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POST UTME SKYLINE UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 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 + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

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

Correct Answer: A

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Question 10 View Details

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 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard 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 View Details

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. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 13 View Details

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 View Details

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 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'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )

Correct Answer: A

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Question 16 View Details

Find the equation of the line passing 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 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. \(x^2\) + \\((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 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. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 19 View Details

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 View Details

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 View Details

A rectangular 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 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. \(x^2\) + \\((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 View Details

Solve the inequality (\(\frac{x}{x-2}\(> 2\)\) for \\((frac{x}{x-2} > 2\(x > 2\)\).

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 24 View Details

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 View Details

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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