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POST UTME UNILAG 2022 Mathematics | Objective

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Question 1 View Details

Determine the volume of the frustum of a cone with height 12 cm, lower base radius 6 cm, and upper base radius 4 cm.

A. 120π cm³

Correct B. 240π cm³

C. 360π cm³

D. 480π cm³

Correct Answer: B

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Question 2 View Details

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

A. 1792

B. 2046

Correct C. 2187

D. 2430

Correct Answer: C

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Question 3 View Details

A vector α has magnitude 5 and direction 60°. Find the magnitude of the vector 2α.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 4 View Details

Find the determinant of the matrix Θ = egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5 View Details

A histogram represents the distribution of exam scores. If the mean score is 60 and the standard deviation is 10, what is the probability that a randomly selected score is between 50 and 70?

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 6 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 7 View Details

Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8 View Details

A sequence is defined by \(a_n = 2n + 1\). Find the sum of the first 5 terms.

A. 15

B. 30

C. 45

Correct D. 60

Correct Answer: D

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Question 9 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 10 View Details

A set of numbers is defined as \(S = \{1, 2, 3, 4, 5 \} \\). Find the number of subsets of S.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 11 View Details

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

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

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

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

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

Correct Answer: C

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Question 12 View Details

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

Correct A. \(\frac{-5 + \sqrt{25 + 24}\)}{4}\)

B. \(\frac{-5 - \sqrt{25 + 24}\)}{4}\)

C. \(\frac{-5 + \sqrt{25 + 24}\)}{4}\)

D. \(\frac{-5 - \sqrt{25 + 24}\)}{4}\)

Correct Answer: A

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Question 13 View Details

Find the area of the triangle with vertices ( A(0, 0), B(2, 3), ) and ( C(4, 0) ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 14 View Details

Solve the system of equations \(x + y = 2\) and \(xy = 3\).

Correct A. \left\(1, 1 \right\)

B. \left\(-1, -1 \right\)

C. \left\(1, -1 \right\)

D. \left\(-1, 1 \right\)

Correct Answer: A

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Question 15 View Details

Find the derivative of the function ( f(x) = \(x^2\) \sin x ) using the product rule.

Correct A. \left\(2x \(1x + x^2\)1x \right\)

B. \left\(2x \(1x - x^2\)1x \right\)

C. \left\(2x \(1x + x^2\)1x \right\)

D. \left\(2x \(1x - x^2\)1x \right\)

Correct Answer: A

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Question 16 View Details

Solve the inequality \(x^2 - 4x + 3 > 0\) using the quadratic formula.

Correct A. \left\(1, 3 \right\)

B. \left\(-1, -3 \right\)

C. \left\(1, -3 \right\)

D. \left\(-1, 3 \right\)

Correct Answer: A

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Question 17 View Details

Find the area of the circle with radius \(r = 4\) cm.

Correct A. 50.24

B. 50.26

C. 50.28

D. 50.30

Correct Answer: A

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Question 18 View Details

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

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 19 View Details

Solve the inequality \(\frac{x-2}{x+1}\)\\() > 0.\)

Correct A. \(-\infty, -1\) \cup \(2, \infty\)

B. \(-\infty, -1\) \cup \(1, \infty\)

C. \(-\infty, 1\) \cup \(2, \infty\)

D. \(-\infty, 1\) \cup \(2, \infty\)

Correct Answer: A

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Question 20 View Details

Find the area of the region bounded by the curve (y = x\^3 - \(6x^2 + 9x + 2\)\), the x-axis, and the lines \\((y = x^3 - 6x^2 + 9x + 2\(x = 0\) and \(x = 3\).

A. 18

B. 36

Correct C. 54

D. 72

Correct Answer: C

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Question 21 View Details

A circle with center (0, 0) and radius 4 is revolved about the x-axis. Find the volume of the solid formed.

Correct A. 256\pi

B. 128\pi

C. 64\pi

D. 32\pi

Correct Answer: A

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Question 22 View Details

Find the equation of the plane passing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9).

Correct A. \(x - y + z = 0\)

B. \(x + y - z = 0\)

C. \(x - y + z = 0\)

D. \(x + y + z = 0\)

Correct Answer: A

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Question 23 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. \(y = 2x - 1\)

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

D. \(y = x + 2\)

Correct Answer: A

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Question 24 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2}\)\)\\() > 0.\)

A. \(x < -2\)\text{ or } \(x > 2\)

Correct B. \(x > -2\)\text{ and } \(x < 2\)

C. \(x < -2\)\text{ and } \(x > 2\)

D. \(x > -2\)\text{ or } \(x < 2\)

Correct Answer: B

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Question 25 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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