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POST UTME BSU 2021 Mathematics | Objective

Are you preparing for POST UTME BSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 2cm.

A. 120\pi

Correct B. 240\pi

C. 360\pi

D. 480\pi

Correct Answer: B

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Question 3

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

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

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

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

Correct Answer: A

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Question 4

A binary operation \(*\) on the set \{0, 1\} is defined as follows: \(0 * 0 = 0, 0 * 1 = 1, 1 * 0 = 1, 1 * 1 = 1\). Find the result of \(1 * \( 0 * 1)\ \).

A. 0

Correct B. 1

C. 0 * 1

D. 1 * 0

Correct Answer: B

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Question 5

A circle with center \(A\) and radius \(5\) units has equation \(x^2 + y^2 = 25\). Find the equation of the circle with center \(B\) and radius \(3\) units that passes through the point \(\( 2, 1)\ \).

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 9

C. x^2 + y^2 = 25

D. x^2 + y^2 = 36

Correct Answer: A

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Question 6

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

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

B. x^2 + y^2 - 2x - 2y + 3 = 0

C. x^2 + y^2 + 2x + 2y - 1 = 0

D. x^2 + y^2 + 4x + 4y - 9 = 0

Correct Answer: A

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Question 7

Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.

A. \( -3, -1 \) \cup (1, 3)

B. \( -3, -1 \) \cup \( 1, \infty \)

Correct C. \( -\infty, -3 \) \cup \( -1, 1 \) \cup \( 3, \infty \)

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

Correct Answer: C

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Question 8

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

Correct A. \frac{14}{3}

B. \frac{13}{3}

C. \frac{15}{3}

D. \frac{16}{3}

Correct Answer: A

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Question 9

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

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

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

C. \( x - 1 \)\( x + 2 \)\( x - 3 \) = 0

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

Correct Answer: A

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Question 10

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

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

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

Correct A. 0.693

B. 0.785

C. 0.905

D. 1.047

Correct Answer: A

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Question 12

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

A. 10

B. 100

Correct C. 1000

D. 10000

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 = x + 1

B. y = x - 1

C. y = 2x - 1

Correct D. y = 2x + 1

Correct Answer: D

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Question 14

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{1}{\( x^2 + 1 \)^2}

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

Correct Answer: A

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Question 15

Find the area of the circle with radius \( r = 4 \) u\sing the formula \( A = pi r^2 \).

Correct A. 50.265

B. 100.53

C. 157.08

D. 314.16

Correct Answer: A

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Question 16

Let X be a random variable with probability density function (pdf) given by f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}. Find the probability that X is greater than 0.5.

A. 0.5

Correct B. 0.75

C. 0.875

D. 0.9375

Correct Answer: B

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Question 17

Find the equation of the circle with center at (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 18

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 19

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 75% of the scores are below 70, find the total number of scores.

A. 10

B. 20

C. 30

Correct D. 40

Correct Answer: D

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Question 20

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

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 21

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 23

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

A. 15

B. 25

Correct C. 35

D. 45

Correct Answer: C

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Question 24

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

A. -2/x^3

Correct B. 2/x^3

C. -1/x^3

D. 1/x^3

Correct Answer: B

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Question 25

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

A. 25π

Correct B. 50π

C. 75π

D. 100π

Correct Answer: B

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