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POST UTME KSU 2021 Mathematics | Objective

Are you preparing for POST UTME KSU 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.

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 + \frac{1}{2} \)

C. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 - \frac{1}{2} \)

D. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

Correct Answer: A

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Question 2

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

A. \( x = 10^2 \)

Correct B. \( x = 10^4 \)

C. \( x = 10^{-2} \)

D. \( x = 10^{-4} \)

Correct Answer: B

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Question 3

Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis from \( x = 0 \) to \( x = 2 \).

A. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx )

B. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx + pi int_{0}^{2} \( x^2 \)^2 - (2x)^2 , dx )

C. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx - pi int_{0}^{2} \( x^2 \)^2 - (2x)^2 , dx )

Correct D. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx )

Correct Answer: D

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Question 4

A circle with radius 5 cm is inscribed in a square. Find the area of the square.

A. \( 5^2 \times 4 \)

B. \( 5^2 \times 2 \)

C. \( 5^2 \times 3 \)

Correct D. \( 5^2 \times 5 \)

Correct Answer: D

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Question 5

Find the value of \( \sin 2\theta \) given that \( \cos \theta = \frac{3}{5} \) and \( \sin \theta = \frac{4}{5} \).

Correct A. \( \frac{24}{25} \)

B. \( \frac{16}{25} \)

C. \( \frac{20}{25} \)

D. \( \frac{12}{25} \)

Correct Answer: A

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Question 6

In the diagram below, a circle with center O and radius 6cm is \tangent to the x-axis at point A. If the equation of the circle is given by \( x - h \ \)^2 + \( y - k \)^2 = r^2 ), where ( (h, k) ) is the center of the circle and ( r ) is the radius, find the equation of the circle.

Correct A. x^2 + y^2 = 36

B. x^2 + y^2 = 12

C. x^2 + y^2 = 24

D. x^2 + y^2 = 48

Correct Answer: A

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Question 7

A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4, 5 \). Find the probability that X is greater than 3.

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. \frac{3}{4}

D. \frac{5}{8}

Correct Answer: B

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Question 8

A polynomial function f(x) has a root at x = -2 and a root at x = 3. If f(x) has a degree of 4, find the product of the roots of f(x).

Correct A. -6

B. 6

C. 12

D. -12

Correct Answer: A

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Question 9

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 80.

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 10

A circle with center O and radius 4cm is \tangent to the x-axis at point A. If the equation of the circle is given by \( x - h \ \)^2 + \( y - k \)^2 = r^2 ), where ( (h, k) ) is the center of the circle and ( r ) is the radius, find the equation of the circle.

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 8

C. x^2 + y^2 = 24

D. x^2 + y^2 = 32

Correct Answer: A

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \cdot 4^3 + 3 \cdot 4^2 - 2 \cdot 4\ \)

B. \( \frac{1}{2} \cdot 4^2 + 3 \cdot 4 - 2\ \)

C. \( \frac{1}{2} \cdot 4^3 + 3 \cdot 4^2 - 2\ \)

D. \( \frac{1}{2} \cdot 4^2 + 3 \cdot 4^3 - 2\ \)

Correct Answer: A

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Question 12

A circle has equation \( x^2 + y^2 = 16 \). Find the equation of the \tangent line at point (P(2, 4)).

Correct A. \( y = -x + 6 \)

B. \( y = x + 6 \)

C. \( y = -x - 6 \)

D. \( y = x - 6 \)

Correct Answer: A

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Question 13

A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, find the value of the 7th bar.

A. 20

Correct B. 30

C. 40

D. 50

Correct Answer: B

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Question 14

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for (x).

Correct A. \( x = \frac{\pi}{4} \)

B. \( x = \frac{3\pi}{4} \)

C. \( x = \frac{5\pi}{4} \)

D. \( x = \frac{7\pi}{4} \)

Correct Answer: A

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Question 15

A vector \( \vec{a} \) has magnitude 5 and direction \( \theta = 30^\circ \). Find the magnitude of the vector \( \vec{a} + \vec{b} \), where \( \vec{b} \) has magnitude 3 and direction \( \theta = 60^\circ \).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 16

Solve the inequality \( \frac{x}{x+1} > \frac{2}{3} \) for \( x in mathbb{R} setminus {-1} \).

A. \( x > \frac{1}{2} \)

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

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

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

Correct Answer: C

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Question 17

If ( f(x) = \frac{1}{x^2 - 4} ), find \( f^{-1}\( x \ \) ).

Correct A. \( f^{-1}\( x \ \) = \frac{1}{x^2 + 4} )

B. \( f^{-1}\( x \ \) = \frac{1}{x^2 - 4} )

C. \( f^{-1}\( x \ \) = \frac{1}{x^2 + 2} )

D. \( f^{-1}\( x \ \) = \frac{1}{x^2 - 2} )

Correct Answer: A

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Question 18

Solve the equation \( \sin^2 x + \cos^2 x = \frac{3}{4} \) for ( x in [0, 2pi] ).

Correct A. \( x = \frac{pi}{6} \) or \( x = \frac{5pi}{6} \)

B. \( x = \frac{pi}{4} \) or \( x = \frac{3pi}{4} \)

C. \( x = \frac{pi}{3} \) or \( x = \frac{2pi}{3} \)

D. \( x = \frac{pi}{2} \) or \( x = \frac{3pi}{2} \)

Correct Answer: A

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Question 19

If \( A = egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \) and \( B = egin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} \), find ( AB ).

A. \( AB = egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \)

Correct B. \( AB = egin{pmatrix} 3 & 1 \ 1 & 3 \end{pmatrix} \)

C. \( AB = egin{pmatrix} 2 & 2 \ 2 & 2 \end{pmatrix} \)

D. \( AB = egin{pmatrix} 3 & 2 \ 2 & 3 \end{pmatrix} \)

Correct Answer: B

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Question 20

If \( S = {1, 2, 3, 4, 5} \) and \( T = {2, 4, 6} \), find ( S cap T ).

A. \( S cap T = {1, 2, 3, 4, 5} \)

Correct B. \( S cap T = {2, 4} \)

C. \( S cap T = {1, 3, 5} \)

D. \( S cap T = {2, 4, 6} \)

Correct Answer: B

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Question 21

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

Correct A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )

B. \( x-2 \ \)^2 + \( y-3 \)^2 = 4 )

C. \( x-2 \ \)^2 + \( y-3 \)^2 = 64 )

D. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )

Correct Answer: A

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Question 22

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

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

Correct Answer: A

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Question 23

Find the sum of the first 5 terms of the geometric progression with first term 2 and common ratio 3.

Correct A. \( 2 + 6 + 18 + 54 + 162 = 242 \)

B. \( 2 + 6 + 18 + 54 + 162 = 242 \)

C. \( 2 + 6 + 18 + 54 + 162 = 242 \)

D. \( 2 + 6 + 18 + 54 + 162 = 242 \)

Correct Answer: A

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Question 24

Find the determinant of the matrix [ egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} ].

Correct A. ( 0 )

B. ( 1 )

C. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 25

Find the volume of the cylinder with radius 4 and height 6.

Correct A. ( 48pi )

B. ( 96pi )

C. ( 192pi )

D. ( 384pi )

Correct Answer: A

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