WASSCE Mock Examination

Core Mathematics — Papers 1 and 2 with Marking Scheme

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 .

(A)      0.18    (B) 1.8    (C) 18    (D) 0.018

2. Express 0.000472 in standard form.

(A)          (B)     (C)     (D)

3. Simplify .

(A)      2    (B) 4    (C) 3    (D)

4. Evaluate .

(A)      3    (B) 1    (C) 2    (D) 8

5. Solve .

(A)         (B)     (C)     (D)

6. Make  the subject of the formula .

(A)          (B)     (C)     (D)

7. Factorize .

(A)         (B)     (C)     (D)

8. Find the roots of the equation .

(A)      or     (B)  or     (C)  or     (D)  or

9.  varies inversely as . If  when , find  when .

(A)      1    (B) 2    (C) 8    (D) 16

10. Find the equation of the straight line through  with gradient .

(A)         (B)     (C)     (D)

11. If  and , find the value of .

(A)      1    (B) 2    (C) 3    (D) 5

12. Each exterior angle of a regular polygon is . How many sides does the polygon have?

(A)      8    (B) 9    (C) 10    (D) 12

13. An arc of a circle subtends an angle of  at the centre. What angle does the same arc subtend at the circumference?

(A)          (B)     (C)     (D)

14. In a right-angled triangle the hypotenuse is 13 cm and one of the other sides is 5 cm. If  is the angle opposite the 5 cm side, find .

(A)          (B)     (C)     (D)

15. The bearing of  from  is . What is the bearing of  from ?

(A)          (B)     (C)     (D)

16. Find the volume of a cylinder of radius 7 cm and height 10 cm. (Take )

(A)      154 cm³    (B) 440 cm³    (C) 1540 cm³    (D) 3080 cm³

17. A sector of a circle of radius 7 cm has an angle of . Find the length of its arc. (Take )

(A)      8.8 cm    (B) 44 cm    (C) 7.7 cm    (D) 17.6 cm

18. Two fair dice are thrown together. Find the probability that the sum of the scores is 7.

(A)          (B)     (C)     (D)

19. Find the median of the numbers 3, 7, 2, 9, 5, 8, 4.

(A)      4    (B) 7    (C) 5    (D) 6

20. In a class of 40 students, 22 offer Art (), 18 offer Biology () and 8 offer both. How many offer neither subject?

(A)      6    (B) 10    (C) 12    (D) 8

21. Find the 10th term of the sequence

(A)      39    (B) 43    (C) 35    (D) 40

22. Evaluate .

(A)      3    (B) 6    (C) 9    (D) 18

23. Simplify .

(A)         (B)     (C)     (D) 34

24. Solve the inequality .

(A)         (B)     (C)     (D)

25. A trader buys an article for GH¢80 and sells it for GH¢100. Calculate his percentage profit.

(A)      20%    (B) 80%    (C) 120%    (D) 25%

Paper 2: Theory

Section A (Compulsory: 40 marks)

Answer all questions in this section.

1. (a) Evaluate . [4 marks]

(b)       GH¢5,000 is invested at 8% simple interest per annum. Find the total amount after 3 years. [3 marks]

(c)      If  and , evaluate . [3 marks]

2. (a) Solve the equation . [4 marks]

(b)       The sum of two numbers is 17 and their product is 60. Find the numbers. [6 marks]

3. In triangle ,  cm,  cm and . Calculate, correct to 2 decimal places:

(a)     the length of ; [5 marks]

(b)       the area of the triangle. [5 marks]

4. The table shows the scores of 25 students in a quiz.

Calculate:

(a)       the mean score; [4 marks]

(b)       the median score; [2 marks]

(c)       the modal score; [1 mark]

(d)       the probability that a student chosen at random scored at least 4. [3 marks]

Section B (Answer any TWO questions: 40 marks)

5. The points  and  have coordinates  and  respectively. Find:

(a)     the gradient of ; [3 marks]

(b)     the equation of the line ; [5 marks]

(c)      the coordinates of the midpoint  of ; [3 marks]

(d)     the length of , leaving your answer as a surd in its simplest form; [4 marks]

(e)     the equation of the line through  perpendicular to . [5 marks]

6. A sector of a circle of radius 21 cm subtends an angle of  at the centre. (Take .) Calculate:

(a)       the length of the arc of the sector; [3 marks]

(b)       the area of the sector; [4 marks]

(c)       the sector is bent to form a cone so that the arc becomes the circumference of the base. Find the radius of the base of the cone; [4 marks]

(d)       the vertical height of the cone, correct to 1 decimal place; [4 marks]

(e)       the volume of the cone, correct to the nearest cm³. [5 marks]

7. (a)  varies partly as  and partly as . If  when  and  when , find the relationship between  and , and hence find  when . [8 marks]

(b)     Solve the inequality  and list the integer values of  that satisfy it. [6 marks]

(c)       Solve the simultaneous equations

             [6 marks]

8. A ship sails from a port  a distance of 12 km on a bearing of  to a point . It then sails 9 km on a bearing of  to a point .

(a)       Show that . [4 marks]

(b)     Calculate the distance . [4 marks]

(c)      Calculate the bearing of  from , correct to the nearest degree. [6 marks]

(d)     Find the bearing of  from . [3 marks]

(e)     The ship returns directly from  to  at a speed of 30 km/h. How long does the journey take? [3 marks]

Marking Scheme

Paper 1: Answer Key and Working

Paper 2, Section A

Question 1 (10 marks)

(a)       Convert and subtract:

Question 2 (10 marks)

(a)     Let the numbers be  and , so  and . [2]

             The numbers are 5 and 12. [1]

Question 3 (10 marks)

(a)       By the cosine rule:

Question 4 (10 marks)

(a)       The median is the 13th value, which is 3. [2]

(b)       The mode is the score with the highest frequency, which is 3. [1]

Paper 2, Section B

Question 5 (20 marks)

(a)       Perpendicular gradient . [1]

Question 6 (20 marks)

(a)       The arc equals the base circumference:

(b)     The slant height is the radius of the sector,  cm.

Question 7 (20 marks)

(a)       Let .

          Subtracting gives  and . [2]

          When : . [1]

          Integer values: . [2]

(b)     Multiply the first equation by 6: . [2] Substitute :

Question 8 (20 marks)

(a)     The bearing of  from  is . [2]

(b)       By Pythagoras’ theorem: