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

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 View Details

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 View Details

A histogram has a mean of 25 and a standard 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 View Details

A probability experiment has two independent 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 View Details

Find the equation of the line passing 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 View Details

Determine the mean of the data set {2, 4, 6, 8, 10} using 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 View Details

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 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\) using 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 View Details

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

Correct A. \(int_{1}^{2} \frac{1}{x} dx = \(12 -\)11\)

B. \(int_{1}^{2} \frac{1}{x} dx = \(11 -\)12\)

C. \(int_{1}^{2} \frac{1}{x} dx = \(12 +\)11\)

D. \(int_{1}^{2} \frac{1}{x} dx = \(11 +\)12\)

Correct Answer: A

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Question 10 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Solve the equation \(\sin^2 x + 2 \(1x\)\(1x - 1 = 0\)\) 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 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 \(km/h\\((km/h) and returns at an average speed of 40\). 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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using 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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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