POST UTME RSU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations: \( egin{cases} x + y = 4 \ x - y = 2 \end{cases} \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 2
Find the equation of the \tangent line to the curve \( y = x^2 - 2x + 1 \) at the point ( (1, 0) ).
A. \( y = x - 1 \)
B. \( y = x + 1 \)
C. \( y = 2x - 1 \)
D. \( y = 2x + 1 \)
Question 3
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 4
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 18
B. 19
C. 20
D. 21
Question 5
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
A. \frac{1}{2}
B. \frac{2}{5}
C. \frac{3}{5}
D. \frac{4}{5}
Question 6
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 7
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 8
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( -2 \sin x \cos x \)
C. \( 2 \sin^2 x \)
D. \( -2 \sin^2 x \)
Question 9
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 2
D. y = x + 2
Question 10
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = \frac{3}{4} \ \) for ( x ) in the interval \( [0, 2\pi] \).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 11
Find the area of the region bounded by the parabola y = x^2, the line y = 4, and the x-axis.
A. 16
B. 32
C. 48
D. 64
Question 12
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{2}{3^n} \).
A. 1
B. 2
C. 3
D. 4
Question 13
Solve the quadratic equation \( x^2 - 6x + 8 = 0 \) u\sing the quadratic formula.
A. \( x = 2 pm \sqrt{3} \)
B. \( x = 2 pm \sqrt{2} \)
C. \( x = 2 pm \sqrt{4} \)
D. \( x = 2 pm \sqrt{6} \)
Question 14
Solve for ( x ) in the equation \( \begin{vmatrix} 2 & 3 \ 1 & 4 \ \end{vmatrix} = 0 \)
A. 1
B. 2
C. 3
D. 4
Question 15
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. -1
B. 1
C. 0
D. 2

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