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POST UTME RHEMA UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME RHEMA UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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 2

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. \( \frac{2}{3} \)

B. \( \frac{3}{5} \)

C. \( \frac{1}{3} \)

D. \( \frac{4}{5} \)

Correct Answer: A

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Question 3

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

A. \( x = -1 \)

Correct B. \( x = 0 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: B

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Question 4

Find the area of the triangle with vertices ( A(0, 0) ), ( B(2, 0) ), and ( C(1, 3) ).

A. ( 3 )

B. ( 6 )

Correct C. ( 9 )

D. ( 12 )

Correct Answer: C

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Question 5

A circle has a radius of 4 cm. Find the area of the sector with a central angle of 60°.

A. ( 12pi )

Correct B. ( 16pi )

C. ( 20pi )

D. ( 24pi )

Correct Answer: B

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Question 6

Let \( S = {x in mathbb{R} : x^2 + 2x + 1 = 0} \). Find \( lim_{x \to 2} \frac{x^2 - 4}{x - 2} \) if it exists.

A. 4

B. 2

C. \frac{1}{2}

Correct D. \frac{1}{4}

Correct Answer: D

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Question 7

A binary operation ( odot ) on the set \( \mathbb{R} \) is defined as \( x odot y = xy + 1 \). Find ( (2 odot 3) odot 4 ).

A. 25

Correct B. 29

C. 33

D. 37

Correct Answer: B

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Question 8

Find the probability that at least one of two indep\endent events ( A ) and ( B ) occurs, given that ( P(A) = \frac{1}{2} ) and ( P(B) = \frac{1}{3} ).

A. \frac{1}{2}

B. \frac{2}{3}

Correct C. \frac{5}{6}

D. \frac{7}{12}

Correct Answer: C

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Question 9

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{17}

C. \sqrt{25}

D. \sqrt{29}

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

C. \( -\infty, -2 \) \cup \( 2, \infty \)

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

Correct Answer: A

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Question 11

A random sample of 16 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the population mean.

A. 173.2 cm, 177.8 cm

Correct B. 174.1 cm, 176.9 cm

C. 172.9 cm, 178.1 cm

D. 173.5 cm, 177.5 cm

Correct Answer: B

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Question 12

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

A. 10^4

Correct B. 10^8

C. 10^12

D. 10^16

Correct Answer: B

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Question 13

A bakery sells 250 loaves of bread per day at ₦120 per loaf. If the \cost price per loaf is ₦80, calculate the profit per loaf and the total profit per day.

Correct A. ₦40, ₦10,000

B. ₦30, ₦8,000

C. ₦20, ₦6,000

D. ₦10, ₦4,000

Correct Answer: A

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Question 14

In the circuit below, identify the component labeled A.

Correct A. Resistor

B. Battery

C. Capacitor

D. Inductor

Correct Answer: A

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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 = 2, x = 3

D. x = 1, x = 4

Correct Answer: A

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Question 16

Find the value of x in the quadratic equation \( x^2 + 5x + 6 = 0 \).

A. 2

Correct B. -3

C. -2

D. 1

Correct Answer: B

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Question 17

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

Correct A. 22.5

B. 25

C. 20

D. 22

Correct Answer: A

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Question 18

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).

Correct A. 62

B. 64

C. 60

D. 58

Correct Answer: A

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Question 19

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

Correct A. 7

B. 6

C. 5

D. 4

Correct Answer: A

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Question 20

Solve the inequality \( x^2 - 4x - 5 > 0 \).

Correct A. \( x < -1 \) or \( x > 5 \)

B. \( x < 1 \) or \( x > 5 \)

C. \( x < -1 \) or \( x < 5 \)

D. \( x < 1 \) or \( x < 5 \)

Correct Answer: A

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Question 21

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 22

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. x = 1, y = 2

B. x = 2, y = 3

C. x = 3, y = 4

D. x = 4, y = 5

Correct Answer: A

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Question 23

A circle has a radius of 5 units. Find the area of the circle.

A. 25π

Correct B. 50π

C. 75π

D. 100π

Correct Answer: B

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Question 24

Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 25

A die is rolled. Find the probability that the number obtained is greater than 4.

A. 1/6

B. 1/3

C. 1/2

Correct D. 2/3

Correct Answer: D

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