POST UTME SKYLINE UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details
A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the 95% confidence interval for the mean height of all students in the university.
Correct A. 170.35 cm, 179.65 cm
B. 168.35 cm, 181.65 cm
C. 169.35 cm, 180.65 cm
D. 171.35 cm, 178.65 cm

Correct Answer: A

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Question 2 View Details
Find the derivative of the function \(f(x) = \frac{1}{x^2 + 1}\) using the chain rule.
Correct A. \(f'(x) = \frac{-2x}{x^2 + 1 ^2}\)
B. \(f'(x) = \frac{2x}{x^2 + 1 ^2}\)
C. \(f'(x) = \frac{x}{x^2 + 1 ^2}\)
D. \(f'(x) = \frac{-x}{x^2 + 1 ^2}\)

Correct Answer: A

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Question 3 View Details
A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75 and the standard deviation is 10, find the area under the curve between 60 and 80.
Correct A. 0.4
B. 0.5
C. 0.6
D. 0.7

Correct Answer: A

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Question 4 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 + \(y + 3\)^\(2 = 16\) \)
C. \(x + 3\)^2 + \(y - 2\)^\(2 = 16\) \)
D. \(x - 3\)^2 + \(y + 2\)^\(2 = 16\) \)

Correct Answer: A

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Question 5 View Details
A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the first five terms of the sequence.
Correct A. [3, 7, 15, 31, 63]
B. [3, 5, 7, 9, 11]
C. [3, 6, 12, 24, 48]
D. [3, 8, 16, 32, 64]

Correct Answer: A

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Question 6 View Details
Solve for 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 7 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
A. 64
B. 128
Correct C. 256
D. 512

Correct Answer: C

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Question 8 View Details
Solve the inequality \(x^2 - 4x + 4 \geq 0\).
Correct A. x \leq 2
B. x \geq 2
C. \(x < 2\)
D. \(x > 2\)

Correct Answer: A

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Question 9 View Details
Find the derivative of the function ( f(x) = \(x^3 - 6x^2 + 9x + 2\) ).
Correct A. \(3x^2 - 12x + 9\)
B. \(3x^2 - 12x + 10\)
C. \(3x^2 - 12x + 9 + 2\)
D. \(3x^2 - 12x + 9 - 2\)

Correct Answer: A

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Question 10 View Details
Solve the trigonometric equation \(2 \sin^2 x + 3 $1x - 1 = 0\).
A. \(x =\)\(\frac{\pi}{6}\)\)
Correct B. \(x =\)\(\frac{\pi}{4}\)\)
C. \(x =\)\(\frac{\pi}{3}\)\)
D. \(x =\)\(\frac{\pi}{2}\)\)

Correct Answer: B

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Question 11 View Details
Find the derivative of the function ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using the chain rule.
Correct A. f'\((x) = -\)\(\frac{1}\){\(2x^{\)\(3/2\)}}\)
B. f'\((x) =\)\(\frac{1}\){\(2x^{\)\(3/2\)}}\)
C. f'\((x) = -\)\(\frac{1}\){\(x^{\)\(3/2\)}}\)
D. f'\((x) =\)\(\frac{1}\){\(x^{\)\(3/2\)}}\)

Correct Answer: A

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Question 12 View Details
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
Correct A. \(x - 0\)^2 + \(y - 0\)^\(2 = 16\)
B. \(x - 3\)^2 + \(y - 4\)^\(2 = 16\)
C. \(x - 0\)^2 + \(y - 0\)^\(2 = 9\)
D. \(x - 3\)^2 + \(y - 4\)^\(2 = 9\)

Correct Answer: A

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Question 13 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
Correct A. \(\frac{64}{3}\)\)
B. \(\frac{32}{3}\)\)
C. \(\frac{16}{3}\)\)
D. \(\frac{8}{3}\)\)

Correct Answer: A

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Question 14 View Details
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
Correct A. 312
B. 3120
C. 31200
D. 312000

Correct Answer: A

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Question 15 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. \(x < -\)\(\frac{3}{2}\)\) \text{ or }\(x >\)\(\frac{1}{2}\)\)
B. \(x < -\)\(\frac{1}{2}\)\) \text{ or }\(x >\)\(\frac{3}{2}\)\)
C. \(x < -\)\(\frac{3}{2}\)\) \text{ or }\(x <\)\(\frac{1}{2}\)\)
D. \(x > -\)\(\frac{3}{2}\)\) \text{ or }\(x <\)\(\frac{1}{2}\)\)

Correct Answer: A

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Question 16 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 4\) from \(x = 0\) to \(x = 4\).
A. 64
B. 80
Correct C. 96
D. 112

Correct Answer: C

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Question 17 View Details
Let \(S = \{1, 2, 3, 4, 5 \}\). Find the number of subsets of ( S ) that contain exactly two elements.
A. 10
Correct B. 15
C. 20
D. 25

Correct Answer: B

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Question 18 View Details
Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + \cdots\).
A. 1210
B. 1230
Correct C. 1250
D. 1270

Correct Answer: C

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Question 19 View Details
Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 20 View Details
Find the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\) and the line \(y = 2x\\((y = x^2) and the line\) about the x-axis.
A. \(16/15\)
Correct B. \(32/15\)
C. \(64/15\)
D. \(128/15\)

Correct Answer: B

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Question 21 View Details
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} ) using the formula \(\\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \mathrm{proj}_{\mathbf{a}} \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{a} |^2} \mathbf{a}\).
Correct A. \begin{pmatrix} \\(\frac{4}{13}\)\) \\(\frac{6}{13}\)\) \end{pmatrix}
B. \begin{pmatrix} \\(\frac{2}{13}\)\) \\(\frac{3}{13}\)\) \end{pmatrix}
C. \begin{pmatrix} \\(\frac{1}{13}\)\) \\(\frac{2}{13}\)\) \end{pmatrix}
D. \begin{pmatrix} \\(\frac{3}{13}\)\) \\(\frac{4}{13}\)\) \end{pmatrix}

Correct Answer: A

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Question 22 View Details
Solve the inequality \(\log_{10} x^2 + 1 \\)\(> 3 ).\)
Correct A. \left\(-\infty, -\frac{1}{10} \right\) \cup \left\(\frac{1}{10}, \infty \right\)
B. \left\(-\infty, -\frac{1}{10} \right\) \cup \left\(\frac{1}{10}, 0 \right\) \cup \left\(0, \infty \right\)
C. \left\(-\infty, -\frac{1}{10} \right\) \cup \left\(\frac{1}{10}, 0 \right\)
D. \left\(-\infty, -\frac{1}{10} \right\) \cup \left\(0, \infty \right\)

Correct Answer: A

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Question 23 View Details
Find the value of ( x ) in the equation \(2^x + 3^x = 5^x\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 24 View Details
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. \(\frac{1}{2}\)\)
Correct B. \(\frac{1}{3}\)\)
C. \(\frac{2}{3}\)\)
D. \(\frac{4}{5}\)\)

Correct Answer: B

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Question 25 View Details
Solve the equation \(x^2 + 4x + 4 = 0\).
A. \left\(-2, \infty \right\)
Correct B. \left\(-\infty, -2 \right\)
C. \left\(-\infty, 2 \right\)
D. \left\(2, \infty \right\)

Correct Answer: B

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