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POST UTME OSUSTECH 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

A. 64\pi

Correct B. 128\pi

C. 256\pi

D. 512\pi

Correct Answer: B

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Question 2

Solve the system of equations: \begin{align*} x+y+z&=3 \ 2x+3y+4z&=7 \ 3x+2y+z&=5 \end{align*}

Correct A. x=1, y=1, z=1

B. x=2, y=1, z=0

C. x=1, y=2, z=0

D. x=0, y=1, z=2

Correct Answer: A

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Question 3

Find the area of the triangle with vertices $A(2,3), B(4,5),$ and $C(6,7)$.

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 4

Solve the inequality: \begin{align*} 2x^2 + 5x - 3 &\ge 0 \end{align*}

Correct A. x\le-1 \text{ or } x\ge\frac{3}{2}

B. x\le-1 \text{ or } x\ge\frac{1}{2}

C. x\le-1 \text{ or } x\ge\frac{3}{4}

D. x\le-1 \text{ or } x\ge\frac{1}{4}

Correct Answer: A

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Question 5

Find the value of $\tan 2\theta$ if $\sin \theta = \frac{1}{3}$ and $\cos \theta = \frac{2\sqrt{5}}{5}$.

Correct A. \frac{4}{3}

B. \frac{4}{5}

C. \frac{5}{4}

D. \frac{3}{4}

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 3x - 2}{x^2 - 4} ) u\sing the quotient rule.

Correct A. ( f'(x) = \frac{$ x^2 - 4 $$ 2x + 3 $ - $ x^2 + 3x - 2 $(2x)}{$ x^2 - 4 $^2} )

B. ( f'(x) = \frac{$ x^2 - 4 $$ 2x + 3 $ - $ x^2 + 3x - 2 $(2x)}{$ x^2 - 4 $^2} )

C. ( f'(x) = \frac{$ x^2 - 4 $$ 2x + 3 $ + $ x^2 + 3x - 2 $(2x)}{$ x^2 - 4 $^2} )

D. ( f'(x) = \frac{$ x^2 - 4 $$ 2x + 3 $ - $ x^2 + 3x - 2 $(2x)}{$ x^2 - 4 $^2} )

Correct Answer: A

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Question 7

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

A. $ x = 10^2 $

Correct B. $ x = 10^4 $

C. $ x = 10^{-2} $

D. $ x = 10^{-4} $

Correct Answer: B

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Question 8

Find the area under the curve $ y = \frac{1}{x^2 + 1} $ from $ x = 0 $ to $ x = 1 $.

Correct A. $ \frac{pi}{4} $

B. $ \frac{pi}{2} $

C. $ \frac{pi}{6} $

D. $ \frac{pi}{8} $

Correct Answer: A

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Question 9

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

A. 0.68

Correct B. 0.84

C. 0.95

D. 0.99

Correct Answer: B

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Question 10

Simplify the expression $ \frac{2^3 cdot 3^2}{2^2 cdot 3^4} $.

Correct A. $ \frac{1}{3^2} $

B. $ \frac{1}{3^4} $

C. $ \frac{1}{2^2} $

D. $ \frac{1}{2^4} $

Correct Answer: A

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Question 11

Let $ mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} $ and $ mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} $. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. \begin{pmatrix} 0.8 \\ 1.2 \end{pmatrix}

B. \begin{pmatrix} 1.2 \\ -0.8 \end{pmatrix}

C. \begin{pmatrix} 0.6 \\ 0.9 \end{pmatrix}

D. \begin{pmatrix} 0.4 \\ 0.7 \end{pmatrix}

Correct Answer: A

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Question 12

Find the volume of the solid formed by revolving the region bounded by $ y = x^2 $ and $ x = 1 $ about the x-axis.

A. \frac{1}{3}\pi

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

Correct C. \frac{4}{3}\pi

D. \frac{5}{3}\pi

Correct Answer: C

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Question 13

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

Correct D. \frac{1}{6}

Correct Answer: D

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Question 14

Find the equation of the plane pas\sing through the points ( (1, 2, 3) ), ( (2, 3, 4) ), and ( (3, 4, 5) ).

Correct A. x + y + z = 6

B. x - y - z = 0

C. x + y - z = 0

D. x - y + z = 0

Correct Answer: A

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Question 15

Solve the inequality $ |x - 2| > 3 $.

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

B. $ -\infty, 1 $ \cup $ 5, \infty $

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

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

Correct Answer: A

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Question 16

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 17

Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.

Correct A. \left$ -\infty, -3\right $ \cup \left$ 2, \infty\right $

B. \left$ -\infty, -3\right $ \cup \left$ -3, 2\right $ \cup \left$ 2, \infty\right $

C. \left$ -\infty, -3\right $ \cup \left$ 2, \infty\right $

D. \left$ -\infty, -3\right $ \cup \left$ -3, 2\right $

Correct Answer: A

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Question 18

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

Find the derivative of the function f(x) = \frac{1}{x^2 + 1}.

A. -\frac{2x}{$ x^2 + 1 $^2}

Correct B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{-2x}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: B

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Question 20

Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{1}{2^n}.

Correct A. 1

B. \frac{1}{2}

C. \frac{1}{3}

D. \frac{1}{4}

Correct Answer: A

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Question 21

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $ u\sing the quadratic formula. What is the value of ( x )?

A. 2

Correct B. -3

C. -2

D. 1

Correct Answer: B

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Question 22

A circle with center ( C ) and radius ( r ) passes through the points ( A ) and ( B ). If $ CA = 3 $ and $ CB = 4 $, what is the value of ( r )?

Correct A. 5

B. 3

C. 4

D. 2

Correct Answer: A

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Question 23

Find the determinant of the matrix $ \begin{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 24

A vector $ \vec{a} $ has components $ a_1 = 2 $ and $ a_2 = 3 $. If $ \vec{b} $ is a unit vector in the same direction as $ \vec{a} $, what is the value of $ b_1 $?

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 25

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, 1 $ ∪ (3, ∞)

D. $ -∞, -3 $ ∪ (1, ∞)

Correct Answer: A

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