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POST UTME BOWEN UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME BOWEN UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4 \)

Correct Answer: A

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Question 2

Solve the equation \( \log_{10} \( x^2 \ \) = 4 ) for ( x ).

Correct A. \( x = 10^4 \)

B. \( x = 10^2 \)

C. \( x = 10^{-4} \)

D. \( x = 10^{-2} \)

Correct Answer: A

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Question 3

Find the magnitude of the vector \( vec{a} = egin{pmatrix} 3 \ 4 \end{pmatrix} \).

Correct A. \( \sqrt{3^2 + 4^2} \)

B. \( 3 + 4 \)

C. \( 3 \times 4 \)

D. \( \frac{3}{4} \)

Correct Answer: A

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Question 4

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

Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)

C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)

D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 5

Find the value of \( \sin 2x \) given that \( \sin x = \frac{3}{5} \) and \( \cos x = \frac{4}{5} \).

Correct A. \( \frac{24}{25} \)

B. \( \frac{12}{25} \)

C. \( \frac{16}{25} \)

D. \( \frac{20}{25} \)

Correct Answer: A

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Question 6

A cylindrical \tank with a radius of 7m and height of 10m is filled with water. If the water level is raised by 2m, calculate the increase in volume of water in the \tank.

Correct A. 980\pi \text{ m}^3

B. 980\pi \text{ m}^3

C. 980\pi \text{ m}^3

D. 980\pi \text{ m}^3

Correct Answer: A

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Question 7

Solve for x in the equation \tan x = \sqrt{3} - \cot x.

Correct A. \frac{\pi}{6}

B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{\pi}{4}

Correct Answer: A

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Question 8

A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the new mean is 12. Find the sum of the original 5 numbers.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 9

Solve the inequality \frac{x-2}{x+1} > 0.

Correct A. x < -1 \text{ or } x > 2

B. x < -1 \text{ or } x < 2

C. x > -1 \text{ or } x < 2

D. x > -1 \text{ or } x > 2

Correct Answer: A

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Question 10

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

Correct A. 16\pi \text{ cm}^2

B. 32\pi \text{ cm}^2

C. 64\pi \text{ cm}^2

D. 128\pi \text{ cm}^2

Correct Answer: A

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Question 11

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.

A. 168.3 cm, 182.7 cm

Correct B. 170.1 cm, 180.9 cm

C. 172.9 cm, 178.1 cm

D. 174.5 cm, 176.5 cm

Correct Answer: B

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Question 12

A company produces light bulbs with a mean lifespan of 1200 hours and a s\tandard deviation of 120 hours. If a sample of 36 light bulbs is selected, what is the probability that the sample mean lifespan is less than 1150 hours?

A. 0.025

B. 0.05

Correct C. 0.10

D. 0.20

Correct Answer: C

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Question 13

A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75 and the s\tandard deviation is 10, what is the probability that a student scored above 85?

A. 0.15

B. 0.20

C. 0.25

Correct D. 0.30

Correct Answer: D

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Question 14

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.12

Correct B. 0.20

C. 0.24

D. 0.30

Correct Answer: B

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Question 15

A function f(x) = 2x^2 + 5x - 3 has a local maximum at x = -1. Find the value of the function at this point.

A. -5

Correct B. -3

C. 1

D. 5

Correct Answer: B

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Question 16

A curve is defined by the equation y = 2x^3 - 5x^2 + x + 1. Find the area under the curve between x = 0 and x = 1.

A. 0.5

B. 1.0

Correct C. 1.5

D. 2.0

Correct Answer: C

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Question 17

A polynomial function f(x) = x^4 - 2x^3 + x^2 - x + 1 has a root at x = 1. Find the other roots of the function.

A. x = 0, x = 1, x = 2, x = 3

B. x = 0, x = 1, x = -1, x = 2

C. x = 0, x = 1, x = -1, x = -2

Correct D. x = 0, x = 1, x = 2, x = -1

Correct Answer: D

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Question 18

A variation problem states that the \cost of producing x units of a product is given by the equation C(x) = 2x^2 + 5x + 1. Find the marginal \cost function.

Correct A. 4x + 5

B. 2x + 5

C. x^2 + 5

D. 2x^2 + 5

Correct Answer: A

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Question 19

Find the equation of the circle with center at \( -2, 3 \) and radius 4.

Correct A. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16

B. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16

C. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 20

Find the sum of the first 10 terms of the geometric sequence 3, 6, 12, ...

A. S_{10} = 1230

B. S_{10} = 1240

Correct C. S_{10} = 1250

D. S_{10} = 1260

Correct Answer: C

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Question 21

Find the volume of the sphere with radius 6 cm.

Correct A. V = 904.778 cm^3

B. V = 904.778

C. V = 904.778 cm^3

D. V = 904.778

Correct Answer: A

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Question 22

Solve for x in the equation \log_{10} \( x^2 \) = 4.

Correct A. x = 10^4

B. x = 10^2

C. x = 10^8

D. x = 10^6

Correct Answer: A

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Question 23

Find the surface area of the cube with side length 8 cm.

Correct A. A = 256 cm^2

B. A = 256

C. A = 256 cm^2

D. A = 256

Correct Answer: A

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Question 24

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 25

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

Correct A. S_5 = 30

B. S_5 = 25

C. S_5 = 20

D. S_5 = 15

Correct Answer: A

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