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waec model questions vol2 2025 mathematics | Objective

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Question 1 View Details

A box contains white, black and red balls. The probability of drawing a white ball at random is \( \frac{1}{3} \). If two balls are drawn successively without replacement, the probability that both are black is \( \frac{1}{12} \). Find the number of red balls in the box.

A. 4

B. 5

C. 2

Correct D. 3

Correct Answer: D

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Question 2 View Details

Write \(3,507,642\) in standard form (i.e., as a product of a number between 1 and 10 and a power of 10).

A. 3.507642×10^5

Correct B. 3.507642×10^6

C. 3.507642×10^7

D. 3.50764×10^6

Correct Answer: B

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Question 3 View Details

In a class of 120 students, a survey recorded the following numbers: 30 study only Mathematics, 25 study only Physics, 20 study only Chemistry, 15 study both Mathematics and Physics but not Chemistry, 10 study both Mathematics and Chemistry but not Physics, 5 study both Physics and Chemistry but not Mathematics, and 8 study all three subjects. How many students study none of the three subjects?

Correct A. 7

B. 5

C. 12

D. 9

Correct Answer: A

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Question 4 View Details

A shop offers a discount of 10% on the marked price, and then an additional 5% discount on the reduced price. If the final price paid is \(\text{₦}1{,}800\), what was the original marked price (to the nearest naira)?

A. 2150

B. 2000

C. 2250

Correct D. 2105

Correct Answer: D

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Question 5 View Details

The product of two consecutive integers exceeds twice their sum by 2. Find the pair of positive consecutive integers that satisfy this condition.

A. 6 and 7

Correct B. 4 and 5

C. 5 and 6

D. 3 and 4

Correct Answer: B

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Question 6 View Details

A car travels from town A to town B at a constant speed. On the return journey it travels \(20\%\) faster and arrives \(30\) minutes earlier than the outward journey. If the distance between the towns is \(150\) km, find the speed of the car on the outward journey (in km/h).

A. 55

Correct B. 50

C. 60

D. 45

Correct Answer: B

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Question 7 View Details

What is the smallest integer greater than \(200\) that is divisible by both \(12\) and \(15\)?

A. 252

B. 210

C. 225

Correct D. 240

Correct Answer: D

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Question 8 View Details

In a class of \(80\) students, \(45\) study Mathematics, \(30\) study Physics, and \(25\) study Chemistry. Exactly \(20\) students study both Mathematics and Physics. The number of students who study both Physics and Chemistry is half the number who study both Mathematics and Chemistry. Five students study none of the three subjects. Find the number of students who study all three subjects.

A. 2

B. 0

C. 5

Correct D. 1

Correct Answer: D

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Question 9 View Details

The sum of the first \(n\) terms of an arithmetic progression is given by \(S_n = 2n^{2} + 3n\). Find the 15th term of the progression and its common difference.

A. 61 (common difference 5)

B. 65 (common difference 5)

C. 57 (common difference 3)

Correct D. 61 (common difference 4)

Correct Answer: D

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Question 10 View Details

A closed rectangular tank has a square base. Its height is twice the side length of the base. The tank is to be painted on all outer surfaces except the base at a cost of N250 per square metre. If the total painting cost is N36,000, find (a) the total length of all its edges (in metres) and (b) the volume of the tank (in cubic metres).

A. 56 m, 112 m³

B. 60 m, 120 m³

Correct C. 64 m, 128 m³

D. 68 m, 144 m³

Correct Answer: C

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Question 11 View Details

Twenty‑five students took a test. The frequency distribution of the number of books read by each student is given below: \[\begin{array}{c|c}\text{Books read} & \text{Number of students} \\hline 0 & 4 \\ 1 & x \\ 2 & 7 \\ 3 & 5 \\ 4 & 3 \\ 5 & 2 \end{array}\] The mean number of books read is \(2.2\). After four additional students each read exactly two books, the mean becomes \(2.17\) (rounded to two decimal places). (a) Find the missing frequency \(x\). (b) State the mode of the original distribution. (c) What percentage of the original 25 students read more than three books? Give your answer to the nearest whole percent.

Correct A. x = 4; mode = 2; percentage = 20%

B. x = 4; mode = 2; percentage = 24%

C. x = 5; mode = 2; percentage = 20%

D. x = 4; mode = 3; percentage = 20%

Correct Answer: A

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Question 12 View Details

In triangle \(PQR\) the angles satisfy \(\angle P =30^{\circ}\), \(\angle Q =2\theta\) and \(\angle R =\theta\). The side opposite \(\angle P\) (i.e. side \(p\)) is \(7\) cm. (i) Determine the value of \(\theta\) (in degrees). (ii) Find the length of side \(r\) opposite \(\angle R\), correct to two decimal places. (iii) Compute the area of \(\triangle PQR\) in square centimetres, correct to two decimal places.

Correct A. θ = 50°, r ≈ 10.72 cm, area ≈ 36.96 cm²

B. θ = 50°, r ≈ 12.00 cm, area ≈ 36.96 cm²

C. θ = 45°, r ≈ 9.85 cm, area ≈ 34.20 cm²

D. θ = 55°, r ≈ 11.30 cm, area ≈ 39.50 cm²

Correct Answer: A

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Question 13 View Details

The quadratic equation \(x^{2}-kx+6=0\) has two real roots. One root is exactly one less than twice the other root, and both roots are positive. (i) Find the value of \(k\). (ii) Compute the sum of the squares of the two roots.

Correct A. k = 5; sum of squares = 13

B. k = 5; sum of squares = 12

C. k = 4; sum of squares = 13

D. k = 6; sum of squares = 15

Correct Answer: A

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Question 14 View Details

Simplify the expression \(\displaystyle \frac{(2^{3}\cdot5^{2})^{\frac12}}{\sqrt{20}}\) and write your answer in simplest radical form.

A. 2√5

B. √20

Correct C. √10

D. √5

Correct Answer: C

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Question 15 View Details

In a circle of radius \(10\) cm two chords \(AB\) and \(CD\) intersect at point \(E\) inside the circle. The lengths of the four segments are \(AE=6\) cm, \(EB=8\) cm, \(CE=4\) cm and the chords are perpendicular to each other. (a) Find the length of \(ED\). (b) Determine the area of quadrilateral \(ABCD\) (the region bounded by the four points on the circle), giving your answer in square centimetres.

A. ED = 10 cm; area = 96 cm²

Correct B. ED = 12 cm; area = 108 cm²

C. ED = 12 cm; area = 96 cm²

D. ED = 14 cm; area = 120 cm²

Correct Answer: B

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Question 16 View Details

A set of five test scores is arranged in ascending order as \(a \le b \le c \le d \le e\). The mean of the scores is \(24\), the median (the third score) is \(26\), the range is \(20\) and the sum of the smallest and largest scores equals the sum of the second and fourth scores. Find the smallest score \(a\).

A. 31\/2

B. 13\/2

C. 27\/4

Correct D. 27/2

Correct Answer: D

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Question 17 View Details

In the triangle shown, \(AB = 10\) cm, \(\angle A = 40^{\circ}\), \(\angle B = 70^{\circ}\) and \(\angle C = 70^{\circ}\). Point \(D\) lies on \(BC\) such that \(BD:DC = 1:2\). Find the length of \(AD\) correct to two decimal places.

Correct A. 9.47

B. 8.93

C. 7.85

D. 10.12

Correct Answer: A

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Question 18 View Details

Solve the compound inequality \(|2x-5| < x+3\) together with \(x^{2}-4x+3>0\). Find the sum of all integer values of \(x\) that satisfy both conditions.

A. 24

Correct B. 22

C. 26

D. 20

Correct Answer: B

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Question 19 View Details

In the coordinate plane shown, points \(A(1,2)\) and \(B(5,8)\) are plotted. Find the coordinates of point \(C\) on line \(AB\) such that \(AC = 5\) units. Give your answer to two decimal places.

A. (3.50, 6.50)

B. (4.12, 6.05)

Correct C. (3.77, 6.16)

D. (2.90, 5.20)

Correct Answer: C

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Question 20 View Details

A shop sells \(\frac{3}{4}\) kilogram of sugar for \(\₦1500\). What is the price per kilogram of sugar (in naira)?

A. 375

B. 500

C. 1125

Correct D. 2000

Correct Answer: D

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Question 21 View Details

If the quadratic equation (x^{2} - 6x + c = 0) has roots that are in the ratio (2:3), find the value of (c) and then compute the sum of the squares of the roots.

A. c = \frac{225}{25}; sum of squares = \frac{500}{25}

B. c = \frac{200}{25}; sum of squares = \frac{450}{25}

Correct C. c = \frac{216}{25}; sum of squares = \frac{468}{25}

D. c = \frac{216}{20}; sum of squares = \frac{468}{20}

Correct Answer: C

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Question 22 View Details

Given that \(\log_{2} x = \frac{3}{2}\) and \(\sqrt{x}=y\), find the value of \(\log_{4} (y^{4})\).

Correct A. \frac{3}{2}

B. \frac{9}{4}

C. \frac{1}{2}

D. \frac{5}{2}

Correct Answer: A

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Question 23 View Details

If non‑zero numbers \(a\) and \(b\) satisfy \(\frac{a}{b} + \frac{b}{a} = 5\), evaluate \(\frac{a^{3}+b^{3}}{a^{2}b + ab^{2}}\).

A. 5

B. 3

C. 6

Correct D. 4

Correct Answer: D

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Question 24 View Details

In a class of 120 students, the numbers studying Mathematics (M), Physics (P) and Chemistry (C) are \(|M| = 70\), \(|P| = 55\) and \(|C| = 45\). The number studying both Mathematics and Physics is twice the number studying both Physics and Chemistry, and the number studying both Mathematics and Chemistry equals the difference between the numbers studying Mathematics & Physics and Physics & Chemistry. If 20 students study none of the three subjects, how many students study both Mathematics and Chemistry?

A. 30

Correct B. 20

C. 15

D. 25

Correct Answer: B

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Question 25 View Details

The time \(T\) (in hours) required for a job varies directly as the square of the number of workers \(n\) and inversely as the efficiency \(e\) of each worker. If 5 workers each with efficiency \(80\%\) complete the job in 8 hours, how many workers each with efficiency \(60\%\) are needed to complete the same job in 6 hours? (Assume the number of workers may be taken as a whole number.)

Correct A. 4

B. 3

C. 5

D. 6

Correct Answer: A

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