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POST UTME PAN-ATLANTIC UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME PAN-ATLANTIC UNIVERSITY 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.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3

In the diagram below, identify the type of triangle formed by the points A(1, 2), B(3, 4), and C(5, 6).\n\n{\n \n \n \n}

A. Isosceles

B. Scalene

C. Equilateral

Correct D. Right-angled

Correct Answer: D

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Question 4

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 5

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

A. 50

B. 100

C. 200

Correct D. 400

Correct Answer: D

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Question 6

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.5 cm

C. 10 cm

D. 12.5 cm

Correct Answer: B

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Question 7

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30 cm³

B. 40 cm³

C. 50 cm³

D. 60 cm³

Correct Answer: A

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Question 8

A s\tandard six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \frac{1}{3}

B. \frac{1}{2}

Correct C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: C

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Question 9

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

Correct A. \[ x = -2 \]

B. \[ x = -1 \]

C. \[ x = 0 \]

D. \[ x = 1 \]

Correct Answer: A

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Question 10

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

Correct A. -120

B. -150

C. -180

D. -200

Correct Answer: A

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Question 11

Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 < x < 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 < y < 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y < 1 \).

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 12

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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Question 13

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14

Let ( f(x) = egin{cases} x^2, & x < 0 \ x^3, & x \geq 0 \end{cases} ). Find the value of \( \int_{-1}^{1} f\( x \ \) \, dx ).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 15

Solve the system of equations: \( x + y = 2 \) and \( xy = 1 \).

Correct A. x = 1, y = 1

B. x = 2, y = 0

C. x = 0, y = 2

D. x = -1, y = -1

Correct Answer: A

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Question 16

Find the area under the curve of ( f(x) = 2x^2 + 3x - 1 ) from \( x = 0 \) to \( x = 2 \).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 17

Solve the system of linear equations: \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = - 3 \end{cases} \).

Correct A. \begin{cases} x = 1 \ y = 2 \end{cases}

B. \begin{cases} x = 2 \ y = 1 \end{cases}

C. \begin{cases} x = 3 \ y = 0 \end{cases}

D. \begin{cases} x = 0 \ y = 3 \end{cases}

Correct Answer: A

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Question 18

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

Correct A. \frac{\pi}{12}

B. \frac{\pi}{6}

C. \frac{\pi}{4}

D. \frac{\pi}{2}

Correct Answer: A

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Question 19

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

Correct A. \begin{cases} x = -2 \end{cases}

B. \begin{cases} x = 2 \end{cases}

C. \begin{cases} x = -1 \end{cases}

D. \begin{cases} x = 1 \end{cases}

Correct Answer: A

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Question 20

Find the surface area of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = x \) about the x-axis.

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

B. \frac{\pi}{6}

C. \frac{\pi}{4}

D. \frac{\pi}{2}

Correct Answer: A

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Question 21

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 6.1 cm, calculate the 95% confidence interval for the mean height of the university students.

A. 168.3 cm to 182.7 cm

Correct B. 170.1 cm to 180.9 cm

C. 172.9 cm to 178.1 cm

D. 174.7 cm to 176.3 cm

Correct Answer: B

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Question 22

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 23

A company produces two products, A and B. The profit from the production of product A is ₦120 per unit, while the profit from the production of product B is ₦180 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?

A. ₦48,000

B. ₦54,000

Correct C. ₦60,000

D. ₦66,000

Correct Answer: C

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Question 24

A right-angled triangle has a hypotenuse of 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

B. 7.5 cm

Correct C. 8.66 cm

D. 10 cm

Correct Answer: C

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Question 25

A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of \( \vec{a} \).

Correct A. \( \begin{pmatrix} 2.5 \ 4.33 \end{pmatrix} \)

B. \( \begin{pmatrix} 3.54 \ 2.5 \end{pmatrix} \)

C. \( \begin{pmatrix} 4.33 \ 2.5 \end{pmatrix} \)

D. \( \begin{pmatrix} 2.5 \ 3.54 \end{pmatrix} \)

Correct Answer: A

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