POST UTME BABCOCK UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A sequence is defined by \( a_n = 2n^2 - 3n + 1 \). Find the sum of the first five terms of the sequence.
A. 120
B. 130
C. 140
D. 150
Question 2
A cone has a base radius of 4 cm and a height of 6 cm. Find the volume of the cone.
A. \( \frac{1}{3} pi r^2 h \)
B. \( \frac{1}{3} pi r h \)
C. \( \frac{1}{3} pi r^2 \)
D. \( \frac{1}{3} pi r \)
Question 3
Solve the inequality \( 2x^2 + 3x - 1 > 0 \) for ( x ).
A. \( x < -\frac{1}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x < \frac{1}{2} \)
C. \( x > -\frac{1}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{1}{2} \) or \( x > \frac{1}{2} \)
Question 4
A polynomial is defined by ( p(x) = x^3 - 2x^2 + x - 1 ). Find the value of \( p\( -1 \ \) ).
A. -3
B. -2
C. -1
D. 0
Question 5
A circle with center $C$ and radius $r$ has equation $\( x-h \)^2 + \( y-k \)^2 = r^2$. Find the equation of the circle with center $C\( -2,3 \)$ and radius $r=4$.
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 6
A set of data is given by the following table. Find the mean of the data.
A. 25
B. 30
C. 35
D. 40
Question 7
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8
B. 6
C. 4
D. 2
Question 8
A rec\tangular solid has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 72
B. 80
C. 88
D. 96
Question 9
A survey of 100 students found that 70% of them preferred Mathematics, 20% preferred Science, and 10% preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. \( \frac{9}{10} \)
B. \( \frac{8}{10} \)
C. \( \frac{7}{10} \)
D. \( \frac{6}{10} \)
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) for ( x ) in the interval \( -infty, infty \ \) ).
A. \frac{-5 + \sqrt{49}}{4}
B. \frac{-5 - \sqrt{49}}{4}
C. \frac{-5 + \sqrt{25}}{4}
D. \frac{-5 - \sqrt{25}}{4}
Question 11
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4x$ about the x-axis.
A. 256\pi
B. 512\pi
C. 1024\pi
D. 2048\pi
Question 12
Find the equation of the circle with center ( (3, 4) ) and radius 5.
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 30 )
D. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 30 )
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 derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 15
Find the value of $\int_0^1 x^2 dx$.
A. \frac{1}{3}
B. \frac{1}{2}
C. 1
D. \frac{2}{3}

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