LINEAR LAW

PAPER 1

1 x and y are related by the equation , where p and q are constants. A

straight line is obtained by plotting

, as shown in Diagram 1.

Calculate the value of p and q. [4 marks]

DIAGRAM 1

Answer: ……………………………

……………………………

2. Diagram 2 shows a straight line graph of

. Given that ,

calculate the value of and of . [3 marks]

DIAGRAM 2

Answer: ……………………………

• (2, )

• (, 1)

O

x

……………………………

3. The variables x and y are related by the equation , where k is a constant.(a) Convert the equation to linear form.(b) Diagram 3 shows the straight line obtained by plotting against

. Find the value of (i) (ii) . [4 marks]

DIAGRAM 3

Answer: (a) ……………………………….

(b) (i)

……………………………

(ii) …………………………...

4Diagram 4 shows the graph of against .

Express y in terms of .

[3 marks]

DIAGRAM 4

2

• (4, 13)

x

y

x

1

(, 3) •

O

O

(2, h)

• (, 3)

O

Answer: ………………………………….

5

DIAGRAM 5(a) DIAGRAM 5(b)

Diagram 5(a) shows the curve y = –3 + 5. Diagram 5(b) shows the straight line graph obtained when y = –3 + 5 is expressed in the linear form Y = 5X + c.Express X and Y in terms of x and /or y [3 marks]

Answer: ………………………………….

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PAPER 2

6. Table 1 shows the values of two variables related by the equation , where a and b are constants.

3 4 5 6 812.1 6.46 3.47 1.89 0.52

TABLE 1(a) Draw the graph of against . [4 marks]

(b) From your graph, find (i) the value of y when (ii) the value of (iii) the value of . [6 marks]

7. Table 2 shows the values of two variables, x and y, obtained from an experiment. Variables x and y are related by the equation y = p , where p and k are constants.

2 4 6 8 10 123.16 5.50 9.12 16.22 28.84 46.77

TABLE 2(a) Plot against x by using a scale of 2 cm to 2 units on the x-axis and 2 cm to 0.2

unit on the -axis.Hence, draw the line of best fit. [4 marks]

(b) Use your graph from (a) to find the value of (i) p(ii) k [6 marks]

8. Table 3 shows the values of two variables, x and y, obtained from an experiment. It is known that x and y are related by the equation , where p and k are constants.

1.5 2.0 2.5 3.0 3.5 4.01.59 1.86 2.40 3.17 4.36 6.76

TABLE 3(a) Plot against .

Hence, draw the line of best fit. [5 marks]

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(b) Use the graph in (a) to find the values of (i) (ii) . [5 marks]

9. Table 4 shows the values of two variables, x and y, obtained from an experiment. The

variables x and y are related by the equation , where p and r are constants

1.0 2.0 3.0 4.0 5.0 5.55.5 4.7 5.0 6.5 7.7 8.4

TABLE 4

(a) Plot against , by using a scale of 2 cm to 5 units on both axes. Hence, draw the line of best fit. [5 marks]

(b) Use your graph from (a) to find the value of (i) (ii) . [5 marks]

10. Table 5 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by the equation where p and k are constants

1 2 3 4 5 64.0 5.7 8.7 13.2 20.0 28.8

TABLE 5

(a) Plot log y against (x+1), using a scale of 2 cm to 1 unit on the (x+1)-axis and 2 cm to 0.2 unit on the log y-axis. Hence, draw the line of best fit.

[5 marks]

(b) Use your graph from (a) to find the value of (i) (ii) k. [5 marks]

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Linear Law

Answer

1. 2. 3. (a)

(b) (i) 3 (ii) 114

5. X =

Y =

6. x -1 2 3 4 5 7

Log10y 1.08 0.81 0.54 0.28 -0.28

(b) (i) y = 1 (ii) a = 42.66 (iii) b = 0.5337

6

7 (a)x 2 4 6 8 10 12

Log10y 0.50 0.74 0.96 1.21 1.46 1.67

(b) (i) p = 1.920(ii) k = 1.309

8 (a)

2.25 4.0 6.25 9.0 12.25 16.0

0.20 0.27 0.38 0.50 0.64 0.83

(b) (i) (ii)

7

9(a)1 4 9 16 25 30.25

5.5 9.4 15 26 38.5 46.2

(b) (i) (ii)

10. (a)x+1 2 3 4 5 6 7

Log y 0.60 0.76 0.94 1.12 1.30 1.46

(b) p = 1.778 k = 1.483

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