Exam Body

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POST UTME ACHIEVERS UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME ACHIEVERS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine 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 2

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 3

Solve the matrix equation $ \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. x = 1, y = 2

B. x = 2, y = 3

C. x = 3, y = 4

D. x = 4, y = 5

Correct Answer: A

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Question 4

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

Correct A. 25\pi

B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: A

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Question 5

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 12 cm

Correct Answer: C

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Question 6

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 170.3 cm, 180.7 cm

B. 168.1 cm, 182.9 cm

C. 169.5 cm, 181.5 cm

D. 171.1 cm, 179.9 cm

Correct Answer: A

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Question 7

Find the area under the curve of the function $ f(x) = \frac{1}{x^2 + 1} $ from $ x = 0 $ to $ x = 1 $.

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

B. \frac{\pi}{2}

C. \frac{\pi}{6}

D. \frac{\pi}{3}

Correct Answer: A

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Question 8

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ u\sing the factor theorem.

A. $ x = 1 $

B. $ x = 2 $

Correct C. $ x = 3 $

D. $ x = 4 $

Correct Answer: C

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Question 9

A binary operation $ \ast $ on the set $ \{ 1, 2, 3, 4 \} $ is defined as $ a \ast b = a + b $. Find the value of $ 2 \ast 3 $.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 10

A histogram of exam scores is shown below. If the mean score is 75 and the s\tandard deviation is 10, find the area under the curve between 60 and 80.

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 11

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

A. $ x = -10 $

B. $ x = 3 $

Correct C. $ x = -3 $

D. $ x = 10 $

Correct Answer: C

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Question 12

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

Correct A. ( 1 )

B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: A

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Question 13

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

Correct A. $ x < -1 $ or $ x > 3 $

B. $ x < 1 $ or $ x > 3 $

C. $ x < -3 $ or $ x > 1 $

D. $ x < 3 $ or $ x > 1 $

Correct Answer: A

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Question 14

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

A. ( 6 )

Correct B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: B

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Question 15

Solve the system of equations $ x + y = 4 $ and $ 2x - y = 3 $.

A. $ x = 1, y = 3 $

B. $ x = 2, y = 2 $

Correct C. $ x = 3, y = 1 $

D. $ x = 4, y = 0 $

Correct Answer: C

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Question 16

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

Correct A. -4

B. 4

C. -2

D. 2

Correct Answer: A

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Question 17

Solve the equation [ \sin^2 x + \cos^2 x = 1 ].

Correct A. x = \frac{\pi}{4}

B. x = \frac{\pi}{2}

C. x = \frac{\pi}{6}

D. x = \frac{\pi}{3}

Correct Answer: A

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Question 18

Find the equation of the circle with center (3, 4) and radius 5.

Correct A. $ x - 3 $^2 + $ y - 4 $^2 = 25

B. $ x - 4 $^2 + $ y - 3 $^2 = 25

C. $ x - 5 $^2 + $ y - 3 $^2 = 25

D. $ x - 3 $^2 + $ y - 5 $^2 = 25

Correct Answer: A

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Question 19

Find the derivative of the function [ f(x) = 3x^2 + 2x - 5 ].

Correct A. f'(x) = 6x + 2

B. f'(x) = 6x - 2

C. f'(x) = 3x^2 + 2

D. f'(x) = 3x^2 - 2

Correct Answer: A

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Question 20

Find the area under the curve [ y = x^2 + 2x - 3 ] from x = 0 to x = 4.

Correct A. 20

B. 30

C. 40

D. 50

Correct Answer: A

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Question 21

Find the value of $\int_0^1 x^2 \ln(x) dx$.

Correct A. 1/3

B. 1/2

C. 2/3

D. 1

Correct Answer: A

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Question 22

Solve the inequality $|x^2 - 4| > 2$.

Correct A. $ -∞, -2 $ ∪ (2, ∞)

B. $ -∞, -1 $ ∪ (1, ∞)

C. $ -∞, -3 $ ∪ (3, ∞)

D. $ -∞, -4 $ ∪ (4, ∞)

Correct Answer: A

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Question 23

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

A. 2/3

B. 1/2

C. 1

Correct D. 4/3

Correct Answer: D

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Question 24

Solve the system of equations $x + y = 2$ and $xy = 1$.

Correct A. (1, 1)

B. $ 1, -1 $

C. $ -1, 1 $

D. $ -1, -1 $

Correct Answer: A

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Question 25

Find the derivative of the function $f(x) = \ln$ x^2 $$.

Correct A. 2/x

B. 1/x

C. 2/x^2

D. 1/x^2

Correct Answer: A

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