POST UTME SKYLINE UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME SKYLINE 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.

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Question 1
Find the sum of the first 10 terms of the arithmetic sequence with first term 3 and common difference 2.
Correct A. \( 3 + 5\( 10 \ \) )
B. \( 3 + 5\( 9 \ \) )
C. \( 3 + 5\( 11 \ \) )
D. \( 3 + 5\( 12 \ \) )

Correct Answer: A

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Question 2
In the diagram below, the circle with center A has radius 4cm. The circle with center B has radius 3cm. If the two circles intersect at points C and D, what is the length of CD?
Correct A. \( 4 - 3 \)
B. \( 4 + 3 \)
C. \( 4 \times 3 \)
D. \( 4 - 3 \)

Correct Answer: A

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Question 3
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
Correct A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)

Correct Answer: A

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Question 4
Find the volume of the cylinder with radius 4cm and height 6cm.
Correct A. ( pi (4)^2 (6) )
B. ( pi (4)^2 (5) )
C. ( pi (4)^2 (7) )
D. ( pi (4)^2 (8) )

Correct Answer: A

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Question 5
In the diagram below, the line AB has a slope of 2. If the line passes through the point (3, 4), what is the equation of the line?
Correct A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)

Correct Answer: A

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Question 6
Determine the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 3 \) in base 8.
Correct A. 10
B. 12
C. 14
D. 16

Correct Answer: A

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Question 7
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
Correct A. 1
B. 2
C. 3
D. 4

Correct Answer: A

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Question 8
Solve for x in the equation \( x^2 + 4x + 4 = 0 \).
Correct A. -2
B. -1
C. 1
D. 2

Correct Answer: A

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Question 9
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. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

Correct Answer: A

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Question 10
Solve the inequality \( \frac{x + 2}{x - 1} > 0 \).
Correct A. \( x < -2 \) or \( x > 1 \)
B. \( x < -2 \) or \( x < 1 \)
C. \( x > -2 \) or \( x < 1 \)
D. \( x > -2 \) or \( x > 1 \)

Correct Answer: A

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Question 11
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the sample is normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
Correct A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6179

Correct Answer: A

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Question 12
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
Correct A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 13
In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.
Correct A. \( 2 + 6 + 18 + 54 + 162 \)
B. \( 2 + 6 + 18 + 54 + 162 + 486 \)
C. \( 2 + 6 + 18 + 54 + 162 \)
D. \( 2 + 6 + 18 + 54 + 162 + 486 + 1458 \)

Correct Answer: A

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Question 14
Find the volume of the frustum of a cone with height 10 cm, and radii of the bases 4 cm and 6 cm.
Correct A. \( \frac{1}{3} pi \( 4^2 + 6^2 + 4 cdot 6 cdot 10 \ \) )
B. \( \frac{1}{3} pi \( 4^2 + 6^2 - 4 cdot 6 cdot 10 \ \) )
C. \( \frac{1}{3} pi \( 4^2 + 6^2 + 4 cdot 6 cdot 10 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 6^2 - 4 cdot 6 cdot 10 \ \) )

Correct Answer: A

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Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

Correct Answer: A

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Question 16
Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the coordinate plane.
Correct A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1

Correct Answer: A

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Question 17
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
Correct A. x^2 + y^2 = 16
B. x^2 + y^2 = 20
C. x^2 + y^2 = 24
D. x^2 + y^2 = 28

Correct Answer: A

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Question 18
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).
Correct A. 0.12
B. 0.24
C. 0.36
D. 0.48

Correct Answer: A

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Question 19
A polynomial f(x) has degree 3 and has roots 1, 2, and 3. Find the polynomial.
Correct A. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \)
B. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \) + 1
C. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \) - 1
D. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \) + 2

Correct Answer: A

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Question 20
Find the determinant of the matrix \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}.
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 21
A rec\tangular prism has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the prism.
A. 60
B. 80
Correct C. 100
D. 120

Correct Answer: C

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Question 22
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
Correct A. x^2 + y^2 = 16
B. x^2 + y^2 = 20
C. x^2 + y^2 = 24
D. x^2 + y^2 = 28

Correct Answer: A

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Question 23
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
Correct A. \( x > 4 \)
B. \( x < 4 \)
C. \( x > 2 \)
D. \( x < 2 \)

Correct Answer: A

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Question 24
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{4} - 1 \)
Correct B. \( \frac{pi}{4} \)
C. \( \frac{pi}{4} + 1 \)
D. \( \frac{pi}{4} - 2 \)

Correct Answer: B

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Question 25
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
Correct A. \( x = 1, y = 3 \)
B. \( x = 3, y = 1 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)

Correct Answer: A

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