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

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Question 1

Determine the volume of the solid formed by revolving the region bounded by the curves 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 2

A binary operation * on the set of real numbers is defined as follows: a * b = ab + 2. Find the value of \( 2 * 3 \) * 4.

A. 40

Correct B. 42

C. 44

D. 46

Correct Answer: B

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Question 3

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment stops. What is the probability that the experiment will stop on the third roll?

A. \frac{1}{6}

B. \frac{1}{12}

Correct C. \frac{1}{24}

D. \frac{1}{36}

Correct Answer: C

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Question 4

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

A. \frac{256}{5}

B. \frac{512}{5}

Correct C. \frac{1024}{5}

D. \frac{2048}{5}

Correct Answer: C

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Question 5

Solve the equation x^4 - 6x^3 + 11x^2 - 6x - 12 = 0.

Correct A. \( x + 1 \)\( x - 2 \)\( x^2 - 3x + 6 \) = 0

B. \( x - 1 \)\( x + 2 \)\( x^2 - 3x + 6 \) = 0

C. \( x + 2 \)\( x - 2 \)\( x^2 - 3x + 6 \) = 0

D. \( x - 2 \)\( x + 1 \)\( x^2 - 3x + 6 \) = 0

Correct Answer: A

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Question 6

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and (6, 5).

Correct A. x^2 + y^2 - 4x - 2y + 5 = 0

B. x^2 + y^2 + 4x + 2y - 5 = 0

C. x^2 + y^2 - 2x - 4y + 3 = 0

D. x^2 + y^2 + 2x + 4y - 3 = 0

Correct Answer: A

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Question 7

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 8

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.2

B. 0.24

C. 0.28

D. 0.32

Correct Answer: A

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Question 9

Solve the equation \sin^2 x + \cos^2 x = 1 for x.

Correct A. \sin x = \cos x

B. \sin x = -\cos x

C. \cos x = \sin x

D. \cos x = -\sin x

Correct Answer: A

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Question 10

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 11

In a triangle ABC, angle A = 30°, angle B = 90°, and side AB = 5 cm. Find the length of side AC.

A. 10 cm

B. 12 cm

Correct C. 15 cm

D. 18 cm

Correct Answer: C

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Question 12

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

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 3 \end{bmatrix}

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 1230

B. 1240

Correct C. 1250

D. 1260

Correct Answer: C

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Question 14

In a circle with center O and radius 6 cm, chord AB = 8 cm. Find the length of the perp\endicular from O to AB.

A. 4 cm

Correct B. 5 cm

C. 6 cm

D. 7 cm

Correct Answer: B

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Question 15

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

A. 10

B. 20

Correct C. 40

D. 80

Correct Answer: C

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Question 16

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

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

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

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

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

Correct Answer: A

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Question 17

Solve the system of equations u\sing matrices:\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \).

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

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

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 18

Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 4) ).

Correct A. ( 6 )

B. ( 12 )

C. ( 18 )

D. ( 24 )

Correct Answer: A

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Question 19

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

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

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

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 20

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?

A. ( 0.5 )

B. ( 0.6 )

Correct C. ( 0.7 )

D. ( 0.8 )

Correct Answer: C

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Question 21

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).

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

B. \( x = \frac{3pi}{4} \)

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

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

Correct Answer: A

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Question 22

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the sum of the first 5 terms of the sequence.

Correct A. \( 3 + 7 + 15 + 31 + 63 \)

B. \( 3 + 5 + 11 + 23 + 47 \)

C. \( 3 + 7 + 13 + 25 + 51 \)

D. \( 3 + 9 + 17 + 33 + 65 \)

Correct Answer: A

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Question 23

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.

Correct A. \( \frac{64}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{16}{3} \)

D. \( \frac{8}{3} \)

Correct Answer: A

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Question 24

Solve the system of equations \( egin{cases} x + y = 2 \ 2x - 3y = -1 \end{cases} \) u\sing matrices.

Correct A. \( x = \frac{5}{7}, y = \frac{4}{7} \)

B. \( x = \frac{3}{5}, y = \frac{2}{5} \)

C. \( x = \frac{2}{3}, y = \frac{1}{3} \)

D. \( x = \frac{4}{5}, y = \frac{1}{5} \)

Correct Answer: A

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Question 25

A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is 7.

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

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

Correct D. \( \frac{2}{3} \)

Correct Answer: D

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