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POST UTME EKSU 2023 Mathematics | Objective

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Question 1 View Details

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

Correct A. 5

B. 6

C. 7

D. 8

Correct Answer: A

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Question 2 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using 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 View Details

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

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 View Details

Solve the system of equations \(x + y = 4\) and \(xy = 5\) using 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 View Details

Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using 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 View Details

In a circle of radius 8 cm, a chord of length 12 cm subtends 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 View Details

Find the equation of the tangent to the curve \(y = x\^2 + 2x - 3\\(tangent to the curve (y = x\) 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 View Details

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 View Details

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 View Details

Find the equation of the circle passing 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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using 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 View Details

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 View Details

Solve the equation \(2x^2 + 3x - 1 = 0\) using 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 View Details

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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

A histogram has a mean of 25 and a standard 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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