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POST UTME RHEMA UNIVERSITY 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of x in the equation $ \frac{1}{2}x^2 + 5x - 3 = 0 $ u\sing the quadratic formula.

Correct A. \frac{-5 + \sqrt{109}}{2}

B. \frac{-5 - \sqrt{109}}{2}

C. \frac{5 + \sqrt{109}}{2}

D. \frac{5 - \sqrt{109}}{2}

Correct Answer: A

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Question 2

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

Correct A. $ -\infty, -1 $ \cup $ 3, \infty $

B. $ -\infty, 3 $ \cup $ 1, \infty $

C. $ -\infty, -3 $ \cup $ 1, \infty $

D. $ -\infty, 1 $ \cup $ 3, \infty $

Correct Answer: A

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Question 3

Find the sum of the first 5 terms of the geometric series $ 2, 6, 18, \ldots $.

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 4

Solve the system of linear equations $ \begin{cases} x + 2y = 4 \ 3x - 2y = 2 \end{cases} $ u\sing matrices.

Correct A. \begin{pmatrix} 2 \ 1 \end{pmatrix}

B. \begin{pmatrix} 1 \ 2 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \end{pmatrix}

D. \begin{pmatrix} 4 \ 3 \end{pmatrix}

Correct Answer: A

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Question 5

Find the determinant of the matrix $ \begin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{pmatrix} $.

Correct A. -5

B. -6

C. -7

D. -8

Correct Answer: A

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Question 6

Find the value of $x$ in the equation $2^x = 64$.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 7

Solve the inequality $\frac{x-1}{x+1} > 0$.

Correct A. x < -1 or x > 1

B. x < -1 or x = 1

C. x > -1 or x < 1

D. x > 1 or x < -1

Correct Answer: A

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Question 8

Find the volume of the solid formed by revolving the region bounded by $y = x^2$ and $y = 4 - x^2$ about the x-axis.

A. 16\pi

Correct B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: B

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Question 9

A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.

Correct A. 20

B. 30

C. 40

D. 50

Correct Answer: A

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Question 10

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

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 11

Determine the value of x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ) if $ \sin\( x \ $ = \frac{3}{5} ).

Correct A. $ \frac{4pi}{3} $

B. $ \frac{5pi}{3} $

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

D. $ \frac{2pi}{3} $

Correct Answer: A

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Question 12

A cylindrical \tank with a radius of 4m and a height of 10m is filled with water. If the water level is at 6m, what is the volume of the water in the \tank?

A. ( 800pi ) m³

Correct B. ( 1600pi ) m³

C. ( 2400pi ) m³

D. ( 3200pi ) m³

Correct Answer: B

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Question 13

A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the die is rolled again. If the outcome is an odd number, the die is rolled three more times. What is the probability that the final outcome is a 6?

A. $ \frac{1}{6} $

B. $ \frac{1}{12} $

C. $ \frac{1}{36} $

Correct D. $ \frac{1}{24} $

Correct Answer: D

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Question 14

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

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

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

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

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

Correct Answer: A

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Question 15

A right-angled triangle has a hypotenuse of length 10cm and one leg of length 6cm. Find the length of the other leg.

Correct A. ( 8 ) cm

B. ( 6 ) cm

C. ( 4 ) cm

D. ( 2 ) cm

Correct Answer: A

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Question 16

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.

Correct A. ( f'(x) = \frac{-x}{$ x^2 + 1 $^{3/2}} )

B. ( f'(x) = \frac{x}{$ x^2 + 1 $^{3/2}} )

C. ( f'(x) = \frac{1}{$ x^2 + 1 $^{3/2}} )

D. ( f'(x) = \frac{-1}{$ x^2 + 1 $^{3/2}} )

Correct Answer: A

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Question 17

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 18

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

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

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

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

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

Correct Answer: A

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Question 19

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

Correct A. $ 2\( 1 - 2^{10} \ $ )

B. $ 2\( 1 + 2^{10} \ $ )

C. $ 2\( 1 - 2^{10} \ $ )

D. $ 2\( 1 + 2^{10} \ $ )

Correct Answer: A

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Question 20

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

Correct A. $ \frac{8}{3} $

B. $ \frac{16}{3} $

C. $ \frac{32}{3} $

D. $ \frac{64}{3} $

Correct Answer: A

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Question 21

Find the equation of the \tangent to the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ at the point where $ x = 1 $.

A. $ y = x + 5 $

Correct B. $ y = 2x - 1 $

C. $ y = 3x - 2 $

D. $ y = x - 1 $

Correct Answer: B

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Question 22

A circle has equation $ x^2 + y^2 = 4 $. Find the equation of the \tangent to the circle at the point where $ x = 2 $.

Correct A. $ y = -x + 2 $

B. $ y = x + 2 $

C. $ y = -x - 2 $

D. $ y = x - 2 $

Correct Answer: A

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Question 23

The mean of five numbers is 10. If one of the numbers is 5, find the sum of the other four numbers.

Correct A. 25

B. 30

C. 35

D. 40

Correct Answer: A

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Question 24

A rec\tangular prism has dimensions 5 cm, 6 cm, and 7 cm. Find its volume.

A. 210 cm^3

B. 240 cm^3

Correct C. 270 cm^3

D. 300 cm^3

Correct Answer: C

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Question 25

A histogram has a mean of 20 and a s\tandard deviation of 5. Find the value of the highest bar.

A. 25

B. 30

C. 35

Correct D. 40

Correct Answer: D

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