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POST UTME ACHIEVERS UNIVERSITY 2021 Mathematics | Objective

Prepare for your exams with POST UTME ACHIEVERS UNIVERSITY questions? Reviewing past/model 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.

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Question 1 View Details

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 View Details

Solve the system of linear equations using 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 View Details

Find the equation of the tangent line to the curve $y = x\^2 + 2x - 3\\(tangent line to the curve (y = x$ 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function f(x) = $\frac{x^2}{x$^2 + 1}\)\) using 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 View Details

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 View Details

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 View Details

Find the derivative of ( f(x) = $\frac{x^2}{x$^2 + 1}\)\) ) using 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 View Details

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 View Details

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 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = $x^2$\) and the line $x = 2\\((y = x^2) and the line$ 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the circle passing 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 View Details

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{160\pi}{3}$\) \text{ cm}^3 )

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

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

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

Correct Answer: A

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Question 23 View Details

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$1x Big|_0^1 = \frac{\pi}{4}$

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

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

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

Correct Answer: A

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Question 24 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

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 View Details

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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