Exam Body

Year

Subject

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POST UTME AAUA 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 2

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.135

B. 0.225

Correct C. 0.675

D. 0.975

Correct Answer: C

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Question 3

Find the area under the curve y = 3x² + 2x - 5 from x = 0 to x = 4.

A. 120

B. 140

Correct C. 160

D. 180

Correct Answer: C

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Question 4

Simplify the expression \( \frac{2x^2 - 5x + 3}{x^2 - 2x - 3} \).

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

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

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

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

Correct Answer: A

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Question 5

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 6

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.

A. x = -2

Correct B. x = 2

C. x = -1

D. x = 1

Correct Answer: B

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Question 7

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

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 8

A set of 5 consecutive integers has a median of 9. What is the sum of the integers?

A. 45

B. 50

Correct C. 55

D. 60

Correct Answer: C

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Question 9

A company produces x units of a product, where x is a multiple of 5. If the company produces 25 units, what is the value of x?

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 10

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?

Correct A. 8 cm

B. 6 cm

C. 4 cm

D. 2 cm

Correct Answer: A

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Question 11

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}}mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{|mathbf{a}|^2} mathbf{a} \).

Correct A. \begin{pmatrix} 0.8 \ 1.2 \end{pmatrix}

B. \begin{pmatrix} 1.6 \ 2.4 \end{pmatrix}

C. \begin{pmatrix} 2.4 \ 3.6 \end{pmatrix}

D. \begin{pmatrix} 3.2 \ 4.8 \end{pmatrix}

Correct Answer: A

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Question 12

Find the derivative of ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. 2 \sin x \cos x

B. -2 \sin x \cos x

C. \cos^2 x

D. \sin^2 x

Correct Answer: A

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Question 13

A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \tangent line to the circle at the point ( (5, 7) ).

Correct A. y = -1x + 12

B. y = x + 3

C. y = -x + 9

D. y = x - 5

Correct Answer: A

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Question 14

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. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 15

Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 4 \) about the x-axis.

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

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

C. \frac{96}{3} \pi

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

Correct Answer: A

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Question 16

Let ( S ) be the set of all possible values of ( x ) that satisfy the inequality \( |x - 2| geq 3 \). Find the number of elements in ( S ).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 17

In the diagram below, the graph of a quadratic function is shown. If the vertex of the parabola is at \( -2, 3 \ \) ), find the equation of the axis of symmetry.

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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Question 18

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 19

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

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 20

In the diagram below, the equation of the circle is given by \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ). Find the coordinates of the center of the circle.

Correct A. (1, 2)

B. (2, 1)

C. (3, 4)

D. (4, 3)

Correct Answer: A

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Question 21

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 22

A histogram is constructed from the following data: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23. What is the class width of the histogram?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 23

Solve the equation: \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 24

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30 cm^3

B. 40 cm^3

Correct C. 50 cm^3

D. 60 cm^3

Correct Answer: C

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Question 25

Solve the inequality: \( 2x - 5 > 3 \).

Correct A. x > 4

B. x > 3

C. x > 2

D. x > 1

Correct Answer: A

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