Exam Body

Year

Subject

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POST UTME LASU 2018 Mathematics | Objective

Are you preparing for POST UTME LASU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find 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. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 2

Solve for x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ).

A. $ \sin\( x \ $ = 1 )

B. $ \cos\( x \ $ = 1 )

Correct C. $ \sin\( x \ $ = \cos(x) )

D. $ \sin\( x \ $ = -\cos(x) )

Correct Answer: C

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Question 3

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. ( f'(x) = 6x + 2 )

B. ( f'(x) = 6x - 2 )

C. ( f'(x) = 3x^2 + 2 )

D. ( f'(x) = 3x^2 - 2 )

Correct Answer: A

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Question 4

Solve the system of equations u\sing matrices:

Correct A. $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $

B. $ egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} $

C. $ egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix} $

D. $ egin{bmatrix} 4 & 3 \ 2 & 1 \end{bmatrix} $

Correct Answer: A

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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

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

Correct A. $ \frac{1}{3} pi \( 6^2 + 4^2 + 6 cdot 4 \ $ \times 10 )

B. $ \frac{1}{3} pi \( 6^2 + 4^2 - 6 cdot 4 \ $ \times 10 )

C. $ \frac{1}{3} pi \( 6^2 + 4^2 + 6 cdot 4 \ $ \times 5 )

D. $ \frac{1}{3} pi \( 6^2 + 4^2 - 6 cdot 4 \ $ \times 5 )

Correct Answer: A

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Question 7

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

Correct A. $ x = 10^4 $

B. $ x = 10^8 $

C. $ x = 10^{-4} $

D. $ x = 10^{-8} $

Correct Answer: A

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Question 8

Find the area under the curve $ y = x^2 + 2x + 1 $ from $ x = 0 $ to $ x = 2 $.

Correct A. $ \frac{1}{3} \( 2^3 + 4 cdot 2^2 + 2 cdot 2 \ $ )

B. $ \frac{1}{3} \( 2^3 + 4 cdot 2^2 + 2 cdot 2 + 1 \ $ )

C. $ \frac{1}{3} \( 2^3 + 4 cdot 2^2 + 2 cdot 2 - 1 \ $ )

D. $ \frac{1}{3} \( 2^3 + 4 cdot 2^2 - 2 cdot 2 \ $ )

Correct Answer: A

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Question 9

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 = 4 )

C. $ x - 3 \ $^2 + $ y - 2 $^2 = 16 )

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

Correct Answer: A

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Question 10

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 11

Let ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ). Find the value of $ f\( -2 \ $ ) u\sing the given function.

Correct A. \frac{1}{3}

B. -\frac{1}{3}

C. \frac{1}{2}

D. -\frac{1}{2}

Correct Answer: A

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Question 12

A random variable ( X ) has a probability distribution given by $ P\( X = x \ $ = \frac{1}{2} \) for $ x = -1, 1 \ $. Find the probability that $ X \ $ is greater than 0.

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. \frac{3}{4}

D. 1

Correct Answer: B

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Question 13

Find the value of $ \overrightarrow{a} \cdot \overrightarrow{b} \ $ given that $ \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 1 \end{pmatrix} \ $ and $ \overrightarrow{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \ $.

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 14

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 15

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

A. 0.25

B. 0.30

Correct C. 0.35

D. 0.40

Correct Answer: C

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Question 16

Determine the value of $\frac{1}{2} \int_{0}^{\pi} \sin^2 x \, dx$.

A. 0

B. \frac{\pi}{2}

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

D. 1

Correct Answer: C

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Question 17

A histogram of exam scores for a class of 50 students is shown below. What is the mean score?

A. 60

Correct B. 70

C. 80

D. 90

Correct Answer: B

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Question 18

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 19

A binary operation $\oplus$ is defined by $a \oplus b = a^2 + b^2$. Find $2 \oplus 3$.

A. 13

B. 14

C. 15

Correct D. 16

Correct Answer: D

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Question 20

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{2}

Correct B. \frac{2}{5}

C. \frac{3}{8}

D. \frac{4}{9}

Correct Answer: B

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Question 21

Find the sum of the infinite geometric series $ sum_{n=1}^{infty} \frac{1}{2^n} $ u\sing the formula $ S = \frac{a}{1 - r} $, where (a) is the first term and (r) is the common ratio.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22

A polynomial (p(x)) has roots at $ x = 2, x = 3, $ and $ x = 4 $. If (p(1) = 10), find the value of (p(0)).

A. -10

B. 0

Correct C. 10

D. 20

Correct Answer: C

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Question 23

Solve the inequality $ \frac{x^2 - 4}{x^2 - 9} > 0 $ u\sing interval notation.

Correct A. $ -infty, -3 $ cup (3, infty)

B. $ -3, 3 $

C. $ -infty, -3 $ cup (3, infty) cup $ -9, 9 $

D. $ -infty, -9 $ cup $ -3, 3 $ cup (9, infty)

Correct Answer: A

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Question 24

A curve is defined by the equation $ y = \frac{1}{x^2 + 1} $. Find the equation of the \tangent line to the curve at the point $ 1, \frac{1}{2} \ $).

Correct A. y = x - 1

B. y = x + 1

C. y = -x + 1

D. y = x - 2

Correct Answer: A

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Question 25

A sequence is defined by the formula $ 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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