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POST UTME BELLS UNIVERSITY 2022 Mathematics | Objective

Are you preparing for POST UTME BELLS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).

Correct A. \( x^2 + y^2 + 4x - 6y + 5 = 0 \)

B. \( x^2 + y^2 - 4x + 6y + 5 = 0 \)

C. \( x^2 + y^2 + 2x - 4y + 5 = 0 \)

D. \( x^2 + y^2 - 2x + 4y + 5 = 0 \)

Correct Answer: A

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Question 2

Solve the equation \( \frac{x}{2} + \frac{2}{x} = 5 \) for ( x ).

Correct A. \( x = \frac{10 pm \sqrt{6}}{2} \)

B. \( x = \frac{10 pm \sqrt{4}}{2} \)

C. \( x = \frac{10 pm \sqrt{8}}{2} \)

D. \( x = \frac{10 pm \sqrt{10}}{2} \)

Correct Answer: A

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Question 3

Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).

Correct A. \( \frac{1}{2} \)

B. \( \frac{pi}{2} \)

C. \( \frac{1}{2} pi \)

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

Correct Answer: A

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Question 4

Solve the inequality \( |x - 2| > 3 \).

Correct A. \( x < -1 \) or \( x > 5 \)

B. \( x < 1 \) or \( x > 5 \)

C. \( x < -1 \) or \( x > 4 \)

D. \( x < 1 \) or \( x > 4 \)

Correct Answer: A

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Question 5

Find the equation of the line pas\sing through the points (1,2) and (3,4).

Correct A. \( y = 2x - 1 \)

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

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

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

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 P. If the equation of the circle is \( x - h \ \)^2 + \( y - k \)^2 = r^2 ), where ( (h, k) ) is the center of the circle, find the value of ( h ).

A. 0

B. 3

Correct C. 6

D. 9

Correct Answer: C

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Question 7

Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) for \( x in \mathbb{R} \setminus \{3\} \).

Correct A. \[ \( -\infty, -3 \) \cup \( 3, \infty \) \]

B. \[ \( -\infty, -3 \) \cup \( 3, \infty \) \cup \( 0, \infty \) \]

C. \[ \( -\infty, -3 \) \cup \( 3, \infty \) \cup \( -\infty, 0 \) \]

D. \[ \( -\infty, -3 \) \cup \( 3, \infty \) \cup \( -\infty, 0 \) \cup \( 0, \infty \) \]

Correct Answer: A

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Question 8

A vector \( \mathbf{a} \) has magnitude 5 and direction \( \theta = 30^\circ \). Find the magnitude of the vector \( \mathbf{a} + \mathbf{b} \), where \( \mathbf{b} \) is a unit vector in the direction of \( \mathbf{a} \).

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 9

The mean of a set of 5 numbers is 10. If the largest number is 20, find the sum of the remaining 4 numbers.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 10

A circle with center O and radius 4cm is inscribed in a square with side length 8cm. Find the area of the shaded region.

A. 16\pi

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 11

Determine the value of \( lim_{x \to 0} \frac{\sin x}{x} \) u\sing the definition of a derivative.

A. 1

Correct B. 0

C. -1

D. undefined

Correct Answer: B

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Question 12

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) u\sing the s\tandard form of a circle's equation.

Correct A. \( x - 2 \ \)^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 13

Solve the inequality \( |2x - 3| > 5 \) u\sing the properties of absolute value.

Correct A. \( x < -1 \) or \( x > 4 \)

B. \( x < -4 \) or \( x > 1 \)

C. \( x < 1 \) or \( x > 4 \)

D. \( x < -4 \) or \( x > 1 \)

Correct Answer: A

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \) u\sing the method of substitution.

Correct A. \( x = 1, y = 1 \)

B. \( x = 1, y = 3 \)

C. \( x = 3, y = 1 \)

D. \( x = 3, y = 3 \)

Correct Answer: A

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Question 16

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

A. -3

Correct B. 0

C. 3

D. 6

Correct Answer: B

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Question 17

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

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 18

A set of numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 19

Find the derivative of the function [ f(x) = 3x^2 + 2x - 5 \] u\sing the power rule.

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 20

A sequence is defined by the formula [ a_n = 2n + 1 \]. Find the sum of the first 5 terms of this sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 21

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

Correct A. 10^4

B. 10^2

C. 10^8

D. 10^12

Correct Answer: A

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Question 22

A circle with center (0,0) has equation \( x^2 + y^2 = 25 \). Find the equation of the line perp\endicular to the radius that passes through the point (3,4).

Correct A. y = -\frac{4}{3}x + 5

B. y = \frac{4}{3}x - 5

C. y = -\frac{3}{4}x + 5

D. y = \frac{3}{4}x - 5

Correct Answer: A

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Question 23

A quadratic equation has roots 2 and 5. Write the equation in factored form.

Correct A. \( x - 2 \)\( x - 5 \) = 0

B. \( x - 5 \)\( x - 2 \) = 0

C. \( x + 2 \)\( x + 5 \) = 0

D. \( x + 5 \)\( x + 2 \) = 0

Correct Answer: A

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Question 24

A random experiment has two indep\endent events A and B. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 25

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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