Exam Body

Year

Subject

Paper Type

neco 2025 mathematics | Objective

Prepare for your exams with neco questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 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 two boxes, A and B. Box A has 3 red and 2 blue balls. A box is selected at random with probability \(0.4\) for A and \(0.6\) for B. Box B contains red, blue and green balls totalling 30. The overall probability of drawing a red ball is \(0.5\) and that of drawing a green ball is \(0.2\). Find the number of green balls in Box B.

Correct A. 10

B. 15

C. 6

D. 12

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2 View Details

Two numbers have a sum of 20. After increasing the larger by 4 and decreasing the smaller by 3, the new numbers are in the ratio \(5:3\). Find the original larger number.

A. 75\/8

Correct B. 73/8

C. 71\/8

D. 73\/6

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3 View Details

The diagram shows the graph of a quadratic function \(f(x)\) that opens upwards, has its vertex at \((2,-3)\) and passes through the point \((0,1)\). Determine the value of \(f(4)\).

Correct A. 1

B. 3

C. -1

D. 5

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4 View Details

In a class of 60 students, the numbers studying Mathematics (M), Physics (P) and Chemistry (C) are \(|M| = 35\), \(|P| = 30\) and \(|C| = 15\). The numbers studying both Mathematics and Physics, Mathematics and Chemistry, and Physics and Chemistry are 12, 10 and 7 respectively. Five students study none of the three subjects. How many students study all three subjects?

A. 3

Correct B. 4

C. 6

D. 5

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5 View Details

Let \(a\) and \(b\) be non‑zero real numbers satisfying \(\frac{a}{b}+\frac{b}{a}=5\). Find the value of \(\frac{a^{3}+b^{3}}{ab\,(a+b)}\).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6 View Details

A water tank consists of a right circular cylinder of unknown height \(h\) metres and radius \(2\) m, surmounted by a hemispherical dome of radius \(2\) m. When the tank is filled with water to a depth of \(10\) m from the bottom, the volume of water is \(120\) m\(^3\). Find the height \(h\) of the cylindrical part (to two decimal places).

A. 10.27

Correct B. 9.38

C. 7.95

D. 8.41

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7 View Details

In a class, 30 students sat for Exam\,1 and the mean score was \(68\) with a variance of \(36\). All 30 students also sat for Exam\,2, so there are a total of 60 scores. The combined mean of the two exams (i.e., the mean of the 60 scores) is \(72\) and the combined variance is \(49\). Determine the mean score of Exam\,2 and the variance of the scores in Exam\,2.

Correct A. Mean = 76, Variance = 30

B. Mean = 74, Variance = 36

C. Mean = 78, Variance = 24

D. Mean = 70, Variance = 40

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8 View Details

The time \(t\) (in minutes) required to paint a wall varies directly as the area \(A\) (in square metres) and inversely as the number of painters \(p\). If 3 painters can paint a 120\,m\(^2\) wall in 4\,hours, how long will 5 painters take to paint a 180\,m\(^2\) wall? Give your answer in minutes.

Correct A. 216

B. 240

C. 300

D. 180

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9 View Details

Vectors \(\mathbf{a}\) and \(\mathbf{b}\) lie in the same plane. It is given that \(|\mathbf{a}| = 5\), \(|\mathbf{a}+\mathbf{b}| = 8\) and \(|\mathbf{a}-\mathbf{b}| = 6\). Determine (i) the magnitude \(|\mathbf{b}|\) and (ii) the angle \(\theta\) between \(\mathbf{a}\) and \(\mathbf{b}\) (in degrees, to the nearest integer).

A. |b| = 4, θ ≈ 45°

B. |b| = 7, θ ≈ 60°

C. |b| = 6, θ ≈ 90°

Correct D. |b| = 5, θ ≈ 74°

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10 View Details

Evaluate \( \frac{3}{4} \times 0.8 + \frac{2}{5} \) and give your answer as a decimal rounded to two decimal places.

A. 0.60

Correct B. 1.00

C. 1.20

D. 0.80

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11 View Details

For which integer values of n does the inequality \(\lvert 2x - n\rvert < x + 5\) hold for every integer x from 1 to 10 inclusive?

A. 5, 8

B. 5, 6

C. 7, 8

Correct D. 6, 7

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12 View Details

The time \(t\) (seconds) required for a particle to travel a distance \(s\) (metres) under a constant force \(F\) (newtons) varies directly with \(s\) and inversely with \(\sqrt{F}\). When \(s = 20\) m and \(F = 25\) N, \(t = 8\) s. Find the time required when \(s = 45\) m and \(F = 100\) N.

Correct A. 9

B. 7

C. 18

D. 4.5

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13 View Details

Points \(A(2, -1)\) and \(B(8, 3)\) are joined. Determine the coordinates of the point \(P\) on line \(AB\) that is closest to the origin.

Correct A. (\frac{14}{13}, -\frac{21}{13})

B. (\frac{14}{13}, \frac{21}{13})

C. (-\frac{14}{13}, -\frac{21}{13})

D. (\frac{14}{13}, -\frac{7}{13})

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14 View Details

Write the decimal number 0.000345 in scientific notation.

A. 34.5 \\times 10^{-5}

B. 3.45 \\times 10^{-3}

Correct C. 3.45 \times 10^{-4}

D. 3.45 \\times 10^{-5}

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15 View Details

A solid consists of a right circular cylinder of radius \(r\) cm and height \(h\) cm, with a hemisphere of the same radius attached on top. The total surface area, excluding the base of the cylinder, is \(300\pi\) cm\(^{2}\). Find the radius \(r\), the height \(h\), and the total volume of the solid. Give the volume in terms of \(\pi\).

A. r = 4 cm, h = 30 cm, volume = \frac{1568}{3}\pi cm^{3}

B. r = 6 cm, h = 20 cm, volume = \frac{2592}{3}\pi cm^{3}

C. r = 5 cm, h = 20 cm, volume = \frac{1750}{3}\pi cm^{3}

Correct D. r = 5 cm, h = 25 cm, volume = \frac{2125}{3}\pi cm^{3}

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16 View Details

If \(2\mathbf{a} - \mathbf{b}\) is perpendicular to \(\mathbf{a} + 3\mathbf{b}\) and \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 8\), find the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees (to one decimal place).

A. 90.0°

B. 30.0°

Correct C. 45.4°

D. 60.0°

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17 View Details

The sum of the first five terms of an arithmetic progression equals half the sum of the next five terms. If the first term is \(a\) and the common difference is \(d\), find the ratio \(\frac{a}{d}\).

A. 5

B. 2

C. 4

Correct D. 3

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18 View Details

Simplify the expression \(\frac{\sqrt{50} - \sqrt{2}}{\sqrt{8}} + \log_{10}(2^{3}\times5^{2})\) and give your answer in exact form.

A. 4 - \log_{10}2

B. 4 + \log_{10}5

C. 5 + \log_{10}2

Correct D. 4 + \log_{10}2

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19 View Details

Solve for \(x\): \(\frac{2}{x-1} + \frac{3}{x+2} = \frac{5}{x+1}\). State the solution.

A. -10

Correct B. -11

C. -9

D. -12

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20 View Details

Let \(x\) be the larger root of the equation \(x^{2} - 6x + 5 = 0\). Evaluate \(E = \frac{x^{3} - 3x^{2} + 4x - 12}{x^{2} - 5x + 6}\) and give your answer as a fraction in lowest terms.

A. 31/3

B. 28/3

C. 29/4

Correct D. 29/3

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21 View Details

The quadratic equation \(x^{2} - p x + q = 0\) has two distinct positive roots. It is given that the sum of the roots is 13 and the sum of the squares of the roots is 113. Find the values of \(p\) and \(q\).

A. p = 12, q = 28

B. p = 13, q = 30

Correct C. p = 13, q = 28

D. p = 14, q = 27

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22 View Details

For what value of \(k\) does the quadratic equation \(2x^{2} - (k+4)x + (k-1) = 0\) have two distinct real roots that are reciprocals of each other?

A. 5

B. 4

Correct C. 3

D. 2

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23 View Details

In triangle \(ABC\), \(AB = 10\) cm and \(AC = 6\) cm. The internal angle bisector of \(\angle A\) meets side \(BC\) at \(D\) and it is given that \(BD = 5\) cm. Determine the length of \(CD\) and the area of triangle \(ABC\).

A. CD = 5 cm; area = 18 cm^2

B. CD = 4 cm; area = 20 cm^2

C. CD = 2 cm; area = 30 cm^2

Correct D. CD = 3 cm; area = 24 cm^2

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24 View Details

A solid is formed by drilling a right circular cylinder through the centre of a right rectangular prism. The prism has length twice its width and its height equal to its width. The cylinder has a radius equal to half the width of the prism and a height equal to the height of the prism. The total surface area of the resulting solid (including the interior cylindrical surface and the base of the prism) is \(1500\) cm\(^2\). Find the total volume of the original prism.

A. Approximately 10120 cm^3

B. Approximately 9275 cm^3

Correct C. Approximately 8838 cm^3

D. Approximately 8420 cm^3

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25 View Details

A chemist mixes a solution containing \(12\%\) acid with another solution containing \(35\%\) acid. The total volume of the mixture before any loss is \(50\) L. After the mixture is left to stand, \(5\) L of pure water evaporates, and the concentration of the remaining solution becomes \(25\%\). Determine the volume (in litres) of each original solution used.

A. 12% solution ≈ 30.00 L, 35% solution ≈ 20.00 L

B. 12% solution ≈ 25.00 L, 35% solution ≈ 25.00 L

Correct C. 12% solution ≈ 27.17 L, 35% solution ≈ 22.83 L

D. 12% solution ≈ 28.50 L, 35% solution ≈ 21.50 L

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support