Core Mathematics paper of the 2023 WASSCE will be written on Thursday, 14th September, 2023. It will be the third core subject to be written.

All final year students should try and solve these likely core mathematics questions before 14th September, 2023

QUESTION ONE

1. (a) Solve: 7x + 4 < (4x + 3)

(b) Salem, Sunday and Shaka shared a sum of ¢ 1,100.00. For every ¢2.00 that Salem gets, Sunday gets fifty kobo and for every ¢ 4.00 Sunday gets, Shaka gets ¢ 2.00. Find Shaka’s share.

QUESTION TWO

(a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.

(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.

QUESTION THREE

(a) A boy 1.2 m tall, stands 6 m away from the foot of a vertical lamp pole 4.2 m long. If the lamp is at the tip of the pole, represent this information in a diagram.

(b) Calculate the:

(i) length of the shadow of the boy cast by the lamp;
(ii) angle of elevation of the lamp from the boy, correct to the nearest degree.

QUESTION FOUR

(a) The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be 2 : 1?

(b) The arithmetic mean of x, y and z is 6 while that of x, y, z, t, u, v and w is 9. Calculate the arithmetic mean of t, u, v and w.

QUESTION FIVE

A point H is 20m away from the foot of a tower on the same horizontal ground. From point H, the angle of elevation of point (P) on the tower and the top (T) of the tower are 30° and 50° respectively. Calculate, and correct 3 significant figures:

(a) /PT/;
(b) The distance between H and the top of the tower;
(c) The position of H if the angle of depression of H from the top of the tower is to be 40°.

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QUESTION SIX

In the diagram, /AB/ = 8 km, /BC/ = 13 km, the bearing of A from B is 310° and the bearing of B from C is 230°. Calculate, correct to 3 significant figures,

(a) the distance AC;

(b) the bearing of C from A;

(c) how far east of B, C is

QUESTION SEVEN

(a) In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 Mathematics and Accounts only, 6 Mathematics only, 9 Accounts only, 2 Accounts and Economics only. If each student offered at least one of the subjects.

i. How many students failed in all the subjects?

ii. Find the percentage number who failed in at least one of Economics and Mathematics;

(b) Calculate the probability that a student selected at random failed in Accounts.

OBJECTIVES.

1. In a school, 180 students offer mathematics or physics, or both. If 125 offer mathematics and 105 offer physics. How many students offer mathematics only?
A.75     B. 80     C. 55     D. 125.

2. Find the value of x for which 3(24x + 3) = 96
A. 2     B. -2    C. ½    D. -1/2

3. The cost of renovating a 5m square room is ¢500. What is the cost of renovating a 10m square room?
A. ¢1,000  B. ¢2,500  C. ¢2,000  D. ¢10,000

4. Find the rate of change of the total surface area S of a sphere with respect to its radius r when r = 2
A. 8     B. 16     C. 10     D. 14

5. Differentiate (cosӨ + sinӨ)2 with respect to Ө.
A. 2cos2Ө    B. 2sin2Ө   C. -2cos2Ө    D. -2sin2Ө

6. A binary operation * on the set of rational numbers is defined as x * y = 2x + [x3 – y3/x + y]. find -1*2
A. 11    B. -11    C. 8    D. -8

7. A polynomial in x whose zeroes are 2, 1 and -3 is ______
A. x3 – 7x + 6
B. x3 + 7x – 6
C. x3 – 7x – 6
D. x3 + 7x + 6

8. Find the range of values of x for which 7x – 3 > 3x + 4
A. x < 7/4
B. x > 7/4
C. 7x < 4
D. -4x < 7

9. Some red balls were put in a basket containing 12 white balls and 16 blue balls. If the probability of picking a red ball from the basket is 3/7, how many red balls were introduced?
A. 13 B.20 C. 12 D. 21

10. Convert 12314 to a number in base 6.
A. 1056
B. 3016
C. 1036
D. 5016

11. Find the slope of the curve y = 3×3 + 5×2 – 3 at (-1, 5).
A. 1 B. -1 C. 19 D. -19

12. Find the area of the region bounded by y = x2 + x – 2 and x-axis.
A. 9/2 B. -39/6 C. 8/3 D. 16/3

13. The minimum value of y = x2 – 4x – 5 is ______
A. 2 B. -2 C.13 D. -13

14. There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
A. 3/4    B. 1/3     C. 2/3    D. 1/4

15. H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.
A. H = p /4y^2

B. H = 2p / y^2

C. H = p / 2 y^2

D. H = p / y^2

16. Solve 4x^2 – 16x + 15
A. X = 1 (1/2) or X = -2 (1/2)

B. X = 1 (1/2) or X = 2 (1/2)

C. X = 1 (1/2) or X = -1 (1/2)

D. X = -1 (1/2) or X = -2 (1/2)

17. If (0.25)^y = 32, find the value of y.
A. y = -5/2  B. y = -3/2  C. y = 3/2 D. y = 5/2.

18. Simplify: log 6 – 3log 3 + 2/3log 27.
A. 3log 2   B. Log 2    C. Log 3   D. 2log 3

19. Bala sold an article for 6,900.00 nairas and made a profit of 15 percent. Calculate his percentage profit if he had sold for 6600.00.
A. 5 percent     B. 10 percent    C. 12 percent   D. 13 percent