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POST UTME CALEB UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Solve for x in the equation $ \frac{1}{2}x^2 + 5x - 3 = 0 $ u\sing the quadratic formula.

A. $ x = \frac{-5 \pm \sqrt{25 + 6}}{1} \ $

B. $ x = \frac{-5 \pm \sqrt{25 - 6}}{1} \ $

Correct C. $ x = \frac{-5 \pm \sqrt{25 + 12}}{1} \ $

D. $ x = \frac{-5 \pm \sqrt{25 - 12}}{1} \ $

Correct Answer: C

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Question 2

Find the determinant of the matrix $ \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{bmatrix} $.

Correct A. $ 2\( 1-4 \ $ - 3$ 8-6 $ + 1$ 8-3 $ )

B. $ 2\( 1-2 \ $ - 3$ 4-6 $ + 1$ 12-9 $ )

C. $ 2\( 1-2 \ $ - 3$ 4-3 $ + 1$ 8-12 $ )

D. $ 2\( 1-2 \ $ - 3$ 4-3 $ + 1$ 12-8 $ )

Correct Answer: A

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Question 3

A binary operation $ \odot $ is defined as $ a \odot b = a^2 + b^2 $. Find the value of $ 2 \odot 3 \odot 4 $.

Correct A. $ 2^2 + 3^2 + 4^2 $

B. $ 2^2 + 3^2 - 4^2 $

C. $ 2^2 - 3^2 + 4^2 $

D. $ 2^2 - 3^2 - 4^2 $

Correct Answer: A

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Question 4

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. $ \frac{5}{8} $

B. $ \frac{3}{8} $

C. $ \frac{2}{8} $

D. $ \frac{1}{8} $

Correct Answer: A

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Question 5

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

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

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

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

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

Correct Answer: A

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Question 6

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 7

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

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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Question 8

Solve the system of equations u\sing matrices:

Correct A. $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $

B. $ egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} $

C. $ egin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix} $

D. $ egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix} $

Correct Answer: A

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Question 9

Find the volume of the cylinder with radius 6 and height 8.

A. ( 48pi )

B. ( 64pi )

Correct C. ( 96pi )

D. ( 128pi )

Correct Answer: C

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Question 10

Simplify the expression $ \frac{1}{2} \log_{10} \( x^2 \ $ ).

Correct A. $ \frac{1}{2} \log_{10} x $

B. $ \log_{10} x $

C. $ \frac{1}{2} \log_{10} \( x^2 \ $ )

D. $ \log_{10} \( x^2 \ $ )

Correct Answer: A

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Question 11

Given the matrix A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, find the determinant of A.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12

Solve the trigonometric equation \sin^2(x) + \cos^2(x) = 1 for x.

A. 0

B. \frac{\pi}{2}

Correct C. \frac{\pi}{4}

D. \frac{3\pi}{4}

Correct Answer: C

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Question 13

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 59048

B. 59049

C. 59050

D. 59051

Correct Answer: A

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Question 14

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. \frac{3}{4}

D. \frac{5}{6}

Correct Answer: B

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Question 15

Convert the decimal number 0.5 to a \fraction in lowest terms.

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 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.

Correct A. \frac{1}{3}\pi (6) $ 4^2 + 2^2 + 4\cdot 2 $

B. \frac{1}{3}\pi (6) $ 4^2 + 2^2 - 4\cdot 2 $

C. \frac{1}{3}\pi (6) $ 4^2 - 2^2 + 4\cdot 2 $

D. \frac{1}{3}\pi (6) $ 4^2 - 2^2 - 4\cdot 2 $

Correct Answer: A

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Question 17

Solve the system of linear equations u\sing matrices: \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.

Correct A. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}

C. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 3 \end{bmatrix}

Correct Answer: A

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Question 18

Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.

Correct A. \frac{8}{3} + 3 - 1

B. \frac{8}{3} - 3 - 1

C. \frac{8}{3} + 3 + 1

D. \frac{8}{3} - 3 + 1

Correct Answer: A

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Question 19

Simplify the expression \frac{\sqrt{12}}{\sqrt{3}}.

Correct A. 2\sqrt{3}

B. \sqrt{3}

C. \sqrt{12}

D. \sqrt{3} + \sqrt{12}

Correct Answer: A

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Question 20

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

Correct A. x = -2

B. x = -1

C. x = 1

D. x = 2

Correct Answer: A

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Question 21

Find the value of $\frac{d}{dx} \left$ \frac{1}{x^2} \right $$ u\sing the quotient rule.

Correct A. -\frac{2}{x^3}

B. \frac{2}{x^3}

C. -\frac{1}{x^3}

D. \frac{1}{x^3}

Correct Answer: A

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Question 22

Solve the inequality $|x-2| > 3$.

Correct A. $ -∞, -1 $ ∪ (5, ∞)

B. $ -∞, -1 $ ∪ (1, ∞)

C. $ -∞, 1 $ ∪ (5, ∞)

D. $ -∞, -1 $ ∪ (2, ∞)

Correct Answer: A

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Question 23

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

Correct A. \frac{32\pi}{5}

B. \frac{16\pi}{3}

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

D. \frac{64\pi}{5}

Correct Answer: A

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Question 24

A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from this set is greater than 12.

Correct A. 0.25

B. 0.5

C. 0.75

D. 0.9

Correct Answer: A

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Question 25

Solve the equation $\frac{x^2}{x-1} = 2$.

A. x = 1

Correct B. x = 2

C. x = 3

D. x = 4

Correct Answer: B

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