Exam Body

Year

Subject

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POST UTME BSU 2023 Mathematics | Objective

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Question 1

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \)

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2

A random variable X has a probability distribution given by ( P(X) = \begin{cases} 0.2 & \text{if } X = 1 \\ 0.8 & \text{if } X = 2 \\ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 1.

A. 0.2

B. 0.8

Correct C. 0.6

D. 0.4

Correct Answer: C

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Question 3

The mean of a set of numbers is 15, and the s\tandard deviation is 3. If the largest number in the set is 21, what is the smallest number?

Correct A. 9

B. 12

C. 15

D. 18

Correct Answer: A

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Question 4

Solve the equation \( 2^x + 3^x = 5^x \) for x.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 5

Find the equation of the circle with center (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 6

In the diagram below, the circle has a radius of 4 cm. Find the area of the sector OAB, where ∠AOB = 60°.

A. 10π cm^2

Correct B. 20π cm^2

C. 30π cm^2

D. 40π cm^2

Correct Answer: B

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Question 7

A sequence is defined by the recurrence relation a_n = 2a_\( n-1 \) + 1, where 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 8

In a game of chance, a player rolls a fair six-sided die. If the player rolls an even number, they win twice the amount they bet. If the player rolls an odd number, they lose their bet. What is the expected value of the game?

Correct A. 0

B. 1/6

C. 1/3

D. 2/3

Correct Answer: A

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Question 9

Solve the system of equations: x + y = 4 and x^2 + y^2 = 16.

A. x = 2, y = 2

Correct B. x = 2, y = 4

C. x = 4, y = 2

D. x = 4, y = 4

Correct Answer: B

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Question 10

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

A. 16π/3

Correct B. 32π/3

C. 64π/3

D. 128π/3

Correct Answer: B

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Question 11

Solve the inequality \( \frac{x}{x+2} > \frac{3}{x-1} \) for \( x in \( -infty, -2 \ \) cup \( -2, 1 \) cup (1, infty) ).

Correct A. \( x < -2 \) or \( x > 1 \)

B. \( x > -2 \) and \( x < 1 \)

C. \( x < -2 \) or \( x = 1 \)

D. \( x > -2 \) and \( x > 1 \)

Correct Answer: A

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Question 12

Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 4 - x \) about the x-axis.

A. \( \frac{32}{3} pi \)

Correct B. \( \frac{64}{3} pi \)

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

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

Correct Answer: B

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Question 13

Solve the system of equations \( egin{cases} x + y + z = 6 \ 2x + 3y + z = 12 \ x + 2y + 3z = 10 \end{cases} \).

Correct A. \( x = 1, y = 2, z = 3 \)

B. \( x = 2, y = 1, z = 3 \)

C. \( x = 3, y = 1, z = 2 \)

D. \( x = 1, y = 3, z = 2 \)

Correct Answer: A

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Question 14

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ).

A. ( 5 )

B. ( 10 )

Correct C. ( 15 )

D. ( 20 )

Correct Answer: C

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Question 15

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. \( x = -2, x = -3 \)

B. \( x = -1, x = -6 \)

C. \( x = 1, x = 6 \)

D. \( x = 2, x = 3 \)

Correct Answer: A

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Question 16

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

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

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

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

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

Correct Answer: A

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Question 17

Solve for ( x ) in the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+1} \).

A. \( x = -1 \)

Correct B. \( x = 0 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: B

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Question 18

Find the sum of the first 10 terms of the geometric series \( 2 + 4 + 8 + ldots \).

Correct A. ( 2047 )

B. ( 2048 )

C. ( 2049 )

D. ( 2050 )

Correct Answer: A

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Question 19

A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly 3 elements.

A. ( 10 )

Correct B. ( 15 )

C. ( 20 )

D. ( 25 )

Correct Answer: B

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Question 20

Find the equation of the \tangent line to the curve \( y = x^2 - 4x + 3 \) at the point \( 1, -2 \ \) ).

Correct A. \( y = -x + 1 \)

B. \( y = x - 3 \)

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

D. \( y = x + 1 \)

Correct Answer: A

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Question 21

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

Correct A. -120

B. 120

C. 0

D. -60

Correct Answer: A

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Question 22

If the function [ f(x) = \frac{1}{x^2 + 1} \] has a local maximum at [ x = a \], find the value of [ a \].

A. -1

Correct B. 0

C. 1

D. \frac{1}{2}

Correct Answer: B

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Question 23

The histogram below shows the distribution of exam scores. Find the mean of the scores.

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 24

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

A. 1

B. \frac{1}{2}

Correct C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: C

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Question 25

The sequence [ \{ 1, 2, 4, 8, \ldots \} \] is a geometric sequence. Find the next term in the sequence.

A. 16

B. 32

C. 64

Correct D. 128

Correct Answer: D

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