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POST UTME ABU 2025 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. 48\pi \(cm^3\)

B. 64\pi \(cm^3\)

C. 96\pi \(cm^3\)

D. 128\pi \(cm^3\)

Correct Answer: A

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Question 2 View Details

A bakery sells a total of 250 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?

A. 125

Correct B. 150

C. 175

D. 200

Correct Answer: B

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Question 3 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

A. 8 cm

Correct B. 6\sqrt{5} cm

C. 8\sqrt{5} cm

D. 12 cm

Correct Answer: B

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Question 4 View Details

A set of 4 coins contains 2 nickels and 2 dimes. If a coin is selected at random, what is the probability that it is a nickel?

Correct A. \(\frac{1}{2}\)\)

B. \(\frac{1}{3}\)\)

C. \(\frac{2}{3}\)\)

D. \(\frac{3}{4}\)\)

Correct Answer: A

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Question 5 View Details

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: A

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Question 6 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new median?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7 View Details

Solve for x in the equation \(\frac{1}{x} + 2 = \frac{3}{x}\).

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 8 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi

Correct B. 48\pi

C. 72\pi

D. 96\pi

Correct Answer: B

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Question 9 View Details

A sequence is defined by the recurrence relation (a_\(n = 2a\)_{n-1} + 3\). If \(a_1 = 2\\((a_n = 2a_{n-1} + 3). If\), find the value of \(a_{10}\).

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 10 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, 1\) \cup \(3, \infty\)

C. \(-\infty, -1\) \cup \(1, \infty\)

D. \(-\infty, 1\) \cup \(1, \infty\)

Correct Answer: A

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4\)

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

C. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2\)

D. \(\frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4\)

Correct Answer: A

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Question 12 View Details

Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\) using the quadratic formula.

Correct A. \(x = \frac{-5 \pm \sqrt{25 + 24}}{4}\)

B. \(x = \frac{-5 \pm \sqrt{25 - 24}}{4}\)

C. \(x = \frac{-5 \pm \sqrt{25 + 24}}{2}\)

D. \(x = \frac{-5 \pm \sqrt{25 - 24}}{2}\)

Correct Answer: A

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Question 13 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(x^2\)\) and the line \(x = 2\\((y = x^2) and the line\) about the x-axis.

Correct A. \(\frac{4}{3} \pi \times 2^3\)

B. \(\frac{4}{3} \pi \times 2^2\)

C. \(\frac{4}{3} \pi \times 2\)

D. \(\frac{4}{3} \pi \times 2^2 \times 2\)

Correct Answer: A

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Question 14 View Details

A particle moves along the curve (y = \(x^3 - 6x^2 + 9x + 2\)\) with a velocity of \(\\((y = x^3 - 6x^2 + 9x + 2) with a velocity of \frac{dy}{dx} = 3x^2 - 12x + 9\). Find the acceleration of the particle at the point where \(x = 1\).

Correct A. \(6x - 12\)

B. \(3x^2 - 12x + 9\)

C. \(6x^2 - 12x + 9\)

D. \(3x^2 - 12x + 9\)

Correct Answer: A

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Question 15 View Details

A rectangular box has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the box.

Correct A. \(2 \times 5 \times 3 + 3 \times 2 + 2 \times 5 \\) )

B. \(2 \times 5 \times 3 + 3 \times 2 + 2 \times 5 + 5 \times 2 \\) )

C. \(2 \times 5 \times 3 + 3 \times 2 + 2 \times 5 + 5 \times 2 + 3 \times 2 \\) )

D. \(2 \times 5 \times 3 + 3 \times 2 + 2 \times 5 + 5 \times 2 + 3 \times 2 + 2 \times 5 \\) )

Correct Answer: A

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Question 16 View Details

Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17 View Details

A matrix A is given by \(A = \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\). Find the determinant of A.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 18 View Details

A quadratic equation is given by \(x^2 + 4x + 4 = 0\). Solve for x.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 19 View Details

A probability experiment consists of rolling two fair six-sided dice. What is the probability that the sum of the numbers on the dice is 7?

Correct A. \(1/6\)

B. \(1/12\)

C. \(1/18\)

D. \(1/36\)

Correct Answer: A

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Question 20 View Details

A trigonometric equation is given by \(\sin^2 x + \cos^2 x = 1\). Simplify the equation.

Correct A. \\(\sin^2\) \(x = 1\)

B. \\(\cos^2\) \(x = 1\)

C. \\(sin x =\)\cos x

D. \\(sin x = -\)\cos x

Correct Answer: A

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Question 21 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi

B. 48\pi

Correct C. 96\pi

D. 192\pi

Correct Answer: C

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Question 22 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9}\)\)\\() > 0.\)

Correct A. \(-3, -2\) \cup (2, 3)

B. \(-3, -2\) \cup (2, 3) \cup (4, 5)

C. \(-3, -2\) \cup (2, 3) \cup \(-5, -4\)

D. \(-3, -2\) \cup (2, 3) \cup (4, 5) \cup \(-5, -4\)

Correct Answer: A

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Question 23 View Details

Find the equation of the tangent line to the curve \(y = x\^2 + 2x - 3\\(tangent line to the curve (y = x\) at the point (1, 2).

Correct A. \(y = 4x - 1\)

B. \(y = 4x + 1\)

C. \(y = 4x - 3\)

D. \(y = 4x + 3\)

Correct Answer: A

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Question 24 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.

Correct A. \begin{pmatrix} 1 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ 2 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \end{pmatrix}

D. \begin{pmatrix} 4 \ 0 \end{pmatrix}

Correct Answer: A

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Question 25 View Details

Find the area of the region bounded by the curves \(y = x\^2\) and \(y = 2x\).

Correct A. \(4/3\)

B. \(2/3\)

C. \(1/3\)

D. \(4/5\)

Correct Answer: A

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