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1. A square pyramid and a cuboid have the same height and the areas of their bases are equal.

Find the ratio of their volumes

1/3

1/2

1/4

1/8

1/6

2. The locus of a point which is equidistant from the lines y - x = 0 and y + x = 0, for x > 0, is the

line x = y

line y = 1

y-axis

line x = 1

x-axis

3. Reduce each number in the following expressions to two significant figures and then evaluate:

(0.04371 × 2.44913) ÷ 0.047512

2.2

1.8

2.6

1.6

2.4

4. Solve the simultaneous equations:

2/x + 1/y = 3 3/x - 2/y = 8

x = 1, y = 2

x = 1/2, y = 1

x = 1, y = -2

x = -1, y = 2

x = 1/2, y = -1

5. If Sin θ = -0.6 and Tan θ > 0,

then Sec θ is equal to

0.8

-5/3

-1.25

1.25

-0.8

6. A cylindrical metal rod of radius 10cm and length 35cm is to be melted down and recast into circular cones of base radius 7cm and height 15cm. If π = 22/7, the maximum number of cones which can be cast from the original material is

12

18

7

5

14

7. A clerk is allowed 10% of her income tax-free and pays 15% on the remainder. If her tax amounts to £2,970, what is her income?

£22,000

£28,000

£24,000

£20,000

£25,000

8. A pump P can fill a water tank in 5hrs. With a second pump Q also operating, the tank can be filled in 2hrs. Pump Q operating alone can fill the tank in

4hrs

2hrs

3hrs

10/3hrs

7/2hrs

9. When the monthly budget for a household is displayed on a pie chart, the sectorial angles for the various items of expenditure are as follows: Food (162°), Education (90°), Transportation (36°), Clothing (x°), and miscellaneous (18°). If £900 is the amount budgeted for clothing, then the education budget is

£1,500

£1,250

£2,000

£900

£1,800

10. Four of the interior angles of a pentagon are equal and each is twice the fifth angle. What is the value of each of the four equal angles?

75°

120°

135°

90°

60°

11.

Solve the equation:

9^{(1 + 2k)} = 81^{(2 + k) }/ 3^{k}

2

4

-6

-4

6

12. A worker employed in 1992 on a salary of $50,000 a year had his salary increased annually in arithmetic progression. If his salary in 1997 was $80,000, what was his salary in 1995?