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POST UTME LAUTECH 2017 Mathematics | Objective

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Question 1

Determine the value of x in the equation $ \frac{1}{2}x^2 + 5x - 3 = 17 $.

Correct A. 4

B. -4

C. 6

D. -6

Correct Answer: A

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Question 2

A histogram of exam scores is shown below. What is the mean of the scores?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 3

Solve the system of equations $ egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} $.

Correct A. (2, 2)

B. (3, 1)

C. (4, 0)

D. $ 5, -1 $

Correct Answer: A

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Question 4

Find the sum of the first 10 terms of the geometric series $ 2 + 6 + 18 + ldots $.

A. 1950

B. 2050

Correct C. 2150

D. 2250

Correct Answer: C

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Question 5

A matrix A is given by $ A = \begin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} $. Find the determinant of A.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 6

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 7

A histogram of exam scores is shown below. Find the mean and s\tandard deviation of the scores.

A. Mean: 75, S\tandard Deviation: 10

Correct B. Mean: 80, S\tandard Deviation: 15

C. Mean: 85, S\tandard Deviation: 20

D. Mean: 90, S\tandard Deviation: 25

Correct Answer: B

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Question 8

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

A. $ x = 2 $

B. $ x = 3 $

Correct C. $ x = 4 $

D. $ x = 5 $

Correct Answer: C

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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 - 3 \ $^2 + $ y - 2 $^2 = 16 )

C. $ x - 4 \ $^2 + $ y - 3 $^2 = 16 )

D. $ x - 3 \ $^2 + $ y - 4 $^2 = 16 )

Correct Answer: A

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Question 10

A population of bacteria is growing at a rate of ( 20% ) per hour. If the initial population is ( 1000 ), find the population after ( 3 ) hours.

Correct A. ( 1000(1.2)^3 )

B. ( 1000(1.2)^2 )

C. ( 1000(1.2)^1 )

D. ( 1000(1.2)^0 )

Correct Answer: A

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Question 11

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 12

A circle has a radius of 5 cm. Find the area of the circle u\sing the formula $ A = pi r^2 $.

A. ( 50pi ) cm^2

Correct B. ( 25pi ) cm^2

C. ( 75pi ) cm^2

D. ( 100pi ) cm^2

Correct Answer: B

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Question 13

Find the volume of the frustum of a cone with a height of 10 cm, a base radius of 5 cm, and a top radius of 3 cm.

A. ( 100pi ) cm^3

B. ( 150pi ) cm^3

Correct C. ( 200pi ) cm^3

D. ( 250pi ) cm^3

Correct Answer: C

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Question 14

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ x < -\frac{3}{2} $ or $ x > \frac{1}{2} $

B. $ x < -\frac{1}{2} $ or $ x > \frac{3}{2} $

C. $ x < -\frac{1}{2} $ or $ x < \frac{3}{2} $

D. $ x > -\frac{3}{2} $ or $ x < \frac{1}{2} $

Correct Answer: A

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Question 15

A binary operation ( odot ) is defined as $ a odot b = ab + 2 $. Find the value of ( 3 odot 4 ).

A. ( 14 )

B. ( 16 )

Correct C. ( 18 )

D. ( 20 )

Correct Answer: C

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Question 16

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. $ \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 $

B. $ \frac{1}{2} \times 4^2 + 3 \times 4 - 2 $

C. $ \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 $

D. $ \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 $

Correct Answer: A

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Question 17

Solve the system of equations $ 2x + 3y = 7 $ and $ x - 2y = -3 $.

Correct A. $ x = 1, y = 2 $

B. $ x = 2, y = 1 $

C. $ x = 1, y = -1 $

D. $ x = -1, y = 1 $

Correct Answer: A

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Question 18

A histogram of exam scores is shown below. What is the mean score?

A. ( 50 )

Correct B. ( 60 )

C. ( 70 )

D. ( 80 )

Correct Answer: B

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Question 19

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 + 2x - 5 )

D. ( f'(x) = 3x^2 - 2x - 5 )

Correct Answer: A

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Question 20

A binary operation ( oplus ) is defined as $ a oplus b = a + b - ab $. Find the value of ( 2 oplus 3 ).

A. ( 5 )

Correct B. ( 7 )

C. ( 9 )

D. ( 11 )

Correct Answer: B

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Question 21

A vector ( mathbf{a} ) is given by $ mathbf{a} = 2mathbf{i} + 3mathbf{j} $. Find the magnitude of ( mathbf{a} ).

Correct A. $ \sqrt{13} $

B. $ \sqrt{15} $

C. $ \sqrt{17} $

D. $ \sqrt{19} $

Correct Answer: A

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Question 22

A probability distribution is given by ( P(x) = \frac{1}{2}x^2 ) for ( 0 leq x leq 2 ). Find the expected value of ( X ).

A. ( 1 )

Correct B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: B

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Question 23

A polynomial ( f(x) = x^3 - 2x^2 + x - 1 ) has a root at $ x = 1 $. Find the other two roots.

Correct A. $ x = 2, x = 3 $

B. $ x = 1, x = 2 $

C. $ x = 1, x = 3 $

D. $ x = 2, x = 4 $

Correct Answer: A

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Question 24

A \fraction $ \frac{1}{2} $ is written in base 8. What is its decimal equivalent?

A. ( 0.5 )

B. ( 0.6 )

C. ( 0.7 )

D. ( 0.8 )

Correct Answer: VIEW ANSWER

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Question 25

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

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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