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POST UTME ESUT 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Solve for x in the equation $ \frac{x}{2} + 5 = 11 $:

Correct A. 6

B. 7

C. 8

D. 9

Correct Answer: A

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Question 2

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 3

Solve the inequality $ 2x^2 + 5x - 3 > 0 $:

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 4

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

Correct A. $ 2\( 3^{10}-1 \ $ )

B. $ 2\( 3^{10}+1 \ $ )

C. $ 2\( 3^{10}-2 \ $ )

D. $ 2\( 3^{10}+2 \ $ )

Correct Answer: A

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Question 5

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

Correct A. $ y = \frac{2}{1}x + 0 $

B. $ y = \frac{2}{1}x + 1 $

C. $ y = \frac{2}{1}x - 1 $

D. $ y = \frac{2}{1}x + 2 $

Correct Answer: A

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Question 6

Find the sum of the first 10 terms of the geometric series $ sum_{n=1}^{10} 2^n cdot 3^{n-1} $.

Correct A. 12167

B. 12345

C. 12543

D. 12879

Correct Answer: A

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Question 7

A circle passes through points ( A(1, 2) ) and ( B(3, 4) ). Find the equation of the circle in the form $ x - h \ $^2 + $ y - k $^2 = r^2 ).

A. \left$ x - 2 \right $^2 + \left$ y - 3 \right $^2 = 5

Correct B. \left$ x - 1 \right $^2 + \left$ y - 2 \right $^2 = 4

C. \left$ x - 3 \right $^2 + \left$ y - 4 \right $^2 = 9

D. \left$ x - 4 \right $^2 + \left$ y - 5 \right $^2 = 16

Correct Answer: B

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Question 8

Find 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}{$ x^2 + 1 $^2}

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

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

Correct Answer: A

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Question 9

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \frac{1}{6}

Correct B. \frac{1}{12}

C. \frac{1}{18}

D. \frac{1}{24}

Correct Answer: B

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Question 10

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. \left$ -\infty, -\frac{3}{2} \right $ \cup \left$ \frac{1}{2}, \infty \right $

B. \left$ -\infty, -\frac{1}{2} \right $ \cup \left$ \frac{3}{2}, \infty \right $

C. \left$ -\infty, \frac{1}{2} \right $ \cup \left$ -\frac{3}{2}, \infty \right $

D. \left$ -\infty, \frac{3}{2} \right $ \cup \left$ -\frac{1}{2}, \infty \right $

Correct Answer: A

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Question 11

Determine the value of $\int_0^1 x^2 \sin(x) dx$.

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 12

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 13

Solve the system of equations: $\begin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases}$

Correct A. (x,y) = (1,1)

B. (x,y) = (2,0)

C. (x,y) = (0,2)

D. (x,y) = (1,0)

Correct Answer: A

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Question 14

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$

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

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

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

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

Correct Answer: B

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Question 15

Solve the inequality $|x - 2| > 3$

Correct A. x < -1 or x > 5

B. x < 1 or x > 5

C. x < -1 or x > 2

D. x < 1 or x > 2

Correct Answer: A

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Question 16

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 4^3 - 2 $

Correct Answer: A

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Question 17

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

A. $ x = 2 $

Correct B. $ x = 3 $

C. $ x = 4 $

D. $ x = 5 $

Correct Answer: B

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Question 18

A matrix ( A ) is given by $ A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $. Find the determinant of ( A ).

Correct A. $ 1 \times 4 - 2 \times 3 $

B. $ 1 \times 3 - 2 \times 4 $

C. $ 1 \times 2 - 3 \times 4 $

D. $ 2 \times 3 - 1 \times 4 $

Correct Answer: A

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Question 19

Find the probability that at least one of two indep\endent events ( A ) and ( B ) occurs, given that ( P(A) = 0.4 ) and ( P(B) = 0.6 ).

Correct A. $ 1 - \( 1 - 0.4 $$ 1 - 0.6 \ $ )

B. $ 0.4 + 0.6 - \( 0.4 \ $(0.6) )

C. $ 0.4 + 0.6 - 0.4 \times 0.6 $

D. $ 1 - \( 0.4 \ $(0.6) )

Correct Answer: A

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Question 20

Solve for ( x ) in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. $ x = 10^2 $

Correct B. $ x = 10^4 $

C. $ x = 10^{-2} $

D. $ x = 10^{-4} $

Correct Answer: B

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Question 21

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

Correct A. $ \frac{1}{2} \times 3 \times 2 $

B. $ \frac{1}{2} \times 3 \times 3 $

C. $ \frac{1}{2} \times 2 \times 3 $

D. $ \frac{1}{2} \times 2 \times 2 $

Correct Answer: A

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Question 22

Solve for ( x ) in the equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = 2 $

C. $ x = -1 $

D. $ x = 1 $

Correct Answer: A

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Question 23

Find the value of $ \sin 60^circ $.

A. $ \frac{1}{2} $

Correct B. $ \frac{\sqrt{3}}{2} $

C. $ \frac{1}{\sqrt{3}} $

D. $ \frac{\sqrt{3}}{\sqrt{2}} $

Correct Answer: B

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Question 24

A circle has a radius of 4 cm. Find the area of the circle.

A. $ pi \times 4^2 $

B. $ 2 \times pi \times 4 $

C. $ pi \times 2^2 $

D. $ 2 \times pi \times 2 $

Correct Answer: VIEW ANSWER

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Question 25

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

Correct A. $ \frac{-x}{\( 1 - x^2 \ $^{3/2}} )

B. $ \frac{x}{\( 1 - x^2 \ $^{3/2}} )

C. $ \frac{1}{\( 1 - x^2 \ $^{3/2}} )

D. $ \frac{-1}{\( 1 - x^2 \ $^{3/2}} )

Correct Answer: A

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