POST UTME BELLS UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10^4
B. 10^2
C. 10^8
D. 10^12
Question 3
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. \frac{8}{3}
B. \frac{16}{3}
C. \frac{32}{3}
D. \frac{64}{3}
Question 4
Solve the inequality $\frac{x}{x+1} > \frac{2}{x+2}$.
A. x > -2
B. x > -1
C. x > 2
D. x < -2
Question 5
Determine the value of \( lim_{x \to 0} \frac{\sin x}{x} \) u\sing the definition of a derivative.
A. 1
B. 0
C. -1
D. undefined
Question 6
A quadratic equation has roots 2 and 5. Write the equation in factored form.
A. \( x - 2 \)\( x - 5 \) = 0
B. \( x - 5 \)\( x - 2 \) = 0
C. \( x + 2 \)\( x + 5 \) = 0
D. \( x + 5 \)\( x + 2 \) = 0
Question 7
Find the equation of the line pas\sing through the points (1,2) and (3,4).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = -2x + 1 \)
D. \( y = -2x - 1 \)
Question 8
Find the vector projection of \vec{a} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} onto \vec{b} = \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix}
A. \begin{bmatrix} 1.6 \\ 2.4 \\ 3.2 \end{bmatrix}
B. \begin{bmatrix} 2.4 \\ 3.2 \\ 4.0 \end{bmatrix}
C. \begin{bmatrix} 3.2 \\ 4.0 \\ 4.8 \end{bmatrix}
D. \begin{bmatrix} 4.0 \\ 4.8 \\ 5.6 \end{bmatrix}
Question 9
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
C. 6
D. 9
Question 10
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) u\sing the s\tandard form of a circle's equation.
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 )
Question 11
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 12
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
C. 48\pi
D. 64\pi
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 14
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 15
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) for \( x in \mathbb{R} \setminus \{3\} \).
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 \( 0, \infty \) \]

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