# 2023 WASSCE: Likely Core Mathematics Questions

All 2023 WASSCE candidates must solve the following likely core mathematics questions. These questions were set based on some analysis and patterns of how WAEC set their questions.

The questions were also set based on some confirmed topics from WAEC such as;

1. Sets and binary operation

2. Modular arithmetic

3. Statistics & Probability

4. Logarithm and indices

5. Mensuration 1&2

6. Business mathematics [profit loss, depression, ratio]

7. Trigonometry

8. Bearing and vectors

9. Simultaneous equations.

10. Matrix and coordinate geometry (equation of a line)

11. Logic Reasoning

12. Transformation

13. Quadratic graphs, quadratics & functions

14. Series & Sequence

**The Questions Are As Follows**;

### Candidates Should Also Solve The Following Questions

**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..