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POST UTME EKSU 2023 Mathematics | Objective

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Question 1

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

Correct A. 5

B. 6

C. 7

D. 8

Correct Answer: A

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Question 2

Solve for x in the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 1792

B. 1992

C. 2092

D. 2192

Correct Answer: A

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Question 4

A histogram is shown below. What is the class width?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 5

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x.

A. 0

Correct B. \frac{\pi}{4}

C. \frac{\pi}{2}

D. \frac{3\pi}{4}

Correct Answer: B

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

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

Correct C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

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

Correct Answer: C

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Question 7

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

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

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

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

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

Correct Answer: A

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Question 8

Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.

A. \frac{16}{3}\pi

B. \frac{32}{3}\pi

Correct C. \frac{64}{3}\pi

D. \frac{128}{3}\pi

Correct Answer: C

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Question 9

Solve the system of equations \( x + y = 4 \) and \( xy = 5 \) u\sing substitution.

Correct A. x = 1, y = 3

B. x = 3, y = 1

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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Question 10

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. 2\sin x \cos x

B. 2\sin x \cos x + \sin^2 x

C. 2\sin x \cos x - \sin^2 x

D. 2\sin x \cos x - \cos^2 x

Correct Answer: A

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Question 11

In a circle of radius 8 cm, a chord of length 12 cm subt\ends an angle of 60° at the centre. Find the area of the sector.

A. 48\u03c0 cm^2

Correct B. 64\u03c0 cm^2

C. 72\u03c0 cm^2

D. 96\u03c0 cm^2

Correct Answer: B

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Question 12

Find the equation of the \tangent to the curve y = x^2 + 2x - 3 at the point (1, 2).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 13

A histogram of the heights of 20 students is shown. Find the mean height of the students.

A. 165 cm

Correct B. 170 cm

C. 175 cm

D. 180 cm

Correct Answer: B

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Question 14

Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

A. 16\u03c0 cm^3

B. 32\u03c0 cm^3

Correct C. 64\u03c0 cm^3

D. 128\u03c0 cm^3

Correct Answer: C

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Question 15

Find the equation of the circle pas\sing through the points (1, 2), (2, 3), and (3, 4).

Correct A. x^2 + y^2 - 4x - 6y + 5 = 0

B. x^2 + y^2 - 6x - 4y + 5 = 0

C. x^2 + y^2 - 8x - 2y + 5 = 0

D. x^2 + y^2 - 2x - 8y + 5 = 0

Correct Answer: A

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Question 16

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.

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

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

C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}

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

Correct Answer: A

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Question 17

A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are both blue?

Correct A. \frac{3}{8}

B. \frac{1}{4}

C. \frac{1}{2}

D. \frac{3}{4}

Correct Answer: A

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Question 18

Solve the equation \( 2x^2 + 3x - 1 = 0 \) u\sing the quadratic formula.

Correct A. x = \frac{-3 + \sqrt{17}}{4}

B. x = \frac{-3 - \sqrt{17}}{4}

C. x = \frac{-3 + \sqrt{17}}{2}

D. x = \frac{-3 - \sqrt{17}}{2}

Correct Answer: A

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Question 19

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 4 & 2 \end{bmatrix} \).

Correct A. 2

B. -2

C. 4

D. -4

Correct Answer: A

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Question 20

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

Correct A. x = \frac{\pi}{4}

B. x = \frac{3\pi}{4}

C. x = \frac{5\pi}{4}

D. x = \frac{7\pi}{4}

Correct Answer: A

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Question 21

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 2cm.

A. 100π cm³

B. 200π cm³

Correct C. 300π cm³

D. 400π cm³

Correct Answer: C

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Question 22

In a set of 20 integers, the median is 15 and the mode is 10. What is the sum of the first and last terms?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 23

A circle has a diameter of 12cm. Find the area of the sector with a central angle of 60°.

A. 36π cm²

B. 48π cm²

Correct C. 60π cm²

D. 72π cm²

Correct Answer: C

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Question 24

A sequence is defined by the recurrence relation: an = 2an-1 + 3, with a1 = 2. Find the sum of the first 5 terms.

A. 65

B. 70

Correct C. 75

D. 80

Correct Answer: C

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Question 25

A histogram has a mean of 25 and a s\tandard deviation of 5. Find the value of x such that P\( x < 30 \) = 0.6.

A. 27

B. 28

Correct C. 29

D. 30

Correct Answer: C

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