Exam Body

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POST UTME ACHIEVERS UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME ACHIEVERS UNIVERSITY 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 frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. 64\pi cm^3

B. 128\pi cm^3

C. 192\pi cm^3

D. 256\pi cm^3

Correct Answer: A

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Question 2

Solve the system of linear equations u\sing matrices:

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 3

Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 2).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 4

A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the value of a_5.

Correct A. 31

B. 32

C. 33

D. 34

Correct Answer: A

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Question 5

Find the surface area of the sphere with radius 6 cm.

Correct A. 288\pi cm^2

B. 288\pi cm^3

C. 288\pi cm^4

D. 288\pi cm^5

Correct Answer: A

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Question 6

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. 32\pi

B. 64\pi

Correct C. 96\pi

D. 128\pi

Correct Answer: C

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Question 7

Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 4x + 4} > 0.

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

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

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

D. $ -\infty, 1] \cup \( 2, \infty \ $

Correct Answer: A

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Question 8

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 = 16

D. $ x + 2 $^2 + $ y - 3 $^2 = 32

Correct Answer: A

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Question 9

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

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

B. \frac{2x^3 + 2x}{$ x^2 + 1 $^2}

C. \frac{2x^3 - 2x}{$ x^2 + 1 $^2}

D. \frac{2x^3 + 2}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 10

Solve the system of equations \begin{align*} x + y &= 2 \ x - 2y &= -3 \end{align*}.

Correct A. \begin{cases} x = -1 \ y = 3 \end{cases}

B. \begin{cases} x = 1 \ y = 1 \end{cases}

C. \begin{cases} x = -1 \ y = 1 \end{cases}

D. \begin{cases} x = 1 \ y = 3 \end{cases}

Correct Answer: A

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Question 11

Find the equation of the circle with center at $$ -2,3 $$ and radius $4$.

Correct A. $ x^2 + y^2 + 4x - 6y - 7 = 0 $

B. $ x^2 + y^2 - 4x + 6y - 7 = 0 $

C. $ x^2 + y^2 + 2x - 3y - 7 = 0 $

D. $ x^2 + y^2 - 2x + 3y - 7 = 0 $

Correct Answer: A

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Question 12

Find the derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the chain rule.

Correct A. ( f'(x) = \frac{2x$ x^2 + 1 $ - 2x^3}{$ x^2 + 1 $^2} )

B. ( f'(x) = \frac{2x^2 - 2}{$ x^2 + 1 $^2} )

C. ( f'(x) = \frac{2x^3 - 2x}{$ x^2 + 1 $^2} )

D. ( f'(x) = \frac{2x^2 + 2}{$ x^2 + 1 $^2} )

Correct Answer: A

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Question 13

A histogram of exam scores is shown below. What is the mean score?

A. ( 60 )

Correct B. ( 70 )

C. ( 80 )

D. ( 90 )

Correct Answer: B

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Question 14

Solve the inequality $ x^2 - 4x - 5 > 0 $.

Correct A. $ x < -1 $ or $ x > 5 $

B. $ x < 1 $ or $ x > 5 $

C. $ x < -1 $ or $ x < 5 $

D. $ x > 1 $ or $ x > 5 $

Correct Answer: A

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Question 15

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

A. $ \frac{32}{3} pi $

Correct B. $ \frac{64}{3} pi $

C. $ \frac{128}{3} pi $

D. $ \frac{256}{3} pi $

Correct Answer: B

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Question 16

Determine the number of terms in the expansion of $ 1+x \ $^{10}) when it is expressed as a binomial series.

A. 11

Correct B. 10

C. 9

D. 12

Correct Answer: B

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Question 17

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

Correct A. \frac{π}{4}

B. \frac{π}{2}

C. \frac{π}{3}

D. \frac{π}{5}

Correct Answer: A

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Question 18

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

Correct A. $ -∞, -3 $ ∪ (2, ∞)

B. $ -∞, -3 $ ∪ (2, 3)

C. $ -∞, -3 $ ∪ (3, ∞)

D. $ -∞, 3 $ ∪ (4, ∞)

Correct Answer: A

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Question 19

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

Correct B. 17

C. 16

D. 15

Correct Answer: B

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Question 20

Find the value of (x) in the equation $ 2^x + 2^x = 128 $.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 21

Find the equation of the circle pas\sing through the points ((2,3)), ((4,5)), and ((6,7)).

Correct A. $ x^2 + y^2 - 12x - 6y + 36 = 0 $

B. $ x^2 + y^2 - 8x - 4y + 16 = 0 $

C. $ x^2 + y^2 - 10x - 5y + 25 = 0 $

D. $ x^2 + y^2 - 14x - 7y + 49 = 0 $

Correct Answer: A

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Question 22

A solid cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

Correct A. $ \frac{1}{3} pi \( 4^2 \ $(10) = \frac{160pi}{3} \text{ cm}^3 )

B. $ \frac{1}{3} pi \( 4^2 \ $(5) = \frac{80pi}{3} \text{ cm}^3 )

C. $ \frac{1}{3} pi \( 4^2 \ $(15) = \frac{240pi}{3} \text{ cm}^3 )

D. $ \frac{1}{3} pi \( 4^2 \ $(20) = \frac{320pi}{3} \text{ cm}^3 )

Correct Answer: A

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Question 23

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

Correct A. $ int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{4} $

B. $ int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{2} $

C. $ int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{6} $

D. $ int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{3} $

Correct Answer: A

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Question 24

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. ( P(A cap B) = P(A) cdot P(B) = 0.4 cdot 0.6 = 0.24 )

B. ( P(A cap B) = P(A) + P(B) = 0.4 + 0.6 = 1 )

C. ( P(A cap B) = P(A) - P(B) = 0.4 - 0.6 = -0.2 )

D. ( P(A cap B) = P(A) cdot P(B) = 0.4 cdot 0.6 = 0.24 )

Correct Answer: A

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Question 25

Simplify the expression [ \sqrt[3]{64x^3y^3} ].

Correct A. $ \sqrt[3]{64x^3y^3} = 4x^1y^1 $

B. $ \sqrt[3]{64x^3y^3} = 4x^3y^3 $

C. $ \sqrt[3]{64x^3y^3} = 8x^3y^3 $

D. $ \sqrt[3]{64x^3y^3} = 2x^3y^3 $

Correct Answer: A

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