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POST UTME RSU 2024 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the circle passing 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 View Details

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

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 View Details

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 View Details

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 View Details

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 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. \(x - 3\)^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 View Details

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 View Details

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 View Details

Let ( f(x) = \(\frac{x^2 - 4}{x + 2}\)\)\) ). Find the derivative of ( f(x) ) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 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 + \(y - 3\)^\(2 = 25\)

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 View Details

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

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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