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POST UTME UNIBEN 2023 Mathematics | Objective

Are you preparing for POST UTME UNIBEN 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

Determine the value of x in the equation $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} $.

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 2

Solve the inequality $ 2^x + 5^x geq 7^x $ for x.

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 3

Find the mean and s\tandard deviation of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Correct A. {mean=5.5, std_dev=2.9}

B. {mean=6.0, std_dev=2.8}

C. {mean=5.0, std_dev=2.7}

D. {mean=4.5, std_dev=2.6}

Correct Answer: A

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Question 4

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 5

Determine the value of the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 6

Find the value of $\int_{0}^{\pi/2} \sin^2 x \cos^2 x \, dx$.

Correct A. 1/16

B. 1/8

C. 1/4

D. 1/2

Correct Answer: A

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Question 7

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

Correct A. $ -∞, -1 $ ∪ (4, ∞)

B. $ -∞, 1 $ ∪ (4, ∞)

C. $ -∞, -1 $ ∪ (1, 4)

D. $ -∞, 1 $ ∪ (1, 4)

Correct Answer: A

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Question 8

Find the area of the region bounded by the curves $y = x^2$ and $y = 4 - x^2$.

A. 8\pi/3

Correct B. 16\pi/3

C. 32\pi/3

D. 64\pi/3

Correct Answer: B

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Question 9

A sequence is defined by $a_n = 2n^2 + 3n - 1$. Find the sum of the first 5 terms of the sequence.

A. 65

B. 70

Correct C. 75

D. 80

Correct Answer: C

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Question 10

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

Correct A. 50.24

B. 50.26

C. 50.28

D. 50.30

Correct Answer: A

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Question 11

Solve the inequality $ \frac{x^2 - 4}{x + 2} > 0 $ for ( x in mathbb{R} ).

Correct A. $ x < -2 $ or $ x > 2 $

B. $ x < -2 $ or $ x = 2 $

C. $ x > -2 $ or $ x = 2 $

D. $ x < -2 $ or $ x < 2 $

Correct Answer: A

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Question 12

If ( f(x) = \frac{x^2 - 4}{x + 2} ), find $ f\( -3 \ $ ).

Correct A. -1

B. 1

C. 2

D. -2

Correct Answer: A

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Question 13

Solve the equation $ \sin^2 x + \cos^2 x = 1 $ for ( x in [0, 2pi] ).

Correct A. $ x = \frac{pi}{2} $ or $ x = \frac{3pi}{2} $

B. $ x = \frac{pi}{4} $ or $ x = \frac{5pi}{4} $

C. $ x = \frac{pi}{6} $ or $ x = \frac{11pi}{6} $

D. $ x = \frac{pi}{3} $ or $ x = \frac{2pi}{3} $

Correct Answer: A

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Question 14

A random variable ( X ) has a probability distribution given by $ P\( X = x \ $ = \frac{1}{2} ) for $ x = 1, 2, 3 $. Find the expected value of ( X ).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 15

Find the derivative of ( 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 16

Solve the inequality $ \frac{x-2}{x+1} > 0 $ for $ x in \( -infty, -1 \ $ cup $ -1, 2 $ cup (2, infty) ).

Correct A. $ x < -1 $ or $ x > 2 $

B. $ x < -1 $ or $ x = 2 $

C. $ x > -1 $ and $ x < 2 $

D. $ x < -1 $ or $ x > 2 $

Correct Answer: A

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Question 17

A histogram of exam scores is shown below. If the mean score is 60, find the value of ( k ).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 18

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-2 \ $^2 + $ y-3 $^2 = 9 )

D. $ x-2 \ $^2 + $ y-3 $^2 = 25 )

Correct Answer: A

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Question 19

Solve the equation $ x^2 + 4x - 5 = 0 $ u\sing the quadratic formula.

Correct A. $ x = -2 pm \sqrt{6} $

B. $ x = -2 pm \sqrt{3} $

C. $ x = -2 pm \sqrt{2} $

D. $ x = -2 pm \sqrt{1} $

Correct Answer: A

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Question 20

A polynomial function has zeros at $ x = -2 $ and $ x = 3 $. If the leading coefficient is ( 2 ), find the polynomial function.

Correct A. ( f(x) = 2$ x+2 $$ x-3 $ )

B. ( f(x) = 2$ x-2 $$ x-3 $ )

C. ( f(x) = 2$ x+2 $$ x+3 $ )

D. ( f(x) = 2$ x-2 $$ x+3 $ )

Correct Answer: A

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Question 21

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

A. 2 < x < 3

Correct B. x > 3

C. x < 2

D. x = 3

Correct Answer: B

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Question 22

A circle with center ( C(2, 3) ) and radius $ r = 4 $ has an equation of the form $ x - h \ $^2 + $ y - k $^2 = r^2 ). Find the equation of the circle.

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

B. $ x + 2 $^2 + $ y + 3 $^2 = 16

C. $ x - 3 $^2 + $ y - 2 $^2 = 16

D. $ x + 3 $^2 + $ y + 2 $^2 = 16

Correct Answer: A

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Question 23

A random experiment consists of two indep\endent events, ( A ) and ( B ). If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find the probability that both events occur.

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 24

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

Correct A. y = 1x + 1

B. y = 1x - 1

C. y = -1x + 1

D. y = -1x - 1

Correct Answer: A

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Question 25

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

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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