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POST UTME AL-HIKMAH UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 2 View Details

A particle moves along the curve (y = \(x^3 - 6x^2 + 9x + 2\)\). Find the equation of the \tangent line at the point where \\((y = x^3 - 6x^2 + 9x + 2). Find the equation of the \(x = 2\).

Correct A. \(y = 3x - 7\)

B. \(y = 2x - 5\)

C. \(y = x - 3\)

D. \(y = 4x - 9\)

Correct Answer: A

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Question 3 View Details

Simplify the expression \(\frac{\sqrt{3} + \sqrt{6}}{\sqrt{3} - \sqrt{6}}\).

A. \(\sqrt{3} + \sqrt{6}\)

B. \(\sqrt{3} - \sqrt{6}\)

C. \(\frac{1}{\sqrt{3} - \sqrt{6}}\)

Correct D. \(\frac{\sqrt{3} + \sqrt{6}}{\sqrt{3} - \sqrt{6}}\)

Correct Answer: D

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

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

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

Correct Answer: A

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Question 5 View Details

A line passes through the points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line.

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

B. \(y = x - 1\)

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

D. \(y = -x + 3\)

Correct Answer: A

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Question 6 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.07 cm

C. 8 cm

D. 9 cm

Correct Answer: B

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Question 7 View Details

Find the equation of the circle with centre \(-2, 3\) 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 8 View Details

A rectangular \tank measures 2 m by 3 m by 4 m. Find the volume of the \tank in cubic metres.

A. 24 \(m^3\)

B. 30 \(m^3\)

Correct C. 36 \(m^3\)

D. 48 \(m^3\)

Correct Answer: C

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Question 9 View Details

If f(x) = \(3x^2 + 2x - 5\), find f'(x).

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 10 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, find the probability that it is blue.

A. \(1/2\)

Correct B. \(2/7\)

C. \(3/8\)

D. \(5/8\)

Correct Answer: B

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Question 11 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'\((x) =\)\(\frac{1}{x^2 + 1\) ^2}\)\) )

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

Correct Answer: A

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Question 12 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its surface area.

Correct A. \(2 5 \times 3 + 3 \times 2 + 5 \times 2 \\)\(= 94 )\)\(cm^2\)

B. \(2 5 \times 3 + 3 \times 2 + 5 \times 2 \\)\(= 86 )\)\(cm^2\)

C. \(2 5 \times 3 + 3 \times 2 + 5 \times 2 \\)\(= 98 )\)\(cm^2\)

D. \(2 5 \times 3 + 3 \times 2 + 5 \times 2 \\)\(= 102 )\)\(cm^2\)

Correct Answer: A

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Question 13 View Details

Solve the equation \(x^2 + 4x - 5 = 0\) using the quadratic formula.

Correct A. \(x = \frac{-4 \pm \sqrt{16 + 20}}{2} = \frac{-4 \pm \sqrt{36}}{2} = \frac{-4 \pm 6}{2}\)

B. \(x = \frac{-4 \pm \sqrt{16 - 20}}{2} = \frac{-4 \pm \sqrt{-4}}{2}\)

C. \(x = \frac{-4 \pm \sqrt{16 + 20}}{2} = \frac{-4 \pm \sqrt{36}}{2} = \frac{-4 \pm 6}{2}\)

D. \(x = \frac{-4 \pm \sqrt{16 - 20}}{2} = \frac{-4 \pm \sqrt{-4}}{2}\)

Correct Answer: A

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Question 14 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. \(\sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8\) cm

B. \(\sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136}\) cm

C. \(\sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8\) cm

D. \(\sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136}\) cm

Correct Answer: A

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Question 15 View Details

A circle has a radius of 4 cm. Find its area.

Correct A. \(\pi r^2 = \pi 4 \\)^\(2 = 16\pi\) ) \(cm^2\)

B. \(\pi r^2 = \pi 4 \\)^\(2 = 64\pi\) ) \(cm^2\)

C. \(\pi r^2 = \pi 4 \\)^\(2 = 16\pi\) ) \(cm^2\)

D. \(\pi r^2 = \pi 4 \\)^\(2 = 64\pi\) ) \(cm^2\)

Correct Answer: A

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Question 16 View Details

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

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

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

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

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

Correct Answer: A

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Question 17 View Details

A particle moves along the curve (y = \(x^2 + 2x + 1\)\) with a velocity of 2 \(m/s\\((y = x^2 + 2x + 1) with a velocity of 2\). Find the acceleration at the point where the particle is at \(x = 1\).

Correct A. 4 \(m/s\^2\)

B. 2 \(m/s\^2\)

C. -2 \(m/s\^2\)

D. 6 \(m/s\^2\)

Correct Answer: A

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Question 18 View Details

Find the area under the curve \(y = x^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 2\).

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 19 View Details

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

Correct A. \(x > -2\)

B. \(x < -2\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 20 View Details

A right circular cone has a height of 6 cm and a radius of 4 cm. Find the volume of the cone.

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

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

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

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

Correct Answer: A

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Question 21 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. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 22 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.2\), P\(X = 2 = 0.3\), P\(X = 3 = 0.5\). Find E(X).

Correct A. 1.5

B. 2.0

C. 2.5

D. 3.0

Correct Answer: A

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Question 23 View Details

A right-angled triangle has a base of 5 cm and a height of 12 cm. Find the length of the hypotenuse.

Correct A. 13 cm

B. 14 cm

C. 15 cm

D. 16 cm

Correct Answer: A

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Question 24 View Details

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

A. 160\pi \(cm^3\)

B. 320\pi \(cm^3\)

C. 480\pi \(cm^3\)

D. 640\pi \(cm^3\)

Correct Answer: VIEW ANSWER

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Question 25 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{16}{3}\)

B. \(\frac{32}{3}\)

C. \(\frac{64}{3}\)

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

Correct Answer: A

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