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POST UTME SKYLINE UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

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

A. \(\frac{1}{2} \sqrt{1 - x^2}\)

Correct B. \(\frac{x}{1 - x^2 \\)^{\(3/2\)}} )

C. \(\frac{-x}{1 - x^2 \\)^{\(3/2\)}} )

D. \(\frac{1}{1 - x^2 \\)^{\(3/2\)}} )

Correct Answer: B

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Question 2 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(x < -\frac{5}{4}\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > -\frac{5}{4}\)

C. \(x < -\frac{5}{4}\) or \(x < \frac{3}{2}\)

D. \(x > -\frac{5}{4}\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 3 View Details

Find the area under the curve \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).

Correct A. \(\frac{\pi}{4}\)

B. \(\frac{\pi}{2}\)

C. \(\frac{\pi}{3}\)

D. \(\frac{\pi}{6}\)

Correct Answer: A

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Question 4 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}\).

Correct A. ( 2 )

B. \(-2\)

C. ( 0 )

D. ( 1 )

Correct Answer: A

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Question 5 View Details

Solve the system of equations \(egin{cases} x + y = 2 \ 2x - y = 3 \end{cases}\).

Correct A. \(x = 1, y = 1\)

B. \(x = 2, y = 0\)

C. \(x = 0, y = 2\)

D. \(x = 1, y = 2\)

Correct Answer: A

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Question 6 View Details

Find the value of k such that the equation \(x^2 + kx + 16 = 0\) has exactly one solution.

A. 4

Correct B. -4

C. 8

D. -8

Correct Answer: B

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Question 7 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5

B. 31.4

C. 314

D. 785

Correct Answer: A

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Question 8 View Details

Solve the inequality \(2x - 5 > 3\).

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 1\)

D. \(x < 1\)

Correct Answer: A

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Question 9 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). Find the average speed for the round trip.

A. 48

Correct B. 52

C. 56

D. 60

Correct Answer: B

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Question 10 View Details

Solve the equation \(x^2 - 4x + 4 = 0\).

Correct A. \(x = 2\)

B. \(x = 1\)

C. \(x = 0\)

D. \(x = -2\)

Correct Answer: A

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Question 11 View Details

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

A. \(x = -1 \\)

Correct B. \(x = 2 \\)

C. \(x = -2 \\)

D. \(x = 1 \\)

Correct Answer: B

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Question 12 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\) and the line \(y = 4\\((y = x^2) and the line\) about the x-axis.

Correct A. \(\frac{32}{3} \pi \\)

B. \(\frac{64}{3} \pi \\)

C. \(\frac{16}{3} \pi \\)

D. \(\frac{128}{3} \pi \\)

Correct Answer: A

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Question 13 View Details

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

Correct A. \(x < -1 \\) or \(x > \frac{3}{2} \\)

B. \(x < -1 \\) or \(x < \frac{3}{2} \\)

C. \(x > -1 \\) or \(x < \frac{3}{2} \\)

D. \(x > -1 \\) or \(x > \frac{3}{2} \\)

Correct Answer: A

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Question 14 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 + \(y - 3\)^\(2 = 4\) \)

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) \)

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) \)

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. \(12 \\)

C. \(18 \\)

D. \(24 \\)

Correct Answer: A

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Question 16 View Details

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

A. 32\pi \(cm^3\)

B. 64\pi \(cm^3\)

Correct C. 96\pi \(cm^3\)

D. 128\pi \(cm^3\)

Correct Answer: C

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Question 17 View Details

Evaluate the definite integral \int_\(0^1\) \(x^2\) \sin x dx.

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 18 View Details

Solve the inequality \\((x^2 - 4x - 5\)\(> 0.\)\)

Correct A. \(-\infty, -1\) \cup \(5, \infty\)

B. \(-\infty, -5\) \cup \(0, \infty\)

C. \(-\infty, 1\) \cup \(5, \infty\)

D. \(-\infty, -1\) \cup \(0, \infty\)

Correct Answer: A

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Question 19 View Details

Express the number 240 in base 8.

A. 360

Correct B. 400

C. 420

D. 440

Correct Answer: B

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Question 20 View Details

Find the vector projection of \(\vec{a} = 2\hat{i} + 3\hat{j} onto \vec{b} = \hat{i} + \hat{j}\).

Correct A. \(\frac{5}{2}\)\)\hat{i} + \(\frac{5}{2}\)\)\hat{j}

B. \(\frac{5}{3}\)\)\hat{i} + \(\frac{5}{3}\)\)\hat{j}

C. \(\frac{5}{4}\)\)\hat{i} + \(\frac{5}{4}\)\)\hat{j}

D. \(\frac{5}{6}\)\)\hat{i} + \(\frac{5}{6}\)\)\hat{j}

Correct Answer: A

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Question 21 View Details

Determine the value of (x\) in the equation [ \(2x + 5 = 11\\((x) in the equation [\) ].

Correct A. 4

B. 5

C. 6

D. 7

Correct Answer: A

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Question 22 View Details

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, calculate the volume of water in the \tank.

A. 1200\pi

Correct B. 1500\pi

C. 1800\pi

D. 2000\pi

Correct Answer: B

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Question 23 View Details

Solve the inequality [ \(2x - 5 > 3x + 2\) \].

A. \(x < -1\)

Correct B. \(x > -1\)

C. \(x < 1\)

D. \(x > 1\)

Correct Answer: B

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Question 24 View Details

A car travels from city A to city B at an average speed of \((60km/h\)\) and returns at an average speed of \(40km/h\\((60km/h) and returns at an average speed of\). If the distance between the two cities is 240km, calculate the average speed for the entire trip.

A. 48

B. 50

Correct C. 52

D. 54

Correct Answer: C

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Question 25 View Details

A right-angled triangle has a hypotenuse of length 10cm and one of the other sides has a length of 6cm. Calculate the length of the third side.

A. 8cm

B. 10cm

Correct C. 12cm

D. 14cm

Correct Answer: C

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