POST UTME BELLS UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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
C. 25
D. 30
Question 2
Solve the equation [ x^2 + 5x + 6 = 0 ] u\sing the quadratic formula.
A. -2
B. -3
C. -1
D. 1
Question 3
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 4
Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).
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. \( x^2 + y^2 - 2x + 4y + 5 = 0 \)
Question 5
A right circular cone has a height of $10$ cm and a base radius of $4$ cm. Find the volume of the cone.
A. \(200\pi\) cm$^3$
B. \(400\pi\) cm$^3$
C. \(500\pi\) cm$^3$
D. \(600\pi\) cm$^3$
Question 6
Solve the equation \( \frac{x}{2} + \frac{2}{x} = 5 \) for ( x ).
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. \( x = \frac{10 pm \sqrt{10}}{2} \)
Question 7
Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \) u\sing the method of substitution.
A. \( x = 1, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 3, y = 1 \)
D. \( x = 3, y = 3 \)
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
C. 8
D. 9
Question 9
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the quotient rule.
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} )
Question 10
Solve the inequality $\frac{x}{x+1} > \frac{2}{x+2}$.
A. x > -2
B. x > -1
C. x > 2
D. x < -2
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 12
Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{2} \)
C. \( \frac{1}{2} pi \)
D. \( \frac{pi}{4} \)
Question 13
Find the value of $x$ in the equation $\log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 14
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10^4
B. 10^2
C. 10^8
D. 10^12
Question 15
Find the equation of the circle with center $\( -2, 3 \)$ and radius $4$.
A. \(x^2 + y^2 + 4x - 6y + 13 = 0\)
B. \(x^2 + y^2 - 4x + 6y - 13 = 0\)
C. \(x^2 + y^2 + 2x - 3y + 5 = 0\)
D. \(x^2 + y^2 - 2x + 3y - 5 = 0\)

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