Exam Body

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POST UTME REDEEMERS UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME REDEEMERS 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 area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 2

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

Correct A. x < -1 or x > 3/2

B. x < 1 or x > 3

C. x < -1 or x < 3/2

D. x < 1 or x > 3/2

Correct Answer: A

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Question 3

Find the value of x in the equation x^3 - 6x^2 + 11x - 6 = 0.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 4

A set A has 5 elements, and a set B has 3 elements. What is the number of elements in the union of sets A and B?

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 5

A sequence is defined by the formula an = 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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Question 6

Determine the equation of the circle with centre (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 + \( y-2 \)^2 = 16 )

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

Correct Answer: A

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Question 7

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

B. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

C. \( x > -\frac{5}{4} \) and \( x < \frac{3}{2} \)

D. \( x < -\frac{5}{4} \) and \( x > \frac{3}{2} \)

Correct Answer: A

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Question 8

Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 9

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. U\sing the concept of variation, find the ratio of the time taken for the return journey to the time taken for the outward journey.

A. 1:2

Correct B. 2:1

C. 3:2

D. 4:3

Correct Answer: B

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Question 10

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

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 0 \)

D. \( x = 1 \)

Correct Answer: A

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Question 11

Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \boxed{\( x + 2 \)^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 12

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If 75% of the scores fall below 80, what is the z-score corresponding to 80?

Correct A. \boxed{0.5}

B. 1.0

C. 1.5

D. 2.0

Correct Answer: A

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Question 13

Solve the equation \tan^2 x + 2 \tan x - 6 = 0 for x in the interval [0, \pi/2].

Correct A. \boxed{x = \arc\tan(3)}

B. x = \arc\tan\( -2 \)

C. x = \arc\tan(2)

D. x = \arc\tan\( -3 \)

Correct Answer: A

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Question 14

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

Correct A. \boxed{\frac{16\pi}{15}}

B. \frac{32\pi}{15}

C. \frac{64\pi}{15}

D. \frac{128\pi}{15}

Correct Answer: A

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Question 15

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

Correct A. \boxed{0}

B. 2

C. 4

D. 6

Correct Answer: A

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Question 16

Find the value of ( lambda ) such that the quadratic equation \( x^2 + 4x + lambda = 0 \) has equal roots.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17

Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 3 \end{bmatrix} \)

C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 5 \end{bmatrix} \)

Correct Answer: A

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Question 18

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 + \( y - 5 \)^2 = 16 )

D. \( x - 5 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 19

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

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

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

C. \( x < -\frac{1}{2} \) or \( x > 2 \)

D. \( x < 1 \) or \( x > 2 \)

Correct Answer: A

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Question 20

Find the value of ( k ) such that the equation \( x^2 + kx + 6 = 0 \) has a discriminant of ( 12 ).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 21

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

A. 32\pi cm^3

Correct B. 48\pi cm^3

C. 64\pi cm^3

D. 80\pi cm^3

Correct Answer: B

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Question 22

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

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

B. \( -\infty,-1)\cup\( 0,\infty \ \)

C. \( -\infty,0)\cup\( 1,\infty \ \)

D. \( -\infty,0)\cup\( 1,\infty \ \)

Correct Answer: A

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Question 23

A die is rolled twice. Find the probability that the sum of the numbers on the two dice is 7.

A. \frac{1}{6}

Correct B. \frac{1}{12}

C. \frac{1}{2}

D. \frac{5}{6}

Correct Answer: B

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Question 24

Simplify the expression \sqrt[3]{64x^6y^3}.

Correct A. 4x^2\sqrt[3]{y^3}

B. 4x^2y\sqrt[3]{y^3}

C. 4x^3y\sqrt[3]{y^3}

D. 4x^3y^2\sqrt[3]{y^3}

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points (2,3) and (4,5).

Correct A. y-3=\frac{2}{2}\( x-2 \)

B. y-3=\frac{2}{2}\( x-4 \)

C. y-5=\frac{2}{2}\( x-2 \)

D. y-5=\frac{2}{2}\( x-4 \)

Correct Answer: A

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