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waec model questions vol1 2023 mathematics | Objective

Are you preparing for waec model questions vol1 exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details

A bag contains red, blue and green balls. The probability of drawing a blue ball on the first draw is 0.4. The probability of drawing a red ball is twice that of drawing a green ball. If two balls are drawn without replacement, the probability that one is red and the other is green (in any order) is 0.2. How many red balls are in the bag?

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2 View Details

In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) have magnitudes \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 8\). The resultant vector \(\mathbf{a}+\mathbf{b}\) makes an angle of \(30^{\circ}\) with \(\mathbf{a}\). Find the exact value of the dot product \(\mathbf{a}\cdot\mathbf{b}\).

A. 40/3

Correct B. 80/3

C. 100/3

D. 80/5

Correct Answer: B

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Question 3 View Details

Simplify the expression \(\displaystyle \frac{2^{3/2}\;\times\;8^{1/3}}{\sqrt{32}}\).

A. -1

B. 2

C. 0

Correct D. 1

Correct Answer: D

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Question 4 View Details

Let \(\mathbf{a}=\langle2,-1,3\rangle\) and \(\mathbf{b}=\langle k,4,-2\rangle\). Define \(\mathbf{c}=\mathbf{a}\times\mathbf{b}\). If \(\mathbf{c}\) is perpendicular to the vector \(\mathbf{d}=\langle1,2,k\rangle\), find all possible values of \(k\).

A. -7±√45

B. -7±√49

Correct C. -7±√51

D. -5±√51

Correct Answer: C

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Question 5 View Details

The graph shows a straight line and a parabola. The line passes through the points (2, 3) and (8, 15). The parabola is given by \(y = x^{2} - 4x + 3\). Determine the x‑coordinate(s) of the point(s) where the line and the parabola intersect.

A. 3±2√5

Correct B. 3±√5

C. 3±√6

D. 4±√5

Correct Answer: B

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Question 6 View Details

The time T (in minutes) taken to fill a tank varies directly as the square of the radius r (in cm) of the inlet pipe and inversely as the speed v (in cm min⁻¹) of water flow. When r = 4 cm and v = 6 cm min⁻¹, the tank is filled in 5 minutes. If the radius is increased to 5 cm and the required filling time is 3 minutes, what speed of water flow (in cm min⁻¹) is needed?

A. 135/8

B. 25/4

Correct C. 125/8

D. 15/2

Correct Answer: C

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Question 7 View Details

In a class of 30 students the distribution of test scores (in whole numbers) is partially given below. Score: 40 45 50 55 60 65 70 75 80 Frequency: 2 a 4 b 5 3 c 2 4 The mean score is 58 and the median score is 60. (i) Find the value of a + b + c. (ii) What is the probability that a randomly selected student scored at least 70?

A. 7; 3/14

Correct B. 8; 4/15

C. 6; 2/13

D. 9; 5/16

Correct Answer: B

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Question 8 View Details

A sequence {a_n} is defined by a₁ = 2 and for n ≥ 1, a_{n+1} = 3a_n + (-1)^n. Determine the 5th term a₅ and the sum S₅ = a₁ + a₂ + a₃ + a₄ + a₅.

A. a₅ = 140; S₅ = 209

B. a₅ = 141; S₅ = 211

C. a₅ = 143; S₅ = 213

Correct D. a₅ = 142; S₅ = 212

Correct Answer: D

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Question 9 View Details

In a school of 120 students, 70 study Mathematics, 55 study Physics and 45 study Chemistry. The numbers who study both Mathematics and Physics, Mathematics and Chemistry, and Physics and Chemistry are 30, 25 and 20 respectively. Ten students study none of these subjects. How many students study all three subjects?

A. 5

B. 20

Correct C. 15

D. 10

Correct Answer: C

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Question 10 View Details

In the coordinate plane the points A(2,3) and B(8,3) are joined to form a horizontal segment AB. Point D(5,7) is also plotted. Point C lies on the segment AD. If the area of triangle ABC is 12 square units, find the y‑coordinate of point C.

A. 11

B. 5

Correct C. 7

D. 9

Correct Answer: C

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Question 11 View Details

A three‑digit number has digits a, b, c (in that order). It is known that a + b = 12, b + c = 15 and the three‑digit number is divisible by 3. If all three digits are different, what is the value of the digit a?

Correct A. 3

B. 5

C. 6

D. 4

Correct Answer: A

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Question 12 View Details

In a mixture of water and alcohol, the mass of alcohol is three‑eighths of the total mass. If 250 g of water is added, the percentage of alcohol in the mixture becomes 30 %. What was the original total mass of the mixture (in grams)?

Correct A. 1000

B. 1200

C. 1500

D. 800

Correct Answer: A

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Question 13 View Details

The scores of 120 students in a Mathematics test are grouped as follows: - 0-29 : 15 students - 30-39 : 15 students - 40-49 : 43 students - 50-59 : 27 students - 60-69 : 0 students - 70-100 : 20 students The mean score of the whole class is 48.5. The teacher wishes to raise the overall mean to 52 by awarding the same extra marks to every student who scored in the 0-29 group only. How many extra marks must each of those 15 students receive?

A. 24

Correct B. 28

C. 30

D. 34

Correct Answer: B

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Question 14 View Details

Solve for x: \(2^{x}\times4^{\,x-1}=8^{\,2x+3}\).

A. -10/3

B. 7/3

C. -3

Correct D. -11/3

Correct Answer: D

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Question 15 View Details

In triangle ABC, side a = 7 cm, side b = 9 cm and the altitude from vertex C to side AB is 5 cm. If angle C is acute, find the measure of angle C (to the nearest degree).

A. 9

Correct B. 12

C. 15

D. 18

Correct Answer: B

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Question 16 View Details

For all real numbers x, the inequality |x - 2| + |x - k| \ge 5 holds. Determine all real values of k that satisfy this condition.

A. k \le -2 \text{ or } k \ge 6

B. k \le -3 \text{ and } k \ge 7

Correct C. k \le -3 \text{ or } k \ge 7

D. k < -3 \text{ or } k > 7

Correct Answer: C

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Question 17 View Details

A piecewise linear graph of y = f(x) passes through the points (0,2), (3,8), (5,8) and (7,2). Find the value of x (to three decimal places) at which the area under the curve from x = 0 up to that x equals 30 square units.

Correct A. 4.875

B. 5.125

C. 4.500

D. 4.250

Correct Answer: A

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Question 18 View Details

The quadratic equation 2x^2 - (k+3)x + (k-2) = 0 has real roots \alpha and \beta that satisfy \alpha + 2\beta = 5. Find all possible values of k.

A. k = 0 \text{ or } k = 4

B. k = -2 \text{ or } k = 8

C. k = 1 \text{ or } k = 5

Correct D. k = 2 \text{ or } k = 6

Correct Answer: D

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Question 19 View Details

A closed rectangular box has length twice its width and a total surface area of 48 cm². Determine the dimensions that give the maximum possible volume and state that maximum volume.

A. Maximum volume = 48\/3 cm³, attained when width = 2 cm, length = 4 cm, height = 4 cm

Correct B. Maximum volume = 64/3 cm³, attained when width = 2 cm, length = 4 cm, height = 8/3 cm

C. Maximum volume = 64\/3 cm³, attained when width = 3 cm, length = 6 cm, height = 8\/3 cm

D. Maximum volume = 80\/3 cm³, attained when width = 1 cm, length = 2 cm, height = 8\/3 cm

Correct Answer: B

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Question 20 View Details

In triangle ABC, AB = 13 cm and AC = 15 cm. The median from A meets BC at D. If the area of triangle ABD is 42 cm², find all possible lengths of BC.

A. BC = 16 \text{ cm or } BC = 3\sqrt{50} \text{ cm}

B. BC = 12 \text{ cm or } BC = 6\sqrt{30} \text{ cm}

C. BC = 20 \text{ cm or } BC = 2\sqrt{85} \text{ cm}

Correct D. BC = 14 \text{ cm or } BC = 4\sqrt{37} \text{ cm}

Correct Answer: D

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Question 21 View Details

A three‑digit integer has digits a, b and c (in that order). The sum of its digits is 12 and the integer is divisible by 3. What is the smallest possible value of the integer?

A. 156

B. 138

Correct C. 129

D. 147

Correct Answer: C

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Question 22 View Details

The distance d (in km) travelled by a car varies directly as the square of its speed v (in km/h) and inversely as its fuel efficiency f (in km per litre). When the car travels at 60 km/h with a fuel efficiency of 15 km/l, it covers 180 km. What distance will it cover if the speed is increased to 80 km/h and the fuel efficiency improves by 10%?

Correct A. 291

B. 260

C. 300

D. 280

Correct Answer: A

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Question 23 View Details

The first three terms of a geometric progression are 3, x and 12. The sum of these three terms equals the sum of the first three terms of an arithmetic progression whose first term is 2 and common difference d. Find the values of x and d.

A. 9 and 2

Correct B. 6 and 5

C. 4 and 7

D. 8 and 3

Correct Answer: B

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Question 24 View Details

If \log_{2}x + \log_{2}(x-3) = 3, find x and then evaluate \;x^{\log_{2}8}.

Correct A. 64

B. 32

C. 128

D. 16

Correct Answer: A

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Question 25 View Details

A distance-time graph for a car shows that from t = 0 to t = 4 h the car travels at a constant speed covering 240 km. It then rests for 1 h (no distance covered). After the rest, it travels at another constant speed and reaches a total distance of 560 km at t = 9 h. Determine (a) the speed during the first interval, (b) the speed during the second interval, and (c) the average speed for the whole journey (excluding the rest period).

A. 55, 85, 68

B. 50, 90, 70

C. 60, 70, 65

Correct D. 60, 80, 70

Correct Answer: D

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