**WAEC GCE Mathematics questions and answers 2023. Welcome to 2023 WAEC Mathematics Questions and Answers. You will find WAEC GCE Mathematics Objective Answers, WAEC Mathematics Essay Runs 2023, WAEC GCE 2023 Mathematics Expo, and the tips you need to pass your WAEC GCE Mathematics examination with ease.**

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**WAEC GCE Mathematics Essay and Objectives Questions and Answers (Expo/Runz)**

WAEC GCE Mathematics Essay and Objective 2023 questions and answers can be seen here. The WAEC Mathematics to Essay and Objective question paper will be brought in for the exam on **Saturday, 25th November, 2023.**

The Mathematics 3 Essay and Objective exam is held from 9:30am – 12noon. We are writing this post to show the Waec Mathematics specimen from the provided yellow paper, Waec Mathematics Essay and Objective, and materials that were used in the WAEC Mathematics Essay and Objective exam past questions and syllabus.

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**WAEC GCE Mathematics Past Questions**

In this post, we will be posting samples of the waec GCE Mathematics Essay and Objective questions for candidates who will participate in the examination for practice purposes.

Note that below are the questions from WAEC GCE Mathematics’s past questions and answers that we feel are likely questions for exam preparation.

The resources below on Mathematics have been provided by WAEC to assist the student in understanding the required standards expected in the Mathematics final Examination. Students’ performance in the examination under review was done by the Chief examiner, this you will see while exploring links like General Comment, Performance, Weaknesses, Strength, and Observation to respective Questions.

**PAPER 2 [Essay]**

*Answer any … questions.*

*Write your answers in the answer booklet provided.*

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) 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.

4. (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.

5.

6. 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°.

7.

8. (a)

9. 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

10.

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.

**PAPER 1 (Objective)**

*Answer ***ALL*** questions in this section.*

*Shade your answer in the answer booklet provided.*

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(2^{4x + 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 + [x^{3} – y^{3}/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. x^{3} – 7x + 6

B. x^{3} + 7x – 6

C. x^{3} – 7x – 6

D. x^{3} + 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 1231_{4} to a number in base 6.

A. 105_{6
}B. 301_{6
}C. 103_{6
}D. 501_{6}

11. Find the slope of the curve y = 3x^{3} + 5x^{2} – 3 at (-1, 5).

A. 1 B. -1 C. 19 D. -19

12. Find the area of the region bounded by y = x^{2} + x – 2 and x-axis.

A. 9/2 B. -39/6 C. 8/3 D. 16/3

13. The minimum value of y = x^{2} – 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.

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.

**Conclusion **

Please note that the answers presented in this post are a guide to the forthcoming General Certificate Examination (GCE). We have prepared it to aid the student in preparing for the Essay and Objective. If you have any questions about the WAEC GCE 2023 Mathematics Essay and Objective questions and answers, kindly let us know in the comment box

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