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POST UTME AL-HIKMAH UNIVERSITY 2018 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 2018 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 \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 \)

Correct Answer: A

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Question 2

A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the point ( (6, 8) ) and has a center at ( (3, 4) ), find the radius.

A. \( \sqrt{5} \)

Correct B. \( \sqrt{10} \)

C. \( \sqrt{15} \)

D. \( \sqrt{20} \)

Correct Answer: B

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Question 3

A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has a total of 20 bars, find the sum of the products of the heights and widths of the bars.

A. ( 500 )

B. ( 1000 )

Correct C. ( 1500 )

D. ( 2000 )

Correct Answer: C

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Question 4

A probability experiment has two indep\endent events, A and B, with probabilities 0.4 and 0.6, respectively. Find the probability that both events occur.

Correct A. ( 0.2 )

B. ( 0.4 )

C. ( 0.6 )

D. ( 0.8 )

Correct Answer: A

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Question 5

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

Correct A. \( y = \frac{1}{2}x + 1 \)

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

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

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

Correct Answer: A

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Question 6

Determine the mean of the data set {2, 4, 6, 8, 10} u\sing the formula for population mean.

Correct A. \( \frac{2+4+6+8+10}{5} = 6 \)

B. \( \frac{2+4+6+8+10}{4} = 6.5 \)

C. \( \frac{2+4+6+8+10}{3} = 6.67 \)

D. \( \frac{2+4+6+8+10}{2} = 6 \)

Correct Answer: A

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Question 7

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 2 cdot 4 \ \) \times 6 )

B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 4 \ \) \times 6 )

C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 2 cdot 2 \ \) \times 6 )

D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 2 \ \) \times 6 )

Correct Answer: A

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Question 8

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

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

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

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 9

Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) u\sing integration.

Correct A. \( int_{1}^{2} \frac{1}{x} dx = ln 2 - ln 1 \)

B. \( int_{1}^{2} \frac{1}{x} dx = ln 1 - ln 2 \)

C. \( int_{1}^{2} \frac{1}{x} dx = ln 2 + ln 1 \)

D. \( int_{1}^{2} \frac{1}{x} dx = ln 1 + ln 2 \)

Correct Answer: A

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Question 10

A set of 5 numbers has a mean of 10. If the largest number is 20, find the sum of the remaining 4 numbers.

Correct A. \( 4 \times 10 + 20 = 48 \)

B. \( 4 \times 10 - 20 = 28 \)

C. \( 4 \times 10 + 20 = 28 \)

D. \( 4 \times 10 - 20 = 48 \)

Correct Answer: A

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Question 11

In the diagram below, the graph of \( y = \frac{1}{2}x^2 + 3x - 2 \) intersects the x-axis at two points. Find the sum of the x-coordinates of these points.

Correct A. -1

B. 2

C. 4

D. 6

Correct Answer: A

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Question 12

A survey of 50 students found that 30 students preferred Mathematics, 15 preferred Science, and 5 preferred both subjects. What is the probability that a randomly selected student prefers Mathematics?

Correct A. 0.6

B. 0.7

C. 0.8

D. 0.9

Correct Answer: A

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Question 13

In the diagram below, the circle with center A passes through points B and C. Find the length of arc BC.

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 14

Solve the equation \( \sin^2 x + 2 \sin x \cos x - 1 = 0 \) for ( x ) in the interval ( [0, 2 pi] ).

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

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

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

D. \( \frac{5 pi}{6} \)

Correct Answer: B

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Question 15

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. What is the average speed of the car for the entire trip?

A. 45

B. 50

Correct C. 55

D. 60

Correct Answer: C

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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. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )

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

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

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

Correct Answer: A

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Question 17

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

Correct A. \( x = -2 pm \sqrt{21} \)

B. \( x = 2 pm \sqrt{21} \)

C. \( x = -2 pm \sqrt{6} \)

D. \( x = 2 pm \sqrt{6} \)

Correct Answer: A

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Question 18

A histogram of exam scores is shown below. Find the mean score.

A. \( ar{x} = 75 \)

Correct B. \( ar{x} = 80 \)

C. \( ar{x} = 85 \)

D. \( ar{x} = 90 \)

Correct Answer: B

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Question 19

Simplify the expression \( \sqrt[3]{64x^3y^3} \).

Correct A. \( 4x^1y^1 \)

B. \( 4x^3y^3 \)

C. \( 4x^3y^1 \)

D. \( 4x^1y^3 \)

Correct Answer: A

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Question 20

Find the surface area of the sphere with radius \( r = 5 \) cm.

A. ( 50pi ) cm^2

Correct B. ( 100pi ) cm^2

C. ( 150pi ) cm^2

D. ( 200pi ) cm^2

Correct Answer: B

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Question 21

In the diagram below, a circle with center O and radius 6 units intersects a line segment AB at point C. If angle AOB measures 60 degrees, what is the length of AC?

A. 4 units

Correct B. 6 units

C. 8 units

D. 10 units

Correct Answer: B

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Question 22

Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 23

A vector (vec{a}) has a magnitude of 5 units and makes an angle of 30 degrees with the positive x-axis. Find the x and y components of (vec{a}).

Correct A. x-component: 4 units, y-component: 2.5 units

B. x-component: 2.5 units, y-component: 4 units

C. x-component: 3 units, y-component: 4.33 units

D. x-component: 4.33 units, y-component: 3 units

Correct Answer: A

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Question 24

A polynomial function f(x) has a degree of 3 and a leading coefficient of 2. If f(1) = 6 and f\( -2 \) = -10, find the value of f(0).

A. -2

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 25

A circle with center O and radius 4 units is inscribed in a square with side length 8 units. Find the area of the shaded region.

Correct A. 16 square units

B. 32 square units

C. 48 square units

D. 64 square units

Correct Answer: A

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