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POST UTME UNILAG 2024 Mathematics | Objective

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Question 1 View Details

In a base-8 number system, what is the value of the digit (x\) in the number \(x_8\\((x) in the number\) such that \(x_8 + 12_8 = 23_8\)?

Correct A. 2

B. 3

C. 4

D. 5

Correct Answer: A

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Question 2 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism in cubic centimeters?

A. 72

B. 80

Correct C. 96

D. 108

Correct Answer: C

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Question 3 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} using the cofactor expansion method.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 4 View Details

A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of the vector.

Correct A. 3, 4.33

B. 4.33, 3

C. 5, 5

D. 2, 3

Correct Answer: A

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Question 5 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 6 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or x > \(-3/2\)

C. \(x <\)\(-3/2\) or \(x > 1\)

D. \(x < 3/2\)\) or x > -1

Correct Answer: A

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Question 8 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.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 9 View Details

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

Correct A. \(x = 2\)

B. \(x = 1\)

C. \(x = 0\)

D. \(x = -2\)

Correct Answer: A

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Question 10 View Details

Find the surface area 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.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 11 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using the chain rule.

Correct A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 12 View Details

Solve the inequality \(\log_2 x^2 - 4 \\)\(> 2 ).\)

A. \(x > 2\)

B. \(x < -2\)

Correct C. \(x > 2\) or \(x < -2\)

D. \(x > 4\)

Correct Answer: C

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Question 13 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 + \(y - 3\)^\(2 = 4\) )

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

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

Correct Answer: A

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Question 14 View Details

A histogram of exam scores is shown below. Find the mean score.

A. ( 60 )

B. ( 70 )

Correct C. ( 80 )

D. ( 90 )

Correct Answer: C

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Question 15 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. ( 64 )

B. ( 16 )

C. ( 32 )

D. ( 128 )

Correct Answer: A

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Question 16 View Details

Find the value of x in the equation \(\frac{1}{2}x + 5 = \frac{3}{4}x - 3\)

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 17 View Details

Solve for x in the equation \(x^2 - 6x + 8 = 0\)

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 18 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\)

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 19 View Details

A circle has a radius of 5 cm. Find the area of the circle

A. 25

Correct B. 50

C. 75

D. 100

Correct Answer: B

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Question 20 View Details

Find the equation of the line passing through the points (2,3) and (4,5)

Correct A. \(y = 2x + 1\)

B. \(y = 2x - 1\)

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 21 View Details

In triangle ABC, angle (A = 30\)°, angle \(B = 60\\((A = 30)°, angle\)°, and side \(AB = 6\) cm. Find the length of side AC.

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 10 cm

Correct Answer: C

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Question 22 View Details

A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.

A. 32π cm³

B. 64π cm³

Correct C. 128π cm³

D. 256π cm³

Correct Answer: C

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Question 23 View Details

Solve for x in the equation: \(2^x\) + \\((5^x\)\(= 7\)\\()^x\).

A. \(x = 1\)

Correct B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: B

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Question 24 View Details

Find the sum of the first 10 terms of the arithmetic progression: 1, 3, 5, ...

A. 50

B. 55

Correct C. 60

D. 65

Correct Answer: C

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Question 25 View Details

In the diagram below, ABC is a right-angled triangle with \(AB = 6\) cm and \(BC = 8\) cm. Find the length of AC.

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 10 cm

Correct Answer: C

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