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Subject

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POST UTME NILE UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME NILE UNIVERSITY 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

Determine the probability that a randomly selected student from a class of 30 students will be taller than 1.75m, given that 60% of the students are taller than 1.75m.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 2

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 = 16

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

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

Correct Answer: A

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Question 3

Evaluate the definite integral \(int_0^1 x^2 dx\).

Correct A. 1/3

B. 1/2

C. 2/3

D. 1

Correct Answer: A

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Question 4

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

Correct A. \( x - 1 \)\( x - 2 \)\( x - 3 \) = 0

B. \( x + 1 \)\( x - 2 \)\( x - 3 \) = 0

C. \( x - 1 \)\( x + 2 \)\( x - 3 \) = 0

D. \( x + 1 \)\( x + 2 \)\( x - 3 \) = 0

Correct Answer: A

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Question 5

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 2\).

Correct A. 4/3

B. 2/3

C. 1/3

D. 1/2

Correct Answer: A

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Question 6

Find the value of 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 7

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

Correct A. \frac{x^2 + 1}{2x}

B. \frac{x^2 - 1}{2x}

C. \frac{x^2 + 2}{2x}

D. \frac{x^2 - 2}{2x}

Correct Answer: A

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Question 8

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 9

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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Question 10

A matrix A has the following elements: \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of matrix A.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 11

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

A. 20

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 12

Solve the inequality \( \frac{x}{x - 2} > 0 \) for \( x \neq 2 \).

Correct A. x < 0 or x > 2

B. x < 2

C. x > 2

D. x < 0

Correct Answer: A

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Question 13

A circle has equation \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ). Find the equation of the \tangent line at the point ( (3, 5) ).

Correct A. y = -2x + 11

B. y = 2x - 7

C. y = -x + 6

D. y = x - 3

Correct Answer: A

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Question 14

A histogram has a mean of 25 and a s\tandard deviation of 5. Find the value of ( k ) if the area under the histogram is ( k ) square units.

A. 100

Correct B. 200

C. 300

D. 400

Correct Answer: B

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Question 15

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. x = -2

B. x = 0

C. x = -1

D. x = 1

Correct Answer: A

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Question 16

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. 32\pi

B. 64\pi

Correct C. 96\pi

D. 128\pi

Correct Answer: C

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Question 17

A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.

Correct A. \( x - 4 \)^2 + \( y - 5 \)^2 = 9

B. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

C. \( x - 5 \)^2 + \( y - 6 \)^2 = 25

D. \( x - 6 \)^2 + \( y - 7 \)^2 = 36

Correct Answer: A

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Question 18

Solve the equation \[ \sin^2 x + \cos^2 x = 1 \] for x.

Correct A. \[ x = \frac{\pi}{4} \]

B. \[ x = \frac{\pi}{2} \]

C. \[ x = \frac{3\pi}{4} \]

D. \[ x = \frac{5\pi}{4} \]

Correct Answer: A

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Question 19

Find the area under the curve \[ y = \frac{1}{x} \] from x = 1 to x = 2.

Correct A. \[ \ln 2 \]

B. \[ \ln 1 \]

C. \[ \ln 3 \]

D. \[ \ln 4 \]

Correct Answer: A

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Question 20

A histogram has a mean of 25 and a s\tandard deviation of 5. Find the median.

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 21

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 6cm.

A. 100\pi cm^3

B. 200\pi cm^3

Correct C. 300\pi cm^3

D. 400\pi cm^3

Correct Answer: C

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Question 22

Solve the inequality \frac{x}{x-1} > 2.

A. x < -1 or x > 2

Correct B. x < 1 or x > 2

C. x < 1 or x > 3

D. x < -1 or x > 3

Correct Answer: B

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Question 23

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 24

Solve the system of equations \begin{align*} x+y+z &= 6, \ x+2y+3z &= 11, \ x+3y+6z &= 16. \end{align*}

Correct A. x = 1, y = 2, z = 3

B. x = 2, y = 3, z = 1

C. x = 3, y = 1, z = 2

D. x = 1, y = 3, z = 2

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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