Exam Body

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POST UTME AAUA 2018 Mathematics | Objective

Are you preparing for POST UTME AAUA 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

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

Correct A. \( -\infty, 2 \) \cup \( 2, \infty \)

B. \( -\infty, 0 \) \cup \( 2, \infty \)

C. \( -\infty, 0 \) \cup (0, 2)

D. (0, 2)

Correct Answer: A

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Question 2

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

Correct A. y = \frac{1}{2}x + 1

B. y = 2x - 1

C. y = -\frac{1}{2}x + 2

D. y = x + 2

Correct Answer: A

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Question 3

A histogram is shown below. What is the mean of the data set?

A. 20

B. 22

Correct C. 25

D. 30

Correct Answer: C

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Question 4

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

Correct A. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 5

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

Correct A. x = -2

B. x = 0

C. x = -1

D. x = 1

Correct Answer: A

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Question 6

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 - 2y + 12 = 0

B. x^2 + y^2 - 4x + 2y - 10 = 0

C. x^2 + y^2 + 2x - 4y + 15 = 0

D. x^2 + y^2 + 4x + 2y - 20 = 0

Correct Answer: A

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Question 7

Evaluate the definite integral \int_0^1 \( 2x + 1 \) dx.

Correct A. 3

B. 2

C. 1

D. 4

Correct Answer: A

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Question 8

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

Correct A. 55

B. 60

C. 65

D. 70

Correct Answer: A

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Question 9

Find the equation of the \tangent to the curve y = x^2 at the point (1, 1).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 10

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

Correct A. \frac{32\pi}{3}

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

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

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

Correct Answer: A

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Question 11

Let ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( int_{0}^{\frac{pi}{4}} f\( x \ \) , dx ).

Correct A. \frac{1}{2}

B. \frac{1}{4}

C. \frac{1}{3}

D. \frac{1}{5}

Correct Answer: A

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Question 12

In a set of 10 students, 5 are boys and 5 are girls. If 2 students are selected at random, what is the probability that at least one of them is a girl?

A. \frac{1}{2}

B. \frac{2}{5}

Correct C. \frac{3}{5}

D. \frac{4}{5}

Correct Answer: C

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Question 13

Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).

Correct A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)

B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

C. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

D. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)

Correct Answer: A

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Question 14

Find the area of the region bounded by the curves \( y = x^2 \) and \( y = 2x \).

A. \frac{1}{3}

B. \frac{2}{3}

Correct C. \frac{4}{3}

D. \frac{5}{3}

Correct Answer: C

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Question 15

Let \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find the product ( AB ).

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

B. \begin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix}

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

D. \begin{bmatrix} 25 & 28 \ 49 & 56 \end{bmatrix}

Correct Answer: A

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Question 16

Find the derivative of the function ( f(x) = \frac{x^2 + 3x - 2}{x^2 - 4} ) u\sing the quotient rule.

A. \( \frac{\( 2x + 3 \)\( x^2 - 4 \ \) - \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )

B. \( \frac{\( 2x + 3 \)\( x^2 - 4 \ \) + \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )

Correct C. \( \frac{\( 2x + 3 \)\( x^2 - 4 \ \) - \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )

D. \( \frac{\( 2x + 3 \)\( x^2 - 4 \ \) + \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )

Correct Answer: C

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Question 17

Solve the inequality \( \frac{x - 2}{x + 1} > 0 \) u\sing interval notation.

Correct A. \( -infty, -1 \ \) cup (2, infty) )

B. \( -infty, -1 \ \) cup (1, 2) )

C. \( -infty, -1 \ \) cup (2, infty) )

D. \( -infty, -1 \ \) cup (1, 2) )

Correct Answer: A

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Question 18

Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \) u\sing integration.

A. \( \frac{pi}{2} \)

Correct B. \( \frac{pi}{4} \)

C. \( \frac{pi}{2} \)

D. \( \frac{pi}{4} \)

Correct Answer: B

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Question 19

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

Correct A. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)

B. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi \)

C. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)

D. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi \)

Correct Answer: A

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Question 20

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

A. \( x = 2 \)

Correct B. \( x = 4 \)

C. \( x = 2 \)

D. \( x = 4 \)

Correct Answer: B

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Question 21

A random sample of 16 students from a population of 50 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 22

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student will score above 80?

A. 0.1587

B. 0.3413

Correct C. 0.4772

D. 0.6745

Correct Answer: C

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Question 23

Solve for x in the equation \( x^2 + 5x + 6 = 0 \).

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 24

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 25

A company has two factories, A and B, producing a total of 1000 units per day. Factory A produces 60% of the total units, while factory B produces the remaining 40%. If the profit per unit from factory A is ₦50 and from factory B is ₦30, what is the total profit per day?

A. ₦3500

Correct B. ₦4000

C. ₦4500

D. ₦5000

Correct Answer: B

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