POST UTME RSU 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function f(x) = \frac{x^2 + 2x - 3}{x^2 + 1} u\sing the quotient rule.
A. \frac{2x + 2}{\( x^2 + 1 \)^2}
B. \frac{2x + 2}{x^2 + 1}
C. \frac{2x - 2}{x^2 + 1}
D. \frac{2x + 2}{x^2 + 1} + \frac{2x - 2}{x^2 + 1}
Question 2
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 3
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 4
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \frac{x}{\( 1 - x^2 \)^{3/2}}
B. \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. \frac{1}{\( 1 - x^2 \)^{3/2}}
D. \frac{2x}{\( 1 - x^2 \)^{3/2}}
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \frac{-1}{2x^{3/2}}
B. \frac{1}{2x^{3/2}}
C. \frac{-1}{x^{3/2}}
D. \frac{1}{x^{3/2}}
Question 6
A 3x3 matrix A has the following elements: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]. Find the determinant of A.
A. 0
B. 1
C. 2
D. 3
Question 7
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 10
B. 12
C. 14
D. 16
Question 8
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. \( x = 3, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)
Question 9
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 6
B. 8
C. 10
D. 12
Question 10
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 11
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{2}
B. x = \frac{\pi}{4}
C. x = \frac{\pi}{6}
D. x = \frac{\pi}{3}
Question 12
A cube has a side length of 5 cm. Find the volume of the cube in cubic centimeters.
A. 125 cm^3
B. 250 cm^3
C. 500 cm^3
D. 1000 cm^3
Question 13
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 14
A vector ( mathbf{a} ) has components \( a_x = 3 \) and \( a_y = 4 \). Find the magnitude of the vector.
A. ( 5 )
B. ( 10 )
C. ( 15 )
D. ( 20 )
Question 15
A vector \( \mathbf{a} = \begin{bmatrix} 2 \ 3 \ 4 \end{bmatrix} \) is given. Find the magnitude of the vector.
A. \sqrt{29}
B. \sqrt{31}
C. \sqrt{33}
D. \sqrt{35}

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