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POST UTME OSUSTECH 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2

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

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 3

Find the volume of the solid formed by revolving the region bounded by the curves $ y = x^2 $ and $ y = 4 - x $ about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 4

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

Correct A. $ x - 2 $^2 + $ y - 3 $^2 = 16

B. $ x - 3 $^2 + $ y - 2 $^2 = 16

C. $ x + 2 $^2 + $ y + 3 $^2 = 16

D. $ x - 3 $^2 + $ y + 2 $^2 = 16

Correct Answer: A

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Question 5

Solve the inequality $ x^2 - 4x + 3 > 0 $.

Correct A. $ -\infty, 1 $ \cup $ 3, \infty $

B. $ -\infty, 3 $ \cup $ 1, \infty $

C. $ -\infty, 1 $ \cup (1, 3)

D. $ -\infty, 3 $ \cup (3, 1)

Correct Answer: A

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Question 6

Find the equation of the line pas\sing through the points (2,3) and (4,5) in the coordinate plane.

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: B

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Question 7

Find the area of the region bounded by the parabola y = x^2, the x-axis, and the line x = 3.

A. 9

Correct B. 18

C. 27

D. 36

Correct Answer: B

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Question 8

Find the value of x in the equation $ egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 4 \end{bmatrix} $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 9

Find the value of $ \log_{10} \( x^2 \ $ ) given that $ \log_{10} \( x \ $ = 2 ).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 10

Find the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and calculate the s\tandard deviation.

Correct A. 5.5, 2.87

B. 6.5, 2.87

C. 7.5, 2.87

D. 8.5, 2.87

Correct Answer: A

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Question 11

Determine the value of $n$ in the sequence $a_n = 2n^2 + 3n - 1$, given that $a_1 = 0$ and $a_2 = 5$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12

Find the equation of the line pas\sing through the points $$ -2, 3 $$ and $$ 1, -2 $$.

Correct A. y = -x + 5

B. y = x + 1

C. y = -2x - 3

D. y = 2x - 1

Correct Answer: A

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Question 13

A binary operation $\star$ is defined as $a \star b = a^2 + b^2$. Find the value of $x$ such that $2 \star x = 17$.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 14

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 15

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

Correct A. 50.24

B. 50.27

C. 50.29

D. 50.31

Correct Answer: A

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Question 16

Find the volume of the solid formed by rotating the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 17

Solve the inequality $\log_2 $ x^2 + 1 $ > 3$.

Correct A. $ -\infty, -1 $ \cup $ 1, \infty $

B. $ -\infty, -2 $ \cup $ -1, \infty $

C. $ -\infty, 0 $ \cup $ 1, \infty $

D. $ -\infty, -2 $ \cup $ 0, \infty $

Correct Answer: A

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Question 18

Find the surface area of the solid formed by rotating the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 19

Solve the equation $\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}$.

A. x = -1

Correct B. x = 1

C. x = -2

D. x = 2

Correct Answer: B

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Question 20

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

Correct A. 8/3

B. 16/3

C. 32/3

D. 64/3

Correct Answer: A

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Question 21

Determine the value of x in the equation $ \frac{1}{2}x^2 + 3x - 5 = 0 $ u\sing the quadratic formula.

Correct A. $ x = -6 \pm \sqrt{6} \ $

B. $ x = 2 \pm \sqrt{3} \ $

C. $ x = -2 \pm \sqrt{3} \ $

D. $ x = 6 \pm \sqrt{6} \ $

Correct Answer: A

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Question 22

Solve for y in the equation $ y = \frac{1}{2} \log_{10} \( x^2 \ $ ) where x = 10.

Correct A. $ y = 1 \ $

B. $ y = 2 \ $

C. $ y = 3 \ $

D. $ y = 4 \ $

Correct Answer: A

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Question 23

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 24

Solve the system of equations u\sing matrices: $ \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. $ x = 2, y = 3 \ $

B. $ x = 3, y = 2 \ $

C. $ x = 4, y = 5 \ $

D. $ x = 5, y = 4 \ $

Correct Answer: A

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Question 25

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.

Correct A. ( f'(x) = 6x + 2 \)

B. ( f'(x) = 6x - 2 \)

C. ( f'(x) = 6x + 5 \)

D. ( f'(x) = 6x - 5 \)

Correct Answer: A

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