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waec model questions vol6 2024 mathematics | Objective

Are you preparing for waec model questions vol6 exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

In triangle ABC, ∠A = 40°, ∠B = 70°, ∠C = 70° and side AB = 12 cm. Point D lies on BC such that BD : DC = 1 : 2. Find the length of AD (in cm).

A. √144 cm

B. √121 cm

C. √100 cm

Correct D. √129 cm

Correct Answer: D

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Question 2 View Details

The quadratic equation \(x^{2}-(k+5)x+(k^{2}-9)=0\) has two distinct integer roots. Find the sum of the roots.

Correct A. 8

B. 9

C. 6

D. 10

Correct Answer: A

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Question 3 View Details

A parabola passes through the points A(1,2) and B(3,‑4) and its vertex lies on the line x = -1. Determine the coefficient a in its equation \(y = ax^{2}+bx+c\).

A. 1/2

B. -2/3

C. -1/3

Correct D. -1/2

Correct Answer: D

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Question 4 View Details

The simultaneous equations \(kx + 4y = 20\) and \(3x - y = 5\) have integer solutions for x and y. Find the smallest positive integer value of k.

A. 12

Correct B. 8

C. 10

D. 6

Correct Answer: B

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Question 5 View Details

Water flows into a tank at a rate of \(2t+8\) litres per minute, where \(t\) is the time in minutes after the start. Water simultaneously drains from the tank at a constant rate of 5 litres per minute. The tank is initially empty. After 4 minutes it contains 20 litres. If the tank's capacity is 100 litres, to the nearest hundredth of a minute, how long after the start will the tank become full?

Correct A. 9.51 minutes

B. 8.73 minutes

C. 7.95 minutes

D. 10.24 minutes

Correct Answer: A

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Question 6 View Details

A shop sells two types of pens. Let the original price of pen A be a naira and pen B be b naira. The shop sold x pens of type A and y pens of type B. It is known that the number of type A pens sold is twice the number of type B pens and the total number of pens sold is 120. After increasing the price of pen A by 20% and decreasing the price of pen B by 10%, the revenue from selling the same quantities increased by 15%. Find the ratio a : b.

A. 6:1

B. 3:5

C. 4:3

Correct D. 5:2

Correct Answer: D

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Question 7 View Details

Find the smallest positive integer that leaves a remainder of 3 when divided by 5, a remainder of 4 when divided by 7, and a remainder of 5 when divided by 9.

A. 68

B. 128

Correct C. 158

D. 98

Correct Answer: C

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Question 8 View Details

A closed cylindrical tank (including top and bottom) has a total surface area of 600π cm². Determine the radius and height that give the maximum possible volume, and state that maximum volume (expressed in terms of π).

A. r = 8 cm, h = 24 cm, Vmax = 1536π cm³

B. r = 9 cm, h = 22 cm, Vmax = 1782π cm³

Correct C. r = 10 cm, h = 20 cm, Vmax = 2000π cm³

D. r = 12 cm, h = 16 cm, Vmax = 2304π cm³

Correct Answer: C

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Question 9 View Details

In triangle ABC, side a = BC = 14 cm, side b = AC = 13 cm, and angle C = 120°. Find the length of side c = AB and the area of the triangle.

A. c = √529 cm (≈23.00 cm); Area = (84√3)\/2 cm² (≈72.7 cm²)

B. c = √500 cm (≈22.36 cm); Area = (80√3)\/2 cm² (≈69.3 cm²)

C. c = √576 cm (≈24.00 cm); Area = (96√3)\/2 cm² (≈83.1 cm²)

Correct D. c = √547 cm (≈23.38 cm); Area = (91√3)/2 cm² (≈78.8 cm²)

Correct Answer: D

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Question 10 View Details

Solve for x: \(|2x - 5| < \dfrac{x + 3}{x - 1}\), where x ≠ 1.

Correct A. 1 < x < 2 + √3

B. 0 < x < 2 + √3

C. 1 < x < 2 - √3

D. 1 < x < 3 + √3

Correct Answer: A

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Question 11 View Details

The sum of the first n terms of an arithmetic progression is given by S_n = 3n^2 + 5n. Find the 10th term of the progression.

A. 64

B. 60

C. 68

Correct D. 62

Correct Answer: D

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Question 12 View Details

Vectors a and b lie in a plane with magnitudes |a| = 5 and |b| = 8. If the vector (2a - b) is perpendicular to (a + 2b), determine the angle between a and b in degrees, correct to the nearest integer.

A. 30

Correct B. 50

C. 70

D. 60

Correct Answer: B

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Question 13 View Details

In a class of 120 students, 68 study Mathematics, 55 study Physics, and 48 study Chemistry. The number of students studying both Mathematics and Physics is twice the number studying both Physics and Chemistry. Exactly 20 students study all three subjects, and 30 students study none of these subjects. How many students study exactly two of the subjects?

A. 38

B. 44

Correct C. 41

D. 49

Correct Answer: C

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Question 14 View Details

A bag contains red, blue and green balls. The probability of drawing a red ball is twice that of drawing a blue ball, and the probability of drawing a green ball is three times that of drawing a blue ball. Two balls are drawn successively without replacement. Given that at least one of the drawn balls is red, find the probability that both balls are red. Express your answer as a fraction in lowest terms.

A. 2/9

Correct B. 1/9

C. 1/8

D. 1/12

Correct Answer: B

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Question 15 View Details

A factory produces light bulbs, each of which is defective with probability 0.02. Bulbs are packed in boxes of 20. A box is acceptable if it contains at most 2 defective bulbs. If a shipment contains 500 boxes, what is the expected number of acceptable boxes? Give your answer rounded to the nearest whole number.

A. 495

B. 498

Correct C. 496

D. 500

Correct Answer: C

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Question 16 View Details

A speed‑time graph for a car shows the following straight‑line segments: from (0 h, 0 km/h) to (1 h, 40 km/h), from (1 h, 40 km/h) to (3 h, 40 km/h), from (3 h, 40 km/h) to (4 h, 60 km/h) and from (4 h, 60 km/h) to (5 h, 60 km/h). Using the graph, calculate the total distance travelled by the car in the first 4.5 hours.

A. 200 km

B. 150 km

Correct C. 180 km

D. 160 km

Correct Answer: C

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Question 17 View Details

A solid is formed by a right circular cylinder of radius 5 cm and height 4 cm standing on a horizontal plane, with a right circular cone of the same base radius and height 15 cm placed on top of the cylinder. A plane parallel to the bases cuts the solid at a distance x centimetres from the bottom of the cylinder. If the volume of the part of the solid below the plane is exactly half the total volume of the solid, find x (to two decimal places).

A. 4.00 cm

B. 5.13 cm

C. 3.87 cm

Correct D. 4.52 cm

Correct Answer: D

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Question 18 View Details

Two real numbers a and b satisfy a + b = 6 and a² + b² = 28. Find the value of (a³ + b³) ÷ (a + b).

A. 30

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 19 View Details

In three‑dimensional space, vectors \(\mathbf{a}\) and \(\mathbf{b}\) have magnitudes |\(\mathbf{a}\)| = 3 cm and |\(\mathbf{b}\)| = 4 cm, and the angle between them is 60°. Define \(\mathbf{d} = \mathbf{a} + k\mathbf{b}\) where the scalar k is chosen so that \(\mathbf{d}\) is perpendicular to \(\mathbf{a} - 2\mathbf{b}\). Determine the value of k and then give the magnitude of \(\mathbf{d}\) in simplest radical form.

A. k = 3\/26, |d| = 21√3\/13 cm

Correct B. k = -3/26, |d| = 21√3/13 cm

C. k = -3\/26, |d| = 14√3\/13 cm

D. k = -1\/2, |d| = 7√3\/2 cm

Correct Answer: B

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Question 20 View Details

The nth term of a sequence is given by tₙ = 3n - 2. Find the smallest positive integer n for which the sum of the first n terms equals 210.

Correct A. 12

B. 15

C. 10

D. 13

Correct Answer: A

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Question 21 View Details

Given that \(\log_{2}\bigl(2^{x}\cdot 8^{\,x-1}\bigr)=5\), find the value of \(\displaystyle \frac{\sqrt{2^{\,2x+2}}}{2^{\,x-1}}\).

A. 8

B. 16

Correct C. 4

D. 2

Correct Answer: C

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Question 22 View Details

How many integer values of \(x\) satisfy the inequality \(|2x-5|<9-x^{2}\)?

A. 3

B. 5

C. 6

Correct D. 4

Correct Answer: D

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Question 23 View Details

The time \(t\) (in minutes) required to fill a tank varies directly as the volume \(V\) (in litres) and inversely as the square root of the pressure \(P\) (in kPa). If it takes 12 minutes to fill a 180‑litre tank when the pressure is 25 kPa, find the time needed to fill a 300‑litre tank when the pressure is 40 kPa. Give your answer in simplest exact form.

A. 5\sqrt{2}

B. 5\sqrt{5}

Correct C. 5\sqrt{10}

D. 10\sqrt{10}

Correct Answer: C

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Question 24 View Details

A shop sold \(\frac{3}{5}\) of its stock of a product. The remaining stock was 240 items. What was the original stock?

A. 540

Correct B. 600

C. 720

D. 480

Correct Answer: B

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Question 25 View Details

If real numbers \(a\) and \(b\) satisfy \(a+b=6\) and \(a^{2}+b^{2}=20\), find the value of \(a^{3}+b^{3}\).

A. -72

B. 120

Correct C. 72

D. 192

Correct Answer: C

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