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POST UTME AL-HIKMAH UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using 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 View Details

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 View Details

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 View Details

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

A. 13

B. 17

Correct C. 19

D. 21

Correct Answer: C

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Question 5 View Details

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 View Details

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 View Details

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 View Details

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 \(km/h\\((km/h) and returns at an average speed of 40\). 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Solve the system of equations using 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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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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