WASSCE Mock Examination 2

Core Mathematics — Papers 1 and 2 (Questions)

Paper 1: Objective Test

Instructions: Answer all questions. Each question has four options lettered A to D. Choose the correct option. Each question carries 1 mark.

1. Evaluate 2.4×1056×102.

(A) 40    (B) 400    (C) 4000    (D) 4

2. Express 0.375 as a fraction in its lowest terms.

(A) 35    (B) 37100    (C) 58    (D) 38

3. Simplify 32n+132n−1.

(A) 9    (B) 3    (C) 6    (D) 34n

4. Given that log102=0.3010, find log10200.

(A) 0.6020    (B) 1.3010    (C) 2.3010    (D) 3.3010

5. Solve 2x−15=x+43.

(A) x=17    (B) x=21    (C) x=23    (D) x=19

6. Make g the subject of the formula T=2πlg.

(A) g=T24π2l    (B) g=4π2lT2    (C) g=2πlT    (D) g=4πlT2

7. Expand (2x−3)2.

(A) 4x2−9    (B) 4x2−6x+9    (C) 2x2−12x+9    (D) 4x2−12x+9

8. Solve the equation x2−7x+12=0.

(A) x=−3 or −4    (B) x=3 or 4    (C) x=2 or 6    (D) x=−3 or 4

9. y varies directly as x and inversely as z. If y=6 when x=4 and z=2, find y when x=10 and z=3.

(A) 10    (B) 8    (C) 6    (D) 12

10. Find the gradient of the line 3x+4y=12.

(A) 34    (B) 43    (C) −34    (D) −43

11. If x+2y=7 and 3x−y=7, find the value of x.

(A) 1    (B) 2    (C) 4    (D) 3

12. Find the size of each interior angle of a regular octagon.

(A) 120∘    (B) 135∘    (C) 140∘    (D) 150∘

13. One angle of a cyclic quadrilateral is 105∘. Find the angle opposite to it.

(A) 75∘    (B) 105∘    (C) 85∘    (D) 95∘

14. If sinθ=35 and θ is acute, find cosθ.

(A) 34    (B) 54    (C) 53    (D) 45

15. The angle of elevation of the top of a tower from a point 25 m away on level ground is 45∘. Find the height of the tower.

(A) 12.5 m    (B) 35.4 m    (C) 25 m    (D) 50 m

16. Find the volume of a cone of base radius 3 cm and height 7 cm. (Take π=227)

(A) 198 cm³    (B) 66 cm³    (C) 132 cm³    (D) 22 cm³

17. Find the area of a trapezium whose parallel sides are 8 cm and 12 cm and whose height is 5 cm.

(A) 100 cm²    (B) 40 cm²    (C) 60 cm²    (D) 50 cm²

18. A bag contains 5 red, 3 green and 2 white balls. A ball is picked at random. Find the probability that it is not green.

(A) 710    (B) 310    (C) 12    (D) 45

19. The mean of five numbers is 12. When a sixth number, 18, is added, what is the new mean?

(A) 12    (B) 14    (C) 13    (D) 15

20. If A={1,2,3,4,5,6} and B={2,4,6,8}, find n(A∪B).

(A) 10    (B) 7    (C) 8    (D) 6

21. Find the sum of the first 8 terms of the arithmetic progression 2,5,8,…

(A) 100    (B) 86    (C) 92    (D) 112

22. Evaluate 8−13.

(A) −2    (B) 2    (C) −12    (D) 12

23. Express 63 with a rational denominator.

(A) 63    (B) 3    (C) 23    (D) 32

24. Solve the inequality 2(x−1)≤3x+1.

(A) x≤−3    (B) x≥−3    (C) x≥3    (D) x≤3

25. Find the simple interest on GH¢2,000 for 4 years at 5% per annum.

(A) GH¢400    (B) GH¢100    (C) GH¢200    (D) GH¢2,400

Paper 2: Theory

Section A (Compulsory: 40 marks)

Answer all questions in this section.

1. (a) Evaluate 35+12÷56. [4 marks]

2. A shopkeeper marks an article at GH¢250 and allows a discount of 12%. Find the selling price. [3 marks]

3. Express 1x−1x+2 as a single fraction in its simplest form. [3 marks]

2. (a) Solve the equation 3x2−7x+2=0. [4 marks]

2. Solve the simultaneous equations 2x+3y=12 and 5x−2y=11. [6 marks]

3. In triangle XYZ, XY=12 cm, ∠X=40∘ and ∠Y=75∘.

1. Find ∠Z; [1 mark]

2. Calculate the length of YZ, correct to 2 decimal places; [5 marks]

3. Calculate the area of the triangle, correct to 3 significant figures. [4 marks]

4. A bag contains 3 red, 4 blue and 5 yellow balls. Two balls are drawn at random, one after the other, without replacement. Find the probability that:

1. both balls are red; [3 marks]

2. both balls are of the same colour; [4 marks]

3. one ball is blue and the other is yellow. [3 marks]

Section B (Answer any TWO questions: 40 marks)

5. (a) The 3rd term of an arithmetic progression (AP) is 11 and the 8th term is 31. Find the first term and the common difference. [6 marks]

2. Calculate the sum of the first 20 terms of the AP. [4 marks]

3. Which term of the AP is equal to 99? [3 marks]

4. The first term of a geometric progression (GP) is 5 and the common ratio is 2. Find:

  (i) the 6th term; [3 marks]

  (ii) the sum of the first 6 terms. [4 marks]

6. A solid right triangular prism has a base which is a right-angled triangle with perpendicular sides 6 cm and 8 cm. The length of the prism is 15 cm.

1. Find the length of the hypotenuse of the triangular base; [2 marks]

2. Calculate the volume of the prism; [4 marks]

3. Calculate the total surface area of the prism; [5 marks]

4. The prism is melted and recast into a solid cylinder of radius 7 cm. Find the height of the cylinder, correct to 2 decimal places. (Take π=227) [4 marks]

5. Calculate, correct to 1 decimal place, the angle between the hypotenuse and the 8 cm side of the triangular base. [5 marks]

7. (a) The length of a rectangle is 3 cm more than its width. The area of the rectangle is 70 cm².

  (i) Taking the width as w cm, form an equation in w; [3 marks]

  (ii) Solve the equation and hence find the dimensions of the rectangle; [4 marks]

  (iii) Find the length of a diagonal of the rectangle, correct to 2 decimal places. [3 marks]

2. (i) Express x2−6x+5 in the form (x−p)2+q; [4 marks]

  (ii) hence state the minimum value of x2−6x+5 and the value of x at which it occurs; [3 marks]

  (iii) solve x2−6x+5=0. [3 marks]

8. In a survey of 80 people, 45 like rice (R), 40 like yam (Y), and 10 like neither. Let x be the number who like both.

1. Find the value of x; [5 marks]

2. Find the number of people who like rice only and the number who like yam only; [4 marks]

3. If one person is chosen at random, find the probability that the person likes exactly one of the two foods; [3 marks]

4. The mean of six numbers is 8. When a seventh number is added, the mean becomes 9. Find the seventh number; [4 marks]

5. The resistance R of a wire varies directly as its length l and inversely as the square of its diameter d. If R=8 when l=20 and d=2, find R when l=36 and d=3. [4 marks]