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POST UTME OSUSTECH 2023 Mathematics | Objective

Are you preparing for POST UTME OSUSTECH 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 volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm.

A. 100\pi cm^3

B. 200\pi cm^3

Correct C. 300\pi cm^3

D. 400\pi cm^3

Correct Answer: C

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Question 2

Solve for x in the equation \tan x = \frac{1}{\sqrt{3}}.

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

B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{2\pi}{3}

Correct Answer: A

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Question 3

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \frac{1}{6}

Correct B. \frac{1}{3}

C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: B

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Question 4

Find the mean of the numbers 2, 4, 6, 8, 10.

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 5

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

A. 16\pi cm^2

B. 32\pi cm^2

Correct C. 64\pi cm^2

D. 128\pi cm^2

Correct Answer: C

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Question 6

In the diagram below, a circle is inscribed in a square. If the radius of the circle is 4 cm, what is the area of the shaded region?

Correct A. 16π

B. 64

C. 32

D. 128

Correct Answer: A

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Question 7

A polynomial function f(x) is defined as f(x) = x^3 + 2x^2 - 7x - 12. Find the value of f\( -2 \).

Correct A. -2

B. 4

C. -4

D. 12

Correct Answer: A

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Question 8

In a histogram, the class width is 5 and the number of classes is 6. If the total frequency is 30, what is the class frequency?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 9

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism.

A. 400

B. 500

Correct C. 600

D. 800

Correct Answer: C

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Question 10

In a circle, the length of the major axis is 10 cm and the length of the minor axis is 8 cm. Find the area of the circle.

A. 50π

B. 75π

Correct C. 100π

D. 125π

Correct Answer: C

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Question 11

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 12

Solve the system of equations u\sing matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

Correct A. \text{Solution: } x = 3, y = 1

B. \text{Solution: } x = 1, y = 3

C. \text{Solution: } x = 2, y = 2

D. \text{Solution: } x = 4, y = 0

Correct Answer: A

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Question 13

Find the mean and s\tandard deviation of the data set: \{2, 4, 6, 8, 10\}

Correct A. \text{Mean: } 6, \text{S\tandard Deviation: } 2

B. \text{Mean: } 4, \text{S\tandard Deviation: } 2

C. \text{Mean: } 6, \text{S\tandard Deviation: } 4

D. \text{Mean: } 4, \text{S\tandard Deviation: } 4

Correct Answer: A

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Question 14

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{2}

B. \frac{3}{5}

Correct C. \frac{3}{8}

D. \frac{5}{8}

Correct Answer: C

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Question 15

Find the sum of the first 5 terms of the geometric progression: \{2, 6, 18, 54, 162\}

Correct A. 242

B. 242.5

C. 243

D. 243.5

Correct Answer: A

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Question 16

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 17

A particle moves in a straight line with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity of the particle at time \( t = 2 \) seconds.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 18

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

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: A

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Question 19

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 20

A binary operation ( ast ) on the set ( {1, 2, 3, 4} ) is defined by \( a ast b = a + b \). Find the result of ( 2 ast 3 ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 21

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 22

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 = 16

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 23

Solve the system of linear equations u\sing matrices: 2x + 3y = 7 and x - 2y = -3.

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: A

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Question 24

Find the equation of the line pas\sing through the points (1, 2) and (3, 4).

Correct A. y = x + 1

B. y = x - 1

C. y = x + 2

D. y = x - 2

Correct Answer: A

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Question 25

Determine the s\tandard deviation of the dataset: 1, 3, 5, 7, 9.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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