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POST UTME ESUT 2021 Mathematics | Objective

Are you preparing for POST UTME ESUT exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. $ \frac{-2x}{\( x^2 + 1 \ $^2} )

B. $ \frac{-2x^2}{\( x^2 + 1 \ $^2} )

C. $ \frac{2x}{\( x^2 + 1 \ $^2} )

D. $ \frac{2x^2}{\( x^2 + 1 \ $^2} )

Correct Answer: A

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Question 2

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

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

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

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

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

Correct Answer: A

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Question 3

A circle has a radius of 4 cm. Find the area of the circle u\sing the formula $ A = pi r^2 $.

A. $ A = 16pi $ cm^2

B. $ A = 32pi $ cm^2

Correct C. $ A = 64pi $ cm^2

D. $ A = 128pi $ cm^2

Correct Answer: C

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Question 4

A sequence is defined as $ a_n = 2n + 1 $. Find the sum of the first 5 terms of the sequence.

A. ( 15 )

B. ( 25 )

C. ( 35 )

Correct D. ( 45 )

Correct Answer: D

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Question 5

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

Correct A. $ 2^5 $

B. $ 2^3 $

C. $ 2^2 $

D. $ 2^1 $

Correct Answer: A

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Question 6

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

Correct A. $ \frac{16}{3} $

B. ( 8 )

C. ( 12 )

D. ( 16 )

Correct Answer: A

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Question 7

A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly two elements.

A. ( 10 )

Correct B. ( 12 )

C. ( 15 )

D. ( 20 )

Correct Answer: B

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Question 8

Find the volume of the frustum of a cone with radii ( 6 ) and ( 3 ) and height ( 8 ).

A. ( 48pi )

B. ( 64pi )

Correct C. ( 72pi )

D. ( 80pi )

Correct Answer: C

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Question 9

A sequence is defined recursively as $ a_n = 2a_{n-1} + 1 $ with $ a_1 = 3 $. Find the value of $ a_{10} $.

A. ( 1023 )

B. ( 1024 )

Correct C. ( 1025 )

D. ( 1026 )

Correct Answer: C

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Question 10

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

Correct A. $ 0, \frac{pi}{2}, pi, \frac{3pi}{2} $

B. $ 0, \frac{pi}{2}, \frac{3pi}{2} $

C. ( 0, pi, 2pi )

D. $ \frac{pi}{2}, \frac{3pi}{2}, 2pi $

Correct Answer: A

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Question 11

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

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

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

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

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

Correct Answer: A

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Question 12

Solve the inequality $\frac{x^2 - 4}{x^2 - 9} > 0$.

A. $ -3, -1 $ \cup (1, 3)

Correct B. $ -3, -1 $ \cup (1, 3) \cup $ 3, \infty $

C. $ -3, -1 $ \cup (1, 3) \cup $ -\infty, -3 $ \cup $ 3, \infty $

D. $ -3, -1 $ \cup (1, 3) \cup $ -\infty, -3 $ \cup $ 3, \infty $ \cup (0, 1)

Correct Answer: B

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Question 13

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

Correct A. x^2 + y^2 + 4x - 6y - 12 = 0

B. x^2 + y^2 - 4x + 6y - 12 = 0

C. x^2 + y^2 + 4x + 6y - 12 = 0

D. x^2 + y^2 - 4x - 6y - 12 = 0

Correct Answer: A

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Question 14

Solve the equation $\tan^2 x = 3 \sin x \cos x$.

A. x = \frac{\pi}{4} + k\pi

Correct B. x = \frac{\pi}{4} + \frac{k\pi}{2}

C. x = \frac{\pi}{4} + \frac{k\pi}{3}

D. x = \frac{\pi}{4} + \frac{k\pi}{6}

Correct Answer: B

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Question 15

Find the area of the region bounded by the curves $y = x^3$ and $y = 2x^2$.

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. 1

D. 2

Correct Answer: B

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Question 16

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

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

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

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

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

Correct Answer: A

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Question 17

Solve the system of equations: \begin{align*} x + y + z &= 3 \ 2x + 2y + 3z &= 7 \ 3x + y + 2z &= 9 \end{align*}

Correct A. x = 1, y = 1, z = 1

B. x = 2, y = 1, z = 0

C. x = 1, y = 2, z = 0

D. x = 0, y = 1, z = 2

Correct Answer: A

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Question 18

Find the area of the triangle formed by the points $A(1, 2)$, $B(4, 6)$, and $C(2, 1)$.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 19

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

Correct A. x < -1 or x > 2

B. x < -1 or x < 2

C. x > -1 or x < 2

D. x > -1 or x > 2

Correct Answer: A

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Question 20

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

Correct A. y = x + 1

B. y = x - 1

C. y = x + 2

D. y = x - 2

Correct Answer: A

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Question 21

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

A. 19,683

B. 6,009

Correct C. 19,683

D. 6,009

Correct Answer: C

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Question 22

Solve for x in the equation \frac{x}{x+1} + \frac{x}{x-1} = 1.

A. x = 0

B. x = -1

Correct C. x = 1

D. x = -1/2

Correct Answer: C

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Question 23

Find the equation of the circle with center $ -2, 3 $ and radius 4.

Correct A. $ x+2 $^2 + $ y-3 $^2 = 16

B. $ x-2 $^2 + $ y+3 $^2 = 16

C. $ x+2 $^2 + $ y+3 $^2 = 16

D. $ x-2 $^2 + $ y-3 $^2 = 16

Correct Answer: A

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Question 24

Find the determinant of the matrix \begin{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 25

Find the volume of the cylinder with radius 4 and height 6.

A. 48\pi

B. 64\pi

Correct C. 96\pi

D. 192\pi

Correct Answer: C

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