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POST UTME NOUN 2020 Mathematics | Objective

Are you preparing for POST UTME NOUN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 + \frac{1}{2} \times 4 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 + \frac{1}{2} \times 4^2 \)

D. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 + \frac{1}{2} \times 4^2 + 4 \)

Correct Answer: A

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Question 2

Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).

Correct A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)

C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Correct Answer: A

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Question 3

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

Correct A. \( \frac{1}{3} pi \( 2^3 - 1^3 \ \) )

B. \( \frac{1}{3} pi \( 2^3 + 1^3 \ \) )

C. \( \frac{1}{3} pi \( 2^3 - 1^2 \ \) )

D. \( \frac{1}{3} pi \( 2^2 - 1^3 \ \) )

Correct Answer: A

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Question 4

Solve the system of equations \( egin{cases} x + 2y = 3 \ 3x - 2y = 5 \end{cases} \).

Correct A. \( egin{cases} x = 1 \ y = 1 \end{cases} \)

B. \( egin{cases} x = 2 \ y = 1 \end{cases} \)

C. \( egin{cases} x = 1 \ y = 2 \end{cases} \)

D. \( egin{cases} x = 2 \ y = 2 \end{cases} \)

Correct Answer: A

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Question 5

Find the area of the triangle formed by the points ( A(2, 3) ), ( B(4, 5) ), and ( C(6, 2) ).

Correct A. \( \frac{1}{2} \times 4 \times 3 \)

B. \( \frac{1}{2} \times 4 \times 2 \)

C. \( \frac{1}{2} \times 3 \times 2 \)

D. \( \frac{1}{2} \times 3 \times 4 \)

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. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 7

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

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

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

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

D. \( \frac{1}{x^3} \)

Correct Answer: A

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Question 8

Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \) u\sing the method of substitution.

Correct A. \( x = 3, y = 1 \)

B. \( x = 1, y = 3 \)

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

D. \( x = 4, y = 0 \)

Correct Answer: A

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Question 9

Find the mean of the data set ( 2, 4, 6, 8, 10 ).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 10

Find the area of the triangle with vertices ( A(0, 0), B(2, 0), C(1, 2) ).

Correct A. ( 2 )

B. ( 4 )

C. ( 6 )

D. ( 8 )

Correct Answer: A

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Question 11

Let \( S = {1, 2, 3, 4, 5} \). Find the number of subsets of ( S ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 12

Solve the inequality \( 2x^2 - 5x - 3 > 0 \).

Correct A. \left\( -\infty, \frac{3}{2} \right \) \cup \left\( 3, \infty \right \)

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

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

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

Correct Answer: A

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Question 13

Find the value of \( \sin \left\( \frac{\pi}{4} \right \ \) \cos \left\( \frac{\pi}{3} \right \) - \cos \left\( \frac{\pi}{4} \right \) \sin \left\( \frac{\pi}{3} \right \) ).

Correct A. \frac{1}{2}

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

C. \frac{1}{\sqrt{2}}

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

Correct Answer: A

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Question 14

A binary operation \( \ast \) on the set \( \{1, 2, 3, 4, 5\} \) is defined as \( a \ast b = a + b \ \) for all \( a, b \in \{1, 2, 3, 4, 5\} \). Find the value of \( 3 \ast 4 \).

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 15

Solve the equation \( x^2 - 4x + 3 = 0 \).

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

B. \left\( 1, 2 \right \)

C. \left\( 2, 3 \right \)

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

Correct Answer: A

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Question 16

Find the value of \( \frac{d}{dx} \left\( \frac{1}{x} \right \ \) ).

Correct A. -\frac{1}{x^2}

B. \frac{1}{x^2}

C. -\frac{1}{x}

D. \frac{1}{x}

Correct Answer: A

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Question 17

A polynomial ( p(x) ) is defined as ( p(x) = x^3 - 2x^2 + x - 1 ). Find the value of \( p\( -1 \ \) ).

Correct A. 1

B. -1

C. 0

D. 2

Correct Answer: A

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Question 18

Find the value of \( \log_{10} \( 100 \ \) ).

A. 1

B. 2

C. 3

D. 4

Correct Answer: VIEW ANSWER

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Question 19

Let f(x) = 3x^2 + 2x - 5 and g(x) = 2x^2 - 3x + 1. Find the value of \( f + g \)(2).

A. 25

B. 30

Correct C. 35

D. 40

Correct Answer: C

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Question 20

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

Correct A. \( x = \frac{\pi}{4}, \frac{3\pi}{4} \)

B. \( x = \frac{\pi}{2}, \frac{3\pi}{2} \)

C. \( x = \frac{\pi}{4}, \frac{5\pi}{4} \)

D. \( x = \frac{\pi}{2}, \frac{7\pi}{4} \)

Correct Answer: A

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Question 21

Find the magnitude of the vector \( \vec{a} = \langle 3, 4 \rangle \).

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 22

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.68

B. 0.85

Correct C. 0.95

D. 0.99

Correct Answer: C

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Question 23

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.2

Correct B. 0.4

C. 0.6

D. 0.8

Correct Answer: B

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Question 24

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

A. 10

B. 20

Correct C. 40

D. 80

Correct Answer: C

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Question 25

A circle has a radius of 5 cm. Find the area of the circle.

A. 25\pi

Correct B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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