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POST UTME AL-HIKMAH UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME AL-HIKMAH UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

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

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

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

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

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

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

A rec\tangular \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

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

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

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{1}{\( x^2 + 1 \)^2} )

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

Correct Answer: A

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Question 12

A rec\tangular 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

Solve the equation \( x^2 + 4x - 5 = 0 \) u\sing 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

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

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

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

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

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

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

Correct Answer: A

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Question 16

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing 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

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

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

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

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

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 22

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

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

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

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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