Exam Body

Year

Subject

Paper Type

POST UTME UNILAG 2020 Mathematics | Objective

Are you preparing for POST UTME UNILAG 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

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 2

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

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 3

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

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 4

A histogram is shown below. What is the mode of the data set?

A. A

Correct B. B

C. C

D. D

Correct Answer: B

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Question 5

Solve the equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 6

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

A. 48\pi cm^3

B. 64\pi cm^3

Correct C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: C

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Question 7

A circle passes through the points (2, 3), (4, 1), and (6, 5). Find the equation of the circle.

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

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

C. x^2 + y^2 - 6x + 2y - 5 = 0

D. x^2 + y^2 + 6x - 2y - 5 = 0

Correct Answer: A

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Question 8

Solve the equation \frac{x^2 - 4x + 4}{x^2 - 4x + 3} = \frac{x + 2}{x - 1}

Correct A. x = 2

B. x = 3

C. x = 4

D. x = 5

Correct Answer: A

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Question 9

Find the area of the region bounded by the parabola y = x^2, the x-axis, and the line x = 2.

A. \frac{8}{3}

Correct B. \frac{16}{3}

C. \frac{24}{3}

D. \frac{32}{3}

Correct Answer: B

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Question 10

Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11

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

A. 24\pi

B. 36\pi

Correct C. 48\pi

D. 60\pi

Correct Answer: C

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Question 12

Find the area under the curve y = \sin^2 x from x = 0 to x = \frac{\pi}{2}.

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 13

Solve the inequality |x - 2| > 3.

Correct A. \( -\infty, -1 \) \cup \( 4, \infty \)

B. \( -\infty, 1 \) \cup \( 4, \infty \)

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

D. \( -\infty, 1 \) \cup \( 2, \infty \)

Correct Answer: A

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Question 14

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \frac{1}{2}.

A. 1.9999

Correct B. 2.0000

C. 2.0001

D. 2.0002

Correct Answer: B

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Question 15

Solve the equation \log_2 \( x + 1 \) = 3.

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 16

Given that \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \), find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. 0.6

B. 0.8

C. 1.2

D. 1.6

Correct Answer: A

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Question 17

A random variable ( X ) has a probability density function ( f(x) = \begin{cases} 2x & \text{if } 0 < x < 1 \ 0 & \text{otherwise} \end{cases} ). Find the expected value of ( X ).

A. 0.25

Correct B. 0.5

C. 0.75

D. 1.0

Correct Answer: B

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Question 18

The graph of the function \( y = \frac{1}{x} \ \) has a horizontal asymptote at \( y = \boxed{?} \).

A. 0

B. 1

Correct C. ∞

D. -∞

Correct Answer: C

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Question 19

A polynomial ( p(x) ) has roots at \( x = -2, 3, \ \) and ( 5 ). Write the polynomial in factored form.

Correct A. \( x + 2 \)\( x - 3 \)\( x - 5 \)

B. \( x - 2 \)\( x + 3 \)\( x + 5 \)

C. \( x + 2 \)\( x - 3 \)\( x + 5 \)

D. \( x - 2 \)\( x + 3 \)\( x - 5 \)

Correct Answer: A

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Question 20

A set of data has a mean of 25 and a s\tandard deviation of 3. If the data set is normally distributed, what is the probability that a randomly selected value will be between 20 and 30?

A. 0.25

Correct B. 0.5

C. 0.75

D. 0.9

Correct Answer: B

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Question 21

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22

Solve the inequality \( x^2 - 4x + 4 > 0 \).

Correct A. x > 2

B. x < 2

C. x > 0

D. x < 0

Correct Answer: A

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Question 23

Find the derivative of the function ( f(x) = \sin^2 x ).

Correct A. \cos 2x

B. \sin 2x

C. \cos x

D. \sin x

Correct Answer: A

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Question 24

Solve the equation \( \tan x = \sqrt{3} \).

A. \frac{\pi}{3}

Correct B. \frac{2\pi}{3}

C. \frac{4\pi}{3}

D. \frac{5\pi}{3}

Correct Answer: B

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Question 25

Find the value of x in the equation \( 2^x = 16 \).

A. 4

Correct B. 8

C. 12

D. 16

Correct Answer: B

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