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POST UTME CALEB UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME CALEB UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

C. \frac{64\pi}{3}

D. \frac{128\pi}{3}

Correct Answer: A

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Question 2

Solve the equation \frac{1}{2} \log_{10} $ x^2 $ = 4.

Correct A. 10^8

B. 10^4

C. 10^2

D. 10^6

Correct Answer: A

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Question 3

Find the area under the curve y = x^3 from x = -1 to x = 1.

A. \frac{2}{3}

Correct B. \frac{4}{3}

C. \frac{6}{3}

D. \frac{8}{3}

Correct Answer: B

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Question 4

A matrix A has the following elements: \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}. Find the determinant of A.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

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

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 6

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 7

Solve for (x) in the equation $ x^2 - 4x + 4 = 0 $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8

Find the sum of the first 5 terms of the geometric series $ 1 + 2 + 4 + 8 + ldots $.

A. 31

Correct B. 32

C. 33

D. 34

Correct Answer: B

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Question 9

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

Correct A. \left$ x - 2\right $^2 + \left$ y - 3\right $^2 = 16

B. \left$ x - 3\right $^2 + \left$ y - 2\right $^2 = 16

C. \left$ x - 4\right $^2 + \left$ y - 2\right $^2 = 16

D. \left$ x - 2\right $^2 + \left$ y - 4\right $^2 = 16

Correct Answer: A

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Question 10

Find the determinant of the matrix [egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}].

A. 0

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 11

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 12

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, 1 $ ∪ (3, ∞)

D. $ -∞, -3 $ ∪ (1, ∞)

Correct Answer: A

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Question 13

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

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

B. \frac{2x}{$ x^2 + 1 $^2}

C. -\frac{2}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 14

Solve the equation $ x^2 + 4x + 4 = 0 $ u\sing the quadratic formula.

Correct A. $ -2, 0 $

B. $ -1, 1 $

C. $ -2, 2 $

D. $ -1, -1 $

Correct Answer: A

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Question 15

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 2 $.

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: A

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Question 16

Determine the value of x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ) if $ \tan\( x \ $ = \frac{3}{4} ).

Correct A. $ \frac{pi}{4} $

B. $ \frac{3pi}{4} $

C. $ \frac{5pi}{4} $

D. $ \frac{7pi}{4} $

Correct Answer: A

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Question 17

Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, ldots ).

Correct A. ( 2040 )

B. ( 2050 )

C. ( 2060 )

D. ( 2070 )

Correct Answer: A

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Question 18

Solve the system of equations $ egin{cases} x + 2y = 6 \ 3x - 2y = -3 \end{cases} $.

Correct A. $ x = 1, y = 2 $

B. $ x = 2, y = 1 $

C. $ x = 3, y = 2 $

D. $ x = 4, y = 3 $

Correct Answer: A

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Question 19

Find the derivative of the function ( f(x) = 3x^2 \sin(x) ) u\sing the product rule.

Correct A. ( f'(x) = 6x \sin(x) + 3x^2 \cos(x) )

B. ( f'(x) = 6x \cos(x) - 3x^2 \sin(x) )

C. ( f'(x) = 6x \sin(x) - 3x^2 \cos(x) )

D. ( f'(x) = 6x \cos(x) + 3x^2 \sin(x) )

Correct Answer: A

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Question 20

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ x < -\frac{3}{2} $ or $ x > \frac{1}{2} $

B. $ x < -\frac{1}{2} $ or $ x > \frac{3}{2} $

C. $ x < -\frac{1}{2} $ or $ x < \frac{3}{2} $

D. $ x > -\frac{3}{2} $ or $ x < \frac{1}{2} $

Correct Answer: A

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Question 21

Find the value of $\log_{10} $ x^2 $ = 4$.

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 22

Solve the equation $\frac{1}{2}x^2 + 3x - 4 = 0$.

A. 4

Correct B. -2

C. -4

D. 2

Correct Answer: B

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Question 23

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. 1/2

B. 1/3

Correct C. 2/5

D. 3/8

Correct Answer: C

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Question 24

Find the value of $\sqrt{16} + \sqrt{9}$.

A. 5

B. 7

C. 8

Correct D. 10

Correct Answer: D

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Question 25

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. 1/2

B. 1/3

Correct C. 2/3

D. 1/6

Correct Answer: C

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