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POST UTME MADONNA UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation \(\frac{1}{x} + 2 = \frac{3}{x}\).

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

B. \(x = 2\)

C. \(x = -1\)

Correct D. \(x = \frac{1}{2}\)

Correct Answer: D

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Question 2 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{64}{3}\)

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 3 View Details

In the circuit below, identify the part labeled A.

Correct A. Batteries

B. Resistor

C. Capacitor

D. Inductor

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + x - 1\) ).

Correct A. ( f'\((x) =\)\(3x^2 - 4x + 1\) )

B. ( f'\((x) =\)\(x^2 - 2x + 1\) )

C. ( f'\((x) =\)\(3x^2 - 4x - 1\) )

D. ( f'\((x) =\)\(x^2 - 2x - 1\) )

Correct Answer: A

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Question 6 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. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 7 View Details

Solve for x in the equation \\(tan x =\)\(\frac{1}\){\(\sqrt{3}\)}\).

Correct A. \(\frac{\pi}{6}\)\)

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

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

D. \(\frac{2\pi}{3}\)\)

Correct Answer: A

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Question 8 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 9 View Details

Simplify the expression \(\frac{2x^2 - 5x + 3}{x^2 - 2x - 3}\)\)\).

Correct A. 2x - 1

B. 2x + 1

C. x - 1

D. x + 1

Correct Answer: A

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Question 10 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 11 View Details

In a circle of radius 5 cm, a chord of length 8 cm subtends an angle of 60° at the centre. Find the area of the sector.

A. ( 20pi ) cm²

Correct B. ( 30pi ) cm²

C. ( 40pi ) cm²

D. ( 50pi ) cm²

Correct Answer: B

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Question 12 View Details

A die is rolled twice. What is the probability that the sum of the numbers on the two dice is 7?

A. \(\frac{1}{6}\)

Correct B. \(\frac{1}{3}\)

C. \(\frac{1}{2}\)

D. \(\frac{2}{3}\)

Correct Answer: B

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Question 13 View Details

Solve for x: \(2^x + 3^x = 5^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 14 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

A. \(y = 2x - 1\)

Correct B. \(y = 2x + 1\)

C. \(y = -2x + 1\)

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

Correct Answer: B

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Question 15 View Details

A circle has a radius of 4 cm. Find the area of the sector subtended by a central angle of 60°.

A. ( 12pi ) cm²

Correct B. ( 16pi ) cm²

C. ( 20pi ) cm²

D. ( 24pi ) cm²

Correct Answer: B

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Question 16 View Details

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

A. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4x + 3}{x^2 - 2x - 3}\)\)\\() > 0.\)

Correct A. \left\(-\infty, -1 \right\) \cup \left\(1, \infty \right\)

B. \left\(-\infty, 1 \right\) \cup \left\(3, \infty \right\)

C. \left\(-\infty, -3 \right\) \cup \left\(1, \infty \right\)

D. \left\(-\infty, 1 \right\) \cup \left\(3, \infty \right\)

Correct Answer: A

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Question 18 View Details

Find the equation of the circle with center at (2, 3) and radius 4.

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

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

Correct C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: C

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Question 19 View Details

Find the area under the curve \(y = x\^2 + 2x - 3\) from \(x = 0\) to \(x = 4\).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 20 View Details

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 21 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side using the cosine rule.

A. 8 cm

Correct B. 12 cm

C. 6 cm

D. 4 cm

Correct Answer: B

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Question 22 View Details

A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256π cm³

Correct B. 128π cm³

C. 512π cm³

D. 2048π cm³

Correct Answer: B

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Question 23 View Details

Solve for x in the equation \(2^x + 2^{x+1} = 3 \cdot 2^{x+1}\).

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 24 View Details

A set of 5 consecutive integers has a median of 8. Find the sum of the integers.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 25 View Details

A circle has a diameter of 14 cm. Find the area of the circle in square centimeters.

A. 154 cm²

B. 196 cm²

Correct C. 308 cm²

D. 784 cm²

Correct Answer: C

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