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POST UTME CALEB UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )

B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )

C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

Correct Answer: A

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Question 2

Solve the inequality \( left| x - 2 \right| geq 3 \).

Correct A. \( x leq -1 \) or ( x geq 5 )

B. ( x leq 1 ) or ( x geq 5 )

C. \( x leq -1 \) or ( x geq 4 )

D. ( x leq 1 ) or ( x geq 4 )

Correct Answer: A

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Question 3

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?

Correct A. \( \frac{3}{8} \)

B. \( \frac{1}{4} \)

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

D. \( \frac{1}{2} \)

Correct Answer: A

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Question 4

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

Correct A. \( x = -2 \)

B. \( x = 2 \)

C. \( x = -1 \) or \( x = -3 \)

D. \( x = 1 \) or \( x = 3 \)

Correct Answer: A

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Question 5

Find the value of ( x ) in the equation \( 2^x = 16 \).

A. \( x = 2 \)

Correct B. \( x = 4 \)

C. \( x = 1 \)

D. \( x = 3 \)

Correct Answer: B

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Question 6

Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find ( AB ) u\sing the rule of Sarrus.

Correct A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}

B. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}

C. \begin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix}

D. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}

Correct Answer: A

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Question 7

A random experiment has two possible outcomes: A and B. The probability of outcome A is 0.4, and the probability of outcome B is 0.6. If outcome A occurs, there is a 0.7 probability that outcome C will occur. If outcome B occurs, there is a 0.8 probability that outcome C will occur. What is the probability that outcome C will occur?

Correct A. 0.28

B. 0.56

C. 0.84

D. 0.96

Correct Answer: A

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Question 8

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

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

Correct B. \frac{-2x}{\( x^2 + 1 \)^2}

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

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

Correct Answer: B

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Question 9

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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Question 10

Find the area of the triangle formed by the points ( (0, 0) ), ( (3, 4) ), and ( (6, 0) ).

Correct A. 12

B. 15

C. 18

D. 20

Correct Answer: A

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Question 11

Let ( f(x) = \frac{1}{x^2 + 1} ). Find \( lim_{x \to infty} f\( x \ \) ).

Correct A. 0

B. 1

C. ∞

D. undefined

Correct Answer: A

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Question 12

A set ( A ) contains 5 elements. If ( A ) has 3 subsets, what is the number of elements in the power set of ( A )?

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 13

A sequence \( a_n \) is defined as \( a_n = \frac{1}{n} \). Find the sum of the first 5 terms of the sequence.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 14

A histogram has a mean of 20 and a s\tandard deviation of 5. If the histogram has 10 bars, what is the range of the histogram?

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 15

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), what is the probability that both events occur?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 16

A vector ( mathbf{a} ) has a magnitude of 5 and a direction of 30°. If a vector ( mathbf{b} ) has a magnitude of 3 and a direction of 60°, what is the magnitude of the sum of the two vectors?

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 17

A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). If \( a = 2 \) and \( b = 3 \), what is the result of the operation?

A. 13

B. 14

C. 15

Correct D. 16

Correct Answer: D

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Question 18

A set ( A ) contains 3 elements. If ( A ) has 2 subsets, what is the number of elements in the power set of ( A )?

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 19

A sequence \( a_n \) is defined as \( a_n = \frac{1}{n^2} \). Find the sum of the first 4 terms of the sequence.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 20

A histogram has a mean of 25 and a s\tandard deviation of 6. If the histogram has 12 bars, what is the range of the histogram?

A. 20

B. 30

C. 40

D. 50

Correct Answer: VIEW ANSWER

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Question 21

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. x^2 + y^2 + 6x - 4y - 12 = 0

B. x^2 + y^2 - 6x + 4y - 12 = 0

C. x^2 + y^2 + 4x - 6y - 12 = 0

D. x^2 + y^2 - 4x + 6y - 12 = 0

Correct Answer: A

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Question 22

Solve the system of equations u\sing matrices: \begin{align*} x + 2y - z &= 4 \ 2x - 3y + z &= 3 \ -x + y + 2z &= -2 \end{align*}

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

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

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

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

Correct Answer: A

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Question 23

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

A. 256\pi cm^3

Correct B. 512\pi cm^3

C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: B

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Question 24

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 25

Solve the polynomial equation: x^3 - 6x^2 + 11x - 6 = 0.

Correct A. x = 1, 2, 3

B. x = 1, 2, -3

C. x = 1, -2, 3

D. x = 2, -1, 3

Correct Answer: A

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