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POST UTME NILE UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME NILE UNIVERSITY 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.

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Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. \( \frac{1}{2} \)

B. ( 3 )

C. ( 4 )

Correct D. ( 6 )

Correct Answer: D

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Question 2

A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. 0.68

B. 0.84

Correct C. 0.95

D. 0.99

Correct Answer: C

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Question 3

Find the derivative of the function \( y = \sin^2\( x \ \) ) u\sing the chain rule.

Correct A. \( 2\sin\( x \)\cos(x \) )

B. \( \cos^2\( x \ \) )

C. \( \sin^2\( x \ \) )

D. \( \tan^2\( x \ \) )

Correct Answer: A

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Question 4

Solve the equation \( \sin\( x \ \) = \frac{1}{2} ) for ( x ) in the interval ( [0, 2pi] ).

A. \( \frac{pi}{6} \)

Correct B. \( \frac{pi}{3} \)

C. \( \frac{5pi}{6} \)

D. \( \frac{7pi}{6} \)

Correct Answer: B

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Question 5

A sequence is defined by the formula \( a_n = 2n + 1 \). 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 6

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi cm^3

B. 36\pi cm^3

Correct C. 48\pi cm^3

D. 60\pi cm^3

Correct Answer: C

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Question 7

Solve for x in the equation \[ \begin{array}{rcl} 2x + 5 &=& 11 \ 3x - 2 &=& 7 \ \hline \end{array} \]

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 8

Find the surface area of the sphere with radius 5 cm.

A. 100\pi cm^2

B. 150\pi cm^2

Correct C. 200\pi cm^2

D. 250\pi cm^2

Correct Answer: C

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Question 9

Solve the system of equations \[ \begin{array}{rcl} x + y + z &=& 6 \ x + 2y + 3z &=& 11 \ 2x + 3y + 4z &=& 14 \ \hline \end{array} \]

Correct A. [1, 2, 3]

B. [2, 3, 1]

C. [3, 1, 2]

D. [4, 2, 0]

Correct Answer: A

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Question 10

Find the value of \[ \frac{1}{2} \int_{0}^{2} \( 2x + 1 \) dx \]

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 12

B. 16

Correct C. 20

D. 24

Correct Answer: C

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Question 12

Solve the system of equations \( \begin{cases} x + y = 4 \ x - 2y = -3 \end{cases} \).

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 13

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 14

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. 1/2

B. 1/3

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 15

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

Correct A. y = 2x + 1

B. y = 2x - 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: A

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Question 16

In the given diagram, what is the value of x?

A. 1

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

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

D. \frac{\sqrt{3}}{4}

Correct Answer: B

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Question 17

Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 18

A set of numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

A. 0.25

B. 0.5

C. 0.75

Correct D. 0.9

Correct Answer: D

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Question 19

A right circular cylinder has a height of 10 cm and a radius of 5 cm. What is its volume?

A. 500\pi

Correct B. 1000\pi

C. 2000\pi

D. 5000\pi

Correct Answer: B

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Question 20

A sequence is defined as: 1, 2, 4, 8, 16, ... . What is the next term in the sequence?

A. 32

B. 64

C. 128

Correct D. 256

Correct Answer: D

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Question 21

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

Correct A. f'(x) = \frac{-x}{\( 1 + x^2 \)^{3/2}}

B. f'(x) = \frac{x}{\( 1 + x^2 \)^{3/2}}

C. f'(x) = \frac{1}{\( 1 + x^2 \)^{3/2}}

D. f'(x) = \frac{-1}{\( 1 + x^2 \)^{3/2}}

Correct Answer: A

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Question 22

Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing 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 23

Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 2) ) u\sing the formula for the area of a triangle.

A. A = 3

Correct B. A = 6

C. A = 9

D. A = 12

Correct Answer: B

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Question 24

Solve the system of equations \( x + y = 2, x - y = 1 \) u\sing the method of substitution.

Correct A. x = 1, y = 1

B. x = 1, y = 2

C. x = 2, y = 1

D. x = 2, y = 2

Correct Answer: A

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Question 25

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

Correct A. f'(x) = 2x \sin x + x^2 \cos x

B. f'(x) = 2x \sin x - x^2 \cos x

C. f'(x) = x^2 \sin x - 2x \cos x

D. f'(x) = x^2 \sin x + 2x \cos x

Correct Answer: A

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