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POST UTME AAUA 2019 Mathematics | Objective

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Question 1 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

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 View Details

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 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using 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 View Details

Find the equation of the line passing 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 View Details

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 View Details

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 View Details

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 View Details

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} ) using the formula \(\\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \mathrm{proj}_{\mathbf{a}}\mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}|^2} \mathbf{a}\).

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 View Details

Find the derivative of ( f(x) = \\(\sin^2\) x ) using 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 View Details

A circle has equation \(x - 2 \\)^2 + \(y - 3)^\(2 = 4\) ). Find the equation of the \\\\((()^(2\) = 4\)\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 View Details

Two events A and B are independent. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 using the cosine rule.

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 22 View Details

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 View Details

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 View Details

A rectangular 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 View Details

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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