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1. 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

2hrs

10/3hrs

3hrs

7/2hrs

4hrs

2. Find the lower and upper quartiles for the set of numbers

4, 7, 8, 10, 12, 15, 17, 20, 26, 32, 40

8, 20

8, 26

10, 20

7, 32

7, 20

3. If a = x^{1/3}, find log_{a}x^{3}

3

1/3

9

1/9

1

4. The greatest value of an integer x which satisfies the inequality 2 - 4x > 15 is

-4

4

3

-2

-3

5. A ball has diameter 20cm. What is the volume of the ball, correct to two significant figures?

4,200 cm³

5,000 cm³

3,500 cm³

4,000 cm³

6,000 cm³

6. The expression (x² - 6x + 9)/x(x² - 9) is undefined for

x = 0, 3 or -3

x = 0 or -3

x = 0 or 9

x = 0 or 3

x = 3

7. Arrange the following numbers in ascending order of magnitude

5/6, 11/13, 0.837

5/6, 0.837, 11/13

0.837, 5/6, 11/13

11/13, 5/6, 0.837

0.837, 11/13, 5/6

5/6, 11/13, 0.837

8.

Evaluate:

81^{-1/4 } × 36^{1/2 }×10^{0}

10

0

3

1

2

9. A box contains purple, green and yellow balls in the ratio 8 : 3 : 2. There are 10 yellow balls.

If 10 green and 10 purple balls are removed from the bag, find the new ratio.

6 : 2 : 1

7 : 1 : 2

6 : 1 : 1

6 : 1 : 2

7 : 2 : 1

10. Tara received a cash gift from her parents on her 10th birthday. On each succeeding birthday, she received twice the amount received in the previous year.

If she had received a total of £31,500 by the time she was 15, the cash gift for her 12th birthday was

£2,000

£4,000

£3,000

£5,000

£1,000

11. In a mock quiz taken by 40 boys and y girls, the mean scores were 5.5 and 6 respectively. If the total score was 412, find the value of y

30

36

38

34

32

12. Solve the equation 4/(10+x) + 4/(10-x) = 5/6

-1, -2

-2 ,-2

1, 2

-2, 2

-2, 1

13. If 2 log_{4}P + log_{4}Q² = 0 , then P = ?

PQ

Q

Q/2

2/Q

1/Q

14. Jasmin invested a total of $200,000 in two companies which paid dividends of 5% and 7% respectively.

How much did she invest at 7% if she received a total of $11,600?

$160,000

$100,000

$140,000

$80,000

$120,000

15.

Evaluate:

log_{3}27 + log_{3}6 – log_{3}54

2

1

0

1/3

-21

16. Divide (2x³ - xy² + y³) by (x + y)

2x² + xy

2x² + 2xy + y²

2x² - 2xy + y²

2x² - 2xy

2x² - y²

17. Which of the following operations is/are NOT closed over the set of odd integers?

I. Division II. Subtraction III. Addition IV. Multiplication

I, II & III only

I & III only

none of the above

IV only

all of the above

18. Two siblings Taiwo and Kehinde went out to lunch at a restaurant. If Taiwo contributed 40% of the cost and Kehinde contributed the balance, which is £150, the cost of the lunch was

£300

£250

£280

£350

£375

19. The population of a school is 1,376. Express this to three significant figures.

138

1,376

1,380

1,470

1,370

20. A bucket in the form of a truncated cone of end radii 14cm and 21cm, and height of 30cm.