. [4]

(ii) Use your graph to find the value of

A

and of

B

.

[3]

(iii) Estimate the value of

y

when

x

=

50.

[2]

(iv) Estimate the value of

x

when

y

=

12.

[2]

4 (CIE 2012, w, paper 22, question 8)

Step-by-step explanation:

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.