Exam Body

Year

Subject

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POST UTME FUTO 2020 Mathematics | Objective

Are you preparing for POST UTME FUTO exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

In a circle with center O and radius 6, a chord AB is drawn such that AB = 8. Find the dis\tance from O to the midpoint M of AB.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 2

A population of 1000 bacteria grows according to the equation P(t) = 500e^(0.05t), where P(t) is the population at time t. Find the rate of change of the population with respect to time when the population is 750.

Correct A. 0.05

B. 0.1

C. 0.15

D. 0.2

Correct Answer: A

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Question 3

In a triangle ABC, the length of side AB is 5, the length of side BC is 6, and the angle between sides AB and BC is 60 degrees. Find the length of side AC.

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 4

A function f(x) is defined as f(x) = 2x^2 + 3x - 1. Find the derivative of f(x) u\sing the power rule.

Correct A. 4x + 3

B. 2x^2 + 3

C. 4x + 1

D. 2x^2 - 1

Correct Answer: A

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Question 5

A circle with center O and radius 4 is inscribed in a square with side length 8. Find the area of the shaded region.

A. 16

Correct B. 32

C. 64

D. 128

Correct Answer: B

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Question 6

Find the volume of the frustum of a cone with radii 6 cm and 3 cm, and height 8 cm.

A. 120\pi

B. 240\pi

Correct C. 360\pi

D. 480\pi

Correct Answer: C

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Question 7

Evaluate the definite integral \[ \int_0^1 x^2 \sin x \, dx \].

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 8

Solve the equation \[ 2x^2 + 5x - 3 = 0 \] u\sing the quadratic formula.

A. -1/2

Correct B. 1/2

C. -3/2

D. 3/2

Correct Answer: B

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Question 9

Find the area under the curve \[ y = \sin x \] from \[ x = 0 \] to \[ x = \pi/2 \].

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 10

Solve the inequality \[ 2x^2 - 5x + 3 > 0 \].

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

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

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

D. (1, 3)

Correct Answer: A

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Question 11

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm. The frustum is cut off by a plane parallel to the base.

A. 100\pi cm^3

B. 120\pi cm^3

Correct C. 150\pi cm^3

D. 180\pi cm^3

Correct Answer: C

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Question 12

A random variable X has a probability density function f(x) = \frac{1}{2}x, 0 \leq x \leq 2. Find the expected value of X.

A. 1

Correct B. 2

C. 4

D. 8

Correct Answer: B

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Question 13

Solve the equation \frac{1}{x+1} + \frac{1}{x-2} = \frac{3}{2}.

A. x = -1

Correct B. x = 2

C. x = -2

D. x = 4

Correct Answer: B

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Question 14

A histogram of exam scores has a mean of 60 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 50 and 70?

A. 0.25

Correct B. 0.5

C. 0.75

D. 0.9

Correct Answer: B

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Question 15

A circle has a radius of 4cm. Find the area of the circle.

Correct A. 16\pi cm^2

B. 32\pi cm^2

C. 64\pi cm^2

D. 128\pi cm^2

Correct Answer: A

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Question 16

Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).

A. 1

Correct B. -1

C. -2

D. 2

Correct Answer: B

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Question 17

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 18

Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20

A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \ \). Find the number of subsets of S.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 21

In the number system with base 8, what is the value of the expression \( 5 \times 8^2 + 3 \times 8^1 + 2 \times 8^0 \)?

A. 38

Correct B. 40

C. 42

D. 44

Correct Answer: B

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Question 22

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

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 23

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 = 4 )

D. \( x-2 \ \)^2 + \( y+3 \)^2 = 4 )

Correct Answer: A

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Question 24

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 25

Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = 4 \).

Correct A. \( 3mathbf{i} + 4mathbf{j} \)

B. \( 4mathbf{i} + 3mathbf{j} \)

C. \( 3mathbf{i} - 4mathbf{j} \)

D. \( -3mathbf{i} + 4mathbf{j} \)

Correct Answer: A

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