Exam Body

Year

Subject

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POST UTME KSU 2017 Mathematics | Objective

Are you preparing for POST UTME KSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 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 \( x = 4 \).

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 2

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5

B. 78.5

C. 78.5

D. 78.5

Correct Answer: A

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Question 3

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -1 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, 3 \) ∪ (1, ∞)

Correct Answer: A

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Question 4

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

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 5

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 = x - 1

D. y = x + 1

Correct Answer: A

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Question 6

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

Correct Answer: A

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Question 7

A polynomial function is defined as ( f(x) = ax^3 + bx^2 + cx + d ). If ( f(1) = 3 ), \( f\( -1 \ \) = -3 ), and ( f(0) = 2 ), find the value of \( a + b + c + d \).

Correct A. \( 3a + b + c + d \)

B. \( a + 3b + c + d \)

C. \( a + b + 3c + d \)

D. \( a + b + c + 3d \)

Correct Answer: A

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Question 8

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. \( 5 \times 3 \times 2 \)

B. \( 5 \times 3 + 2 \)

C. \( 5 \times 3 + 2 \times 5 \)

D. \( 5 \times 3 \times 2 \times 5 \)

Correct Answer: A

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Question 9

A curve is defined by the equation \( y = \frac{1}{x} \). Find the derivative of the curve.

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 10

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

Correct A. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) + 5 )

B. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) - 5 )

C. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) + 1 )

D. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) - 1 )

Correct Answer: A

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Question 11

In a circle of radius 5 cm, a chord of length 8 cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii.

Correct A. \( \frac{1}{6} pi \( 5 \ \)^2 )

B. \( \frac{1}{6} pi \( 8 \ \)^2 )

C. \( \frac{1}{6} pi \( 5 \ \)^2 - \frac{1}{2} (8)^2 )

D. \( \frac{1}{6} pi \( 5 \ \)^2 + \frac{1}{2} (8)^2 )

Correct Answer: A

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Question 12

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \end{cases} ). Find the expected value of X.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13

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

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

B. \( y = \frac{1}{2} x + \frac{3}{2} \)

Correct C. \( y = 2x + 1 \)

D. \( y = x + 2 \)

Correct Answer: C

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Question 14

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. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 1, y = 1 \)

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

Correct Answer: A

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Question 15

Find the mean deviation about the mean of the data set: 2, 4, 6, 8, 10.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 16

Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 17

Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

Correct A. \frac{32\pi}{3}

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

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

D. \frac{256\pi}{3}

Correct Answer: A

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Question 18

Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.

Correct A. \frac{256}{5}

B. \frac{512}{5}

C. \frac{1024}{5}

D. \frac{2048}{5}

Correct Answer: A

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Question 19

Find the vector projection of the vector \mathbf{a} = 2\mathbf{i} + 3\mathbf{j} onto the vector \mathbf{b} = \mathbf{i} + \mathbf{j}.

Correct A. \frac{5}{\sqrt{2}}\mathbf{i} + \frac{5}{\sqrt{2}}\mathbf{j}

B. \frac{5}{\sqrt{2}}\mathbf{i} - \frac{5}{\sqrt{2}}\mathbf{j}

C. \frac{5}{\sqrt{2}}\mathbf{i} + \frac{5}{\sqrt{2}}\mathbf{j}

D. \frac{5}{\sqrt{2}}\mathbf{i} - \frac{5}{\sqrt{2}}\mathbf{j}

Correct Answer: A

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Question 20

Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{2}{3^n}.

Correct A. \frac{2}{3}

B. \frac{4}{3}

C. \frac{6}{3}

D. \frac{8}{3}

Correct Answer: A

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Question 21

Given that ( f(x) = \frac{1}{x^2 + 1} ), find the derivative of ( f(x) ) u\sing the chain rule.

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

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

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

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

Correct Answer: B

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Question 22

A binary operation ( odot ) is defined as \( a odot b = a^2 + b^2 \). Find the value of ( 2 odot 3 ).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 23

A vector ( mathbf{a} ) is given by \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of ( mathbf{a} ).

A. 3.60555

Correct B. 4.1231

C. 5.19615

D. 6.40312

Correct Answer: B

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Question 24

A probability experiment consists of rolling a fair six-sided die. What is the probability that the number rolled is greater than 4?

A. 1/6

B. 1/3

C. 2/3

Correct D. 5/6

Correct Answer: D

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Question 25

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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