 # 2023 WAEC Mathematics Questions and Answers (Essay & OBJ): Free Success Guide

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## 2023 WAEC Mathematics Questions and Answers (Essay & OBJ)

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## 2023 WAEC Mathematics Questions and Answers

### 2023 WAEC Mathematics Question and Answer.

PAPER 2 [Essay]

1. (a) Solve: 7x + 4  < (4x + 3).

(b) Salem, Sunday and Shaka shared a sum of N 1,100.00. For every N2.00 that Salem gets, Sunday gets fifty kobo and for every N 4.00 Sunday gets, Shaka gets N 2.00. Find Shaka’s share?

2. (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.

3. (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.

4. 5. 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 30o and 50o 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°.

6. (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.

7. 8. (a)

9. 10. 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

### 2023 WAEC Mathematics Questions and Answers

11. (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.

12. ### 2023 WAEC Mathematics Questions and Answers

#### 2023 WAEC Mathematics Objective Questions.

PAPER 1 (Objective)
Answer ALL questions in this section.

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 N500. What is the cost of renovating a 10m square room?
A. N1,000       B. N2,500       C. 2,000       D. N10,000

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 = 3x3 + 5x2 – 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       B. 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

20. If 3P = 4Q and 9P = 8Q-12, find the value of PQ.
A. 12       B. 7       C. -7       D. -12

21. Evaluate 0.42 divided by 2.5 /0.5 x 2.05, leaving the answer in standard form.
A. 1.639 x 10^2       B. 1.639 x 10^1       C. 1.639 x 10^-1       D. 1.639 x 10^-2.

22. A husband contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum (p.a) and his wife earns N4,000 p.a, find the sum of their contribution
to the fund.
A. N1,045                B. N605         C. N545         D. N490.

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23. If the children share N10.50K among themselves in the ratio 6:7:8, How much is the largest share?
A. N3.00         B. N3.50         C. N4.00         D. N4.50.

24. A trader makes a loss of 15% when selling an article. Find the ratio, selling price: cost price.
A. 3:20         B. 3:17         C. 17:20         D. 20:23.

25. The ages of three men are in the ratio 3:4:5. If the difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men.
A. 45 years         B. 72 years         C. 108 years         D. 216 years.

26. A bicycle wheel of a radius of 42cm is rolled over a distance of 66m. How many revolutions does it make?
[Take π=22/7]
A. 2.5         B. 5         C. 25         D. 50.

27. If 2x : (x+1) =3:2, what is the value of x?
A. ½         B. 1         C. 1½         D. 3.

28. What is the probability of having an odd number in a single toss of a fair die?
A. 1/6         B. 1/3         C. ½         C. 2/3.

### 2023 WAEC Mathematics Questions and Answers   ## How to pass 2023 WAEC Maths exams

Below are the tips on how to answer 2023 WAEC Mathematics Objectives and Theory Questions easily:

1. Got to the venue of the Exams early
2. Avoid every distraction/disturbance during the exams period
3. Pray before the start of the exams
4. Carefully read and follow all the instructions provided on the questions paper
7. Start the theory questions with the questions you know best
8. Manage your time appropriately, avoid wasting time unnecessarily especially on the questions you don’t know
9. Attempt the required number of Questions

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