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POST UTME RSU 2024 Mathematics | Objective

Are you preparing for POST UTME RSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

A. 64\pi cm^3

Correct B. 128\pi cm^3

C. 256\pi cm^3

D. 512\pi cm^3

Correct Answer: B

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Question 2

Solve the inequality \frac{x^2 - 4x - 5}{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 3

Find the area under the curve y = \sin^2 x from x = 0 to x = \frac{\pi}{2}.

A. \frac{\pi}{4}

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

C. \frac{\pi}{3}

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

Correct Answer: B

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Question 4

Solve the equation \log_{10} $ x^2 $ = 4.

Correct A. 10^4

B. 10^8

C. 10^12

D. 10^16

Correct Answer: A

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Question 5

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

A. 288\pi cm^2

Correct B. 576\pi cm^2

C. 864\pi cm^2

D. 1152\pi cm^2

Correct Answer: B

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Question 6

Determine the value of $\int_{0}^{\pi} \frac{1}{1 + \sin^2 x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{1}

Correct Answer: A

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Question 7

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

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

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

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

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

Correct Answer: A

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Question 8

Find the equation of the circle pas\sing through the points $(2, 3)$ and $$ -1, 4 $$.

Correct A. $x^2 + y^2 - 5x + 7y + 12 = 0$

B. $x^2 + y^2 + 5x - 7y + 12 = 0$

C. $x^2 + y^2 - 5x - 7y + 12 = 0$

D. $x^2 + y^2 + 5x + 7y + 12 = 0$

Correct Answer: A

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Question 9

A random variable $X$ has a probability density function $f(x) = \begin{cases} \frac{1}{2} & \text{if } 0 < x < 2 \ 0 & \text{otherwise} \end{cases}$. Find $P$ X > 1 $$.

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. \frac{3}{4}

D. \frac{1}{2}

Correct Answer: B

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Question 10

Solve the system of equations $\begin{cases} x^2 + y^2 = 16 \ x + y = 4 \end{cases}$.

Correct A. $(2, 2)$

B. $(4, 0)$

C. $(0, 4)$

D. $(2, 4)$

Correct Answer: A

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Question 11

Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.

A. 120

B. 150

Correct C. 180

D. 200

Correct Answer: C

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Question 12

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

Correct A. $ -∞, -1 $ ∪ (5, ∞)

B. $ -∞, 1 $ ∪ (5, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 1 $ ∪ (5, ∞)

Correct Answer: A

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Question 13

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 - 2 $^2 + $ y + 3 $^2 = 16

Correct Answer: A

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Question 14

Solve the equation x^2 + 4x - 5 = 0.

Correct A. $ -5, 1 $

B. $ -1, 5 $

C. $ 1, -5 $

D. $ -1, 5 $

Correct Answer: A

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Question 15

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 16

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

A. \frac{2x$ x + 2 $ - $ x^2 - 4 $(1)}{$ x + 2 $^2}

B. \frac{2x$ x + 2 $ + $ x^2 - 4 $(1)}{$ x + 2 $^2}

Correct C. \frac{2x$ x + 2 $ - $ x^2 - 4 $(1)}{$ x + 2 $^2}

D. \frac{2x$ x + 2 $ + $ x^2 - 4 $(1)}{$ x + 2 $^2}

Correct Answer: C

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Question 17

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

Correct A. \frac{160\pi}{3}

B. \frac{320\pi}{3}

C. \frac{80\pi}{3}

D. \frac{40\pi}{3}

Correct Answer: A

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Question 18

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

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

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

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

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

Correct Answer: A

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Question 19

A sequence is defined by the formula $ a_n = 2n + 1 $. Find the sum of the first 5 terms of the sequence.

A. 15

Correct B. 25

C. 35

D. 45

Correct Answer: B

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Question 20

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8\sqrt{3}

B. 6\sqrt{3}

C. 8\sqrt{2}

D. 6\sqrt{2}

Correct Answer: A

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Question 21

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22

Solve for y in the equation $ y = \frac{1}{2} \left\( x + \frac{1}{x} \right \ $ ).

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

B. \frac{x^2 - 1}{2x}

C. \frac{x^2 + 2}{2x}

D. \frac{x^2 - 2}{2x}

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 = 25

C. $ x - 2 $^2 + $ y - 3 $^2 = 36

D. $ x - 2 $^2 + $ y - 3 $^2 = 49

Correct Answer: A

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Question 24

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

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

B. \frac{2}{x^3}

C. -\frac{1}{x^3}

D. \frac{1}{x^3}

Correct Answer: A

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Question 25

Solve the system of equations $ x + y = 4 $ and $ x - y = 2 $.

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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