POST UTME KSU 2023 Mathematics | Objective

Are you preparing for POST UTME KSU 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.

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 2
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 3
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the highest score is 90, what is the lowest score?
Correct A. 40
B. 50
C. 60
D. 70

Correct Answer: A

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Question 4
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. 10π
B. 20π
Correct C. 30π
D. 40π

Correct Answer: C

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Question 5
A circle has a radius of 4 cm. Find the area of the circle.
Correct A. 16π
B. 20π
C. 24π
D. 32π

Correct Answer: A

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Question 6
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the 95% confidence interval for the mean height of the university students.
Correct A. 170.35 cm, 179.65 cm
B. 168.35 cm, 181.65 cm
C. 169.35 cm, 180.65 cm
D. 171.35 cm, 178.65 cm

Correct Answer: A

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Question 7
Find the area under the curve y = x^2 + 2x - 3 from x = 1 to x = 3.
A. 20
B. 22
Correct C. 24
D. 26

Correct Answer: C

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Question 8
Simplify the expression \( \sqrt{\frac{16}{25}} \) and express it in the form \( \frac{a}{b} \).
Correct A. \( \frac{4}{5} \)
B. \( \frac{3}{5} \)
C. \( \frac{2}{5} \)
D. \( \frac{1}{5} \)

Correct Answer: A

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Question 9
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?
A. 150
B. 200
Correct C. 250
D. 300

Correct Answer: C

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Question 10
Solve the quadratic 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 11
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
Correct A. \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. \frac{x}{\( x^2 + 1 \)^{3/2}}
C. \frac{1}{\( x^2 + 1 \)^{3/2}}
D. \frac{-1}{\( x^2 + 1 \)^{3/2}}

Correct Answer: A

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Question 12
Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).
A. x = 1
Correct B. x = 2
C. x = 3
D. x = 4

Correct Answer: B

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Question 13
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
Correct C. 18
D. 24

Correct Answer: C

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Question 14
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 15
Find the equation of the circle with center (2, 3) and radius 4.
Correct A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 32
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 64
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 128

Correct Answer: A

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Question 16
Find the volume of the cylinder with radius 5 and height 10.
A. 250\pi
Correct B. 500\pi
C. 750\pi
D. 1000\pi

Correct Answer: B

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Question 17
Find the surface area of the sphere with radius 6.
A. 144\pi
B. 288\pi
Correct C. 432\pi
D. 576\pi

Correct Answer: C

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Question 18
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. y = 2x + 1
B. y = 2x - 1
C. y = -2x + 1
D. y = -2x - 1

Correct Answer: VIEW ANSWER

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Question 19
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
Correct A. -2
B. 2
C. -1
D. 1

Correct Answer: A

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Question 20
A company produces two products, A and B. Product A requires 2 hours of labor and 1 hour of machine time to produce 100 units, while product B requires 1 hour of labor and 2 hours of machine time to produce 150 units. If the company has 120 hours of labor and 180 hours of machine time available, how many units of product A and product B should the company produce to maximize profit?
Correct A. 200 units of A and 300 units of B
B. 300 units of A and 200 units of B
C. 400 units of A and 100 units of B
D. 100 units of A and 400 units of B

Correct Answer: A

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Question 21
A particle moves along the x-axis with its position given by the equation ( x(t) = 2t^2 - 5t + 3 ), where ( t ) is time in seconds. Find the velocity of the particle at time \( t = 2 \) seconds.
A. -1 m/s
Correct B. 1 m/s
C. 2 m/s
D. 3 m/s

Correct Answer: B

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Question 22
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the points ( (1, 2) ) and ( (3, 4) ), find the center of the circle.
Correct A. (2, 3)
B. (3, 2)
C. (4, 5)
D. (5, 4)

Correct Answer: A

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Question 23
A company has two factories, A and B, which produce the same product. Factory A produces 200 units per day, while factory B produces 150 units per day. If the company wants to produce a total of 500 units per day, how many days will it take to produce this amount?
A. 2 days
Correct B. 3 days
C. 4 days
D. 5 days

Correct Answer: B

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Question 24
A particle moves along the x-axis with its position given by the equation ( x(t) = 3t^3 - 2t^2 + t ), where ( t ) is time in seconds. Find the acceleration of the particle at time \( t = 1 \) second.
A. 3 m/s^2
B. 6 m/s^2
Correct C. 9 m/s^2
D. 12 m/s^2

Correct Answer: C

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Question 25
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the points ( (2, 3) ) and ( (4, 5) ), find the radius of the circle.
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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