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POST UTME AL-HIKMAH UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME AL-HIKMAH UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

A. \( x = -2 \ \)

B. \( x = -3 \ \)

Correct C. \( x = 2 \ \)

D. \( x = 3 \ \)

Correct Answer: C

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Question 2

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 3

A set of 5 consecutive integers has a median of 10. If the sum of the integers is 50, find the integers.

A. \( \{ 5, 6, 7, 8, 9 \} \ \)

Correct B. \( \{ 6, 7, 8, 9, 10 \} \ \)

C. \( \{ 7, 8, 9, 10, 11 \} \ \)

D. \( \{ 8, 9, 10, 11, 12 \} \ \)

Correct Answer: B

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Question 4

A binary operation \( \oplus \) is defined as \( a \oplus b = a^2 + b^2 \). Find \( 2 \oplus 3 \).

A. 13

B. 17

Correct C. 19

D. 21

Correct Answer: C

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Question 5

A sequence is defined as \( a_n = 2n + 1 \). Find the 5th term of the sequence.

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 6

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 50\pi

B. 100\pi

Correct C. 200\pi

D. 250\pi

Correct Answer: C

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Question 8

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. What is the average speed for the round trip?

A. 48

B. 50

Correct C. 52

D. 55

Correct Answer: C

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Question 9

Solve the inequality \( x^2 - 6x + 8 > 0 \).

Correct A. \( -\infty, 2 \) \cup \( 4, \infty \)

B. \( -\infty, 2 \) \cup \( 3, \infty \)

C. \( -\infty, 3 \) \cup \( 4, \infty \)

D. \( -\infty, 4 \) \cup \( 5, \infty \)

Correct Answer: A

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Question 10

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

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 11

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 12

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. -2

B. 2

C. -4

D. 4

Correct Answer: A

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Question 13

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

Correct A. 6x + 2

B. 3x^2 + 2

C. 6x - 2

D. 3x^2 - 2

Correct Answer: A

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Question 14

Solve the inequality [ x^2 - 4x - 5 > 0 ].

Correct A. \( -\\infty, -1 \) \\cup \( 5, \\infty \)

B. \( -\\infty, 1 \) \\cup \( 5, \\infty \)

C. \( -\\infty, -5 \) \\cup \( 1, \\infty \)

D. \( -\\infty, 5 \) \\cup \( 1, \\infty \)

Correct Answer: A

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Question 15

Find the area of the triangle with vertices [ A(0, 0), B(2, 3), C(4, 0) ].

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 16

Solve the system of equations [ x + y = 2, 2x - 3y = -3 ].

Correct A. x = 1, y = 1

B. x = 2, y = 0

C. x = 0, y = 2

D. x = -1, y = 3

Correct Answer: A

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Question 17

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 18

Solve the inequality [ |x| > 2 ].

Correct A. \( -\\infty, -2 \) \\cup \( 2, \\infty \)

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

C. \( -\\infty, -4 \) \\cup \( 4, \\infty \)

D. \( -\\infty, -5 \) \\cup \( 5, \\infty \)

Correct Answer: A

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Question 19

Find the equation of the circle with center at ((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. \( x-2 \ \)^2 + \( y-4 \)^2 = 16 )

Correct Answer: A

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Question 20

Solve the system of equations u\sing matrices: [ egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -2 \ 3x + y + 2z = 4 \end{cases} ].

Correct A. \( x = 1, y = 2, z = 3 \)

B. \( x = 2, y = 1, z = -1 \)

C. \( x = 3, y = -1, z = 2 \)

D. \( x = -1, y = 3, z = 1 \)

Correct Answer: A

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Question 21

Find the area under the curve [ y = \frac{1}{x^2 + 1} ] from [ x = 0 ] to [ x = 1 ].

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

B. \( \frac{pi}{4} \)

C. \( \frac{pi}{6} \)

D. \( \frac{pi}{8} \)

Correct Answer: A

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Question 22

Find the sum of the first 10 terms of the geometric progression [ 2, 6, 18, 54, ldots ].

Correct A. ( 1040 )

B. ( 1024 )

C. ( 1020 )

D. ( 1016 )

Correct Answer: A

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Question 23

Solve the inequality [ 2x^2 + 3x - 1 > 0 ].

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

B. \( x < -\frac{1}{2} \) or [ x < \frac{1}{2} ]

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

D. \( x < -\frac{1}{2} \) or [ x > \frac{1}{2} ]

Correct Answer: A

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Question 24

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

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

B. \( y = \frac{1}{2}x - \frac{1}{2} \)

C. \( y = 2x - 1 \)

D. \( y = 2x + 1 \)

Correct Answer: A

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Question 25

Find the area of the triangle with vertices [ (0,0), (3,4), (6,0) ].

Correct A. ( 12 )

B. ( 15 )

C. ( 18 )

D. ( 20 )

Correct Answer: A

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