POST UTME RSU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 1/2.
A. 1.9375
B. 1.96875
C. 1.984375
D. 2.000000
Question 2
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. \begin{bmatrix} 3 \ 1 \end{bmatrix}
B. \begin{bmatrix} 1 \ 3 \end{bmatrix}
C. \begin{bmatrix} 2 \ 2 \end{bmatrix}
D. \begin{bmatrix} 4 \ 0 \end{bmatrix}
Question 3
A set ( A ) contains 5 elements. If 3 elements are randomly selected from set ( A ), find the probability that the selected elements are distinct.
A. \( \frac{3}{10} \)
B. \( \frac{3}{20} \)
C. \( \frac{3}{5} \)
D. \( \frac{3}{15} \)
Question 4
Find the derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. \( \frac{2x\( x^2 + 1 \ \) - 2x^2}{\( x^2 + 1 \)^2} )
B. \( \frac{2x^2}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2x^2 + 2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2x^2 - 2}{\( x^2 + 1 \ \)^2} )
Question 5
Find the area under the curve y = x^2 + 1 from x = 0 to x = 2.
A. 7
B. 9
C. 11
D. 13
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 7
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x > -1 \) or \( x < 5 \)
C. \( x < 1 \) or \( x > 5 \)
D. \( x > 1 \) or \( x < 5 \)
Question 8
Solve the inequality \( \frac{x^2 - 4x - 5}{x + 1} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( -infty, -1 \) \cup (5, infty)
B. \( -infty, -1 \) \cup \( -1, 5 \)
C. \( -infty, 5 \)
D. (5, infty)
Question 9
If a = 2, b = 3, and c = 4, find the value of the expression a^2 + b^2 + c^2.
A. 25
B. 29
C. 33
D. 37
Question 10
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 11
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9
Question 12
Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 13
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = x + 1
B. y = x - 1
C. y = 2x - 1
D. y = 2x + 1
Question 14
A box contains 5 red balls and 3 blue balls. If 2 balls are randomly selected, find the probability that both balls are red.
A. \( \frac{5}{8} \)
B. \( \frac{5}{14} \)
C. \( \frac{3}{14} \)
D. \( \frac{1}{4} \)
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 - 3x + 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 42
C. 44
D. 46

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