Question 1

1. Multiply 3.4×10⁻⁵ by 7.1×10⁸ and leave the answer in standard form.

Accepted Answer

C. 2.414×10⁴

Answer

A. 2.414×10²

Answer

B. 2.414×10³

Answer

D. 2.414×10⁵

Question 2

2. Given that P = {p : 1 < p < 20}, where p is an integer and R = {r : 0 ≤ r ≤ 25, where r is a multiple of 4}, find P∩R.

Accepted Answer

B. {4, 8, 12, 16}

Answer

A. {4, 8, 10, 16, 20}

Answer

C. {4, 8, 12, 16, 20}

Answer

D. {4, 8, 12, 16, 20, 24}

Question 3

3. The first term of an Arithmetic Progression (A.P) is 2 and the last term is 29. If the common difference is 3, how many terms are in the A.P?

Accepted Answer

C. 10

Answer

A. 8

Answer

B. 9

Answer

D. 11

Question 4

4. Express in index form: logₐˣ + logₐʸ = 3

Accepted Answer

D. xy = a³

Answer

A. x + y = 3

Answer

B. xy = 3

Answer

C. x + y = a³

Question 5

5. Simplify: (2p - q)² - (p + q)²

Accepted Answer

A. 3p(p - 2q)

Answer

B. 2p(p - 3q)

Answer

C. 3p(2p - q)

Answer

D. 2p(3p - q)

Question 6

6. If (3 - 4√2)(1 + 3√2) = a + b√2, find the value of b.

Accepted Answer

A. 5

Answer

B. -5

Answer

C. -21

Answer

D. 21

Question 7

7. Find the time for which $1,250.00 will amount to $2,031.25 at 12.5% per annum simple interest.

Accepted Answer

D. 5 years

Answer

A. 2 years

Answer

B. 3 years

Answer

C. 4 years

Question 8

8. If log₃^(2x-1) = 5, find the value of x.

Accepted Answer

D. 122

Answer

A. 8

Answer

B. 16

Answer

C. 64

Question 9

9. The population of a town increases by 3% every year. In the year 2000, the population was 3,000. Find the population in the year 2003.

Accepted Answer

B. 3,278

Answer

A. 3,182

Answer

C. 6,591

Answer

D. 7,515

Question 10

10. A trader gave a change of $540.00 instead of $570.00 to a customer. Calculate the percentage error.

Accepted Answer

A. 5 5/19 %

Answer

B. 5 5/9 %

Answer

C. 5 7/19 %

Answer

D. 5 7/9 %

Question 11

11. An interior angle of a regular polygon is 168°. Find the number of sides of the polygon.

Accepted Answer

A. 30

Answer

B. 24

Answer

C. 15

Answer

D. 12

Question 12

12. If 3x - 2y = -5 and x + 2y = 9, find the value of (x - y)/(x + y).

Accepted Answer

C. -3/5

Answer

A. 5/3

Answer

B. 3/5

Answer

D. -5/3

Question 13

13. A variable W varies partly as M and partly inversely as P. Which of the following correctly represents the relation with k₁ and k₂ constants?

Accepted Answer

C. W = k₁M + k₂/P

Answer

A. W = k₁M / k₂P

Answer

B. W = (k₁+k₂)M / P

Answer

D. W = (k₁+k₂)M + P

Question 14

14. A cylindrical metallic barrel of height 2.5 m and radius 0.245 m is closed at one end. Find, correct to one decimal place, the total surface area of the barrel. [Take π = 22/7]

Accepted Answer

C. 4.0 m²

Answer

A. 2.1 m²

Answer

B. 3.5 m²

Answer

D. 9.4 m²

Question 15

15. Make R the subject of the relation V = πl(R² - r²).

Accepted Answer

A. R = √(V/πl + r²)

Answer

B. R = √(V/πl - r²)

Answer

C. R = √(V - πlr²)

Answer

D. R = √(V + πlr²)

Question 16

16. Consider the following statements: m: Edna is respectful; n: Edna is brilliant. If m ⟹ n, which of the following is valid?

Accepted Answer

C. ~n ⟹ ~m

Answer

A. ~m ⟹ ~n

Answer

B. n ⟹ ~m

Answer

D. n ⟹ m

Question 17

17. A number is added to both the numerator and the denominator of the fraction 1/8. If the result is 1/2, find the number.

Accepted Answer

D. 6

Answer

A. 3

Answer

B. 4

Answer

C. 5

Question 18

18. Gifty, Justina and Frank shared 60 oranges in the ratio 5 : 3 : 7 respectively. How many oranges did Justina receive?

Accepted Answer

A. 12

Answer

B. 16

Answer

C. 20

Answer

D. 28

Question 19

19. Find the quadratic equation whose roots are 2/3 and -1.

Accepted Answer

A. 3x² + x - 2 = 0

Answer

B. 3x² - x - 2 = 0

Answer

C. 3x² + x + 2 = 0

Answer

D. 3x² + x - 1 = 0

Question 20

20. A piece of rod of length 44 m is cut to form a rectangular shape such that the ratio of the length to the breadth is 7 : 4. Find the breadth.

Accepted Answer

A. 8 m

Answer

B. 14 m

Answer

C. 16 m

Answer

D. 24 m

Question 21

21. In the diagram, MN∥KL, ML and KN intersect at X. |MN| = 12 cm, |MX| = 10 cm and |KL| = 9 cm. If the area of ΔMXN is 16 cm², calculate the area of ΔLXK.

Accepted Answer

B. 9 cm²

Answer

A. 8 cm²

Answer

C. 10 cm²

Answer

D. 12 cm²

Question 22

22. A ladder 15 m long leans against a vertical pole, making an angle of 72° with the horizontal. Calculate, correct to one decimal place, the distance between the foot of the ladder and the pole.

Accepted Answer

D. 4.6 m

Answer

A. 15.8 m

Answer

B. 14.3 m

Answer

C. 4.9 m

Question 23

23. In the diagram, O is the centre of the circle. If |OA| = 25 cm and |AB| = 40 cm, find |OH|.

Accepted Answer

A. 15 cm

Answer

B. 20 cm

Answer

C. 25 cm

Answer

D. 30 cm

Question 24

24. Given that P is 25 m on a bearing of 330° from Q, how far south of Q is P?

Accepted Answer

B. 21.7 m

Answer

A. 25.2 m

Answer

C. 19.8 m

Answer

D. 18.5 m

Question 25

25. A car valued at $600,000.00 depreciates by 10% each year. What will be the value of the car at the end of two years?

Accepted Answer

C. $486,000.00

Answer

A. $120,000.00

Answer

B. $480,000.00

Answer

D. $540,000.00

Question 26

26. The length and breadth of a cuboid are 15 cm and 8 cm respectively. If the volume of the cuboid is 1,560 cm³, calculate the total surface area.

Accepted Answer

B. 383 cm²

Answer

A. 976 cm²

Answer

C. 792 cm²

Answer

D. 746 cm²

Question 27

27. The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.

Accepted Answer

A. Seven

Answer

B. Eight

Answer

C. Nine

Answer

D. Ten

Question 28

28. Factorize completely: 27x² - 48y²

Accepted Answer

B. 3(3x + 4y)(3x - 4y)

Answer

A. 3(3x + 4y)(3x + 4y)

Answer

C. 3(9x - 16y)(9x + 16y)

Answer

D. 3(9x - 16y)(9x - 16y)

Question 29

29. For what values of x is (x-3)/4 + (x+1)/8 ≥ 2 ?

Accepted Answer

C. x ≥ 7

Answer

A. x ≥ 5

Answer

B. x ≥ 6

Answer

D. x ≥ 8

Question 30

30. In the diagram, ∠SQR = 52° and ∠PRT = 16°. Find the value of the angle marked y.

Accepted Answer

C. 112°

Answer

A. 64°

Answer

B. 68°

Answer

D. 128°

Question 31

31. In the diagram, JKL is a tangent to the circle GHIK at K. ∠LKG = 38° and ∠KHG = 87°. Calculate the value of the angle marked x.

Accepted Answer

B. 55°

Answer

A. 93°

Answer

C. 42°

Answer

D. 23°

Question 32

32. A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?

Accepted Answer

B. 4 : 3

Answer

A. 5 : 4

Answer

C. 2 : 1

Answer

D. 3 : 4

Question 33

33. Find, correct to the nearest whole number, the value of h in the diagram.

Accepted Answer

C. 23 m

Answer

A. 15 m

Answer

B. 22 m

Answer

D. 18 m

Question 34

34. The gradient of the line joining the points P(2, -8) and Q(1, y) is -4. Find the value of y.

Accepted Answer

C. -4

Answer

A. 2

Answer

B. 4

Answer

D. -3

Question 35

35. In the diagram, PQ∥RS, ∠WYZ = 44° and ∠WXY = 50°. Find ∠WTX.

Accepted Answer

C. 86°

Answer

A. 65°

Answer

B. 68°

Answer

D. 90°

Question 36

36. The perimeter of a rectangular garden is 90 m. If the width is 7 m less than the length, find the length of the garden.

Accepted Answer

D. 26 m

Answer

A. 19 m

Answer

B. 23 m

Answer

C. 24 m

Question 37

37. Four of the angles of a hexagon sum up to 420°. If the remaining angles are equal, find the value of each of the angles.

Accepted Answer

D. 150°

Answer

A. 60°

Answer

B. 100°

Answer

C. 120°

Question 38

38. Find the value of x in the diagram.

Accepted Answer

C. 120°

Answer

A. 60°

Answer

B. 65°

Answer

D. 125°

Question 39

39. The following are the masses (in kg) of members in a club: 59, 44, 53, 57, 49, 40, 48 and 50. Calculate the mean mass.

Accepted Answer

C. 50 kg

Answer

A. 40 kg

Answer

B. 44 kg

Answer

D. 53 kg

Question 40

40. Calculate the variance of the distribution of masses: 59, 44, 53, 57, 49, 40, 48 and 50.

Accepted Answer

A. 35

Answer

B. 36

Answer

C. 40

Answer

D. 50

Question 41

41. Two opposite sides of a rectangle are (5x+3) m and (2x+9) m. If an adjacent side is (6x-7) m, find, in m², the area of the rectangle.

Accepted Answer

B. 65 m²

Answer

A. 45 m²

Answer

C. 125 m²

Answer

D. 165 m²

Question 42

42. A die is tossed once. Find the probability of getting a prime number.

Accepted Answer

A. 1/2

Answer

B. 1/6

Answer

C. 1/3

Answer

D. 2/3

Question 43

43. The area of a sector of a circle with radius 7 cm is 51.3 cm². Calculate, correct to the nearest whole number, the angle of the sector. [Take π = 22/7]

Accepted Answer

B. 120°

Answer

A. 60°

Answer

C. 150°

Answer

D. 180°

Question 44

44. A cliff on the bank of a river is 87 m high. A boat on the river is 22 m away from the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

Accepted Answer

A. 76°

Answer

B. 64°

Answer

C. 36°

Answer

D. 24°

Question 45

45. In the diagram, TU is a tangent to the circle SPQR at P. If ∠PTS = 44° and ∠SQP = 35°, find ∠PST.

Accepted Answer

A. 101°

Answer

B. 125°

Answer

C. 130°

Answer

D. 135°

Question 46

46. The probability that Amaka will pass an examination is 3/7 and that Bala will pass is 4/9. Find the probability that both will pass the examination.

Accepted Answer

B. 4/21

Answer

A. 2/21

Answer

C. 5/21

Answer

D. 9/21

Question 47

47. Which of the following points lies on the line 3x - 8y = 11?

Accepted Answer

B. (1, -1)

Answer

A. (1, 1)

Answer

C. (-1, 1)

Answer

D. (-1, -1)

Question 48

48. Find the range of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15 and 25.

Accepted Answer

B. 24

Answer

A. 22

Answer

C. 25

Answer

D. 27

Question 49

49. The fourth and eighth terms of an Arithmetic Progression are 16 and 40 respectively. Find the common difference.

Accepted Answer

B. 6

Answer

A. -6

Answer

C. -2

Answer

D. 2

Question 50

50. For what values of y is (y+2)/(8y² - 10y + 3) not defined?

Accepted Answer

D. 3/4, 1/2

Answer

A. -3/4, -1/2

Answer

B. -3/4, 1/2

Answer

C. 3/4, -1/2

WAEC Mathematics 2024 Objective Past Questions

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