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POST UTME OSUSTECH 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Solve for 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

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 3

Solve the inequality \( x^2 - 6x + 8 \geq 0 \).

Correct A. \( -\infty, 2 \) \cup \( 4, \infty \)

B. (2, 4)

C. \( -\infty, 2 \) \cup \( 4, \infty \)

D. (2, 4)

Correct Answer: A

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Question 4

A particle moves in a circular path with a cons\tant speed of 5m/s. If the radius of the circle is 3m, find the magnitude of the acceleration of the particle.

A. 5\pi

B. 10\pi

Correct C. 15\pi

D. 20\pi

Correct Answer: C

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Question 5

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 = -2x + 3

D. y = -2x - 3

Correct Answer: A

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Question 6

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. Calculate the coefficient of variation (CV) for the sample.

A. 16.8%

Correct B. 17.4%

C. 18.0%

D. 18.6%

Correct Answer: B

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Question 7

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

A. 10^4

B. 10^8

Correct C. 10^12

D. 10^16

Correct Answer: C

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Question 8

A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \( \vec{a} \).

Correct A. 4.33 \hat{i} + 2.5 \hat{j}

B. 4.33 \hat{i} - 2.5 \hat{j}

C. 2.5 \hat{i} + 4.33 \hat{j}

D. 2.5 \hat{i} - 4.33 \hat{j}

Correct Answer: A

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Question 9

Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.

A. 32

B. 64

Correct C. 96

D. 128

Correct Answer: C

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Question 10

A 3x3 matrix \( A \) has the following elements: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]. Find the determinant of \( A \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 3 & 2 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 12

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

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 13

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 14

Find the derivative of the function [ f(x) = 3x^2 + 2x - 5 ].

Correct A. 6x + 2

B. 3x^2 + 2

C. 6x - 2

D. 3x^2 - 2

Correct Answer: A

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Question 15

A circle has a radius of 4 cm. Find its circumference.

A. 8π

Correct B. 16π

C. 32π

D. 64π

Correct Answer: B

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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

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

Correct A. x < -1 or x > 3/2

B. x > -1 or x < 3/2

C. x < 3/2 or x > -1

D. x > 3/2 or x < -1

Correct Answer: A

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Question 18

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 19

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

Correct A. x = 1, y = 1

B. x = 2, y = 3

C. x = 3, y = 2

D. x = 4, y = 1

Correct Answer: A

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Question 20

Find the vector \( \vec{a} \times \vec{b} \) given that \( \vec{a} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \) and \( \vec{b} = \begin{bmatrix} 4 \ 5 \ 6 \end{bmatrix} \).

Correct A. \begin{bmatrix} -3 \ 6 \ -3 \end{bmatrix}

B. \begin{bmatrix} 3 \ -6 \ 3 \end{bmatrix}

C. \begin{bmatrix} 6 \ -3 \ 3 \end{bmatrix}

D. \begin{bmatrix} -6 \ 3 \ -3 \end{bmatrix}

Correct Answer: A

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Question 21

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 22

Find the \logarithm \( \log_{10} \( 1000 \ \) ).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 23

Solve the inequality \( \frac{x}{2} + 3 > 5 \).

Correct A. x > 2

B. x < 2

C. x > 4

D. x < 4

Correct Answer: A

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Question 24

Find the value of \( \sqrt{16} + \sqrt{9} \).

A. 7

B. 8

C. 9

D. 10

Correct Answer: VIEW ANSWER

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Question 25

In a certain number base, the number 1011 is equivalent to 11 in base 10. What is the value of the number base?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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