POST UTME BABCOCK UNIVERSITY 2017 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 \( 2x^2 + 4x^3 + 8x^4 + ldots \).
A. \( 2x^2\( 1 + 2x + 4x^2 + ldots + 512x^9 \ \) )
B. \( 2x^2\( 1 - 2x + 4x^2 - ldots + 512x^9 \ \) )
C. \( 2x^2\( 1 + 2x + 4x^2 + ldots + 512x^9 \ \) + 1 )
D. \( 2x^2\( 1 - 2x + 4x^2 - ldots + 512x^9 \ \) + 1 )
Question 2
A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
A. 1/3
B. 2/3
C. 3/5
D. 4/5
Question 3
A circle has equation \( x - 2 \)^2 + \( y - 3 \)^2 = 4. Find the equation of the \tangent line to the circle at the point (3, 5).
A. y - 5 = -\frac{1}{2}\( x - 3 \)
B. y - 5 = \frac{1}{2}\( x - 3 \)
C. y - 5 = \( x - 3 \)
D. y - 5 = -\( x - 3 \)
Question 4
In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both Mathematics and Science. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.7
B. 0.6
C. 0.5
D. 0.4
Question 5
Find the area of the triangle formed by the points (0, 0), (2, 0), and (1, 2).
A. \frac{1}{2}bh
B. bh
C. \frac{1}{4}bh
D. \frac{1}{8}bh
Question 6
Determine the value of $k$ in the quadratic equation $x^2 + kx + 16 = 0$, given that one of the roots is $-4$.
A. -8
B. -4
C. 8
D. 4
Question 7
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. 2
D. 3
Question 8
A particle moves along the x-axis with its position given by the equation $s(t) = 2t^3 - 5t^2 + 3t + 1$. Find the velocity of the particle at time $t = 2$ seconds.
A. -14
B. 14
C. -28
D. 28
Question 9
A vector \overrightarrow{a} has magnitude 5 and direction 30°. Find the magnitude of the vector \overrightarrow{a} + \overrightarrow{b}, where \overrightarrow{b} has magnitude 3 and direction 120°.
A. 4
B. 5
C. 6
D. 7
Question 10
Solve for x in the equation \( \log_2\( x^2 \ \) = 4\).
A. 16
B. 32
C. 64
D. 128
Question 11
Solve the matrix equation AX = B, where A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}, X = \begin{pmatrix} x \ y \end{pmatrix}, and B = \begin{pmatrix} 5 \ 6 \end{pmatrix}.
A. \\begin{pmatrix} 1 \\ 2 \\end{pmatrix}
B. \\begin{pmatrix} 2 \\ 1 \\end{pmatrix}
C. \\begin{pmatrix} 3 \\ 4 \\end{pmatrix}
D. \\begin{pmatrix} 4 \\ 3 \\end{pmatrix}
Question 12
A histogram of exam scores is given below. If the mean score is 60 and the s\tandard deviation is 10, calculate the probability that a randomly selected student scored above 70.
A. 0.25
B. 0.30
C. 0.35
D. 0.40
Question 13
A random variable X has a probability distribution given by \[ P(X) = \begin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \ \end{cases} \]. Calculate the expected value of X.
A. 1.4
B. 1.6
C. 1.8
D. 2.0
Question 14
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 15
Find the derivative of the function f(x) = \frac{1}{x^2 - 4} u\sing the quotient rule.
A. \frac{2x}{\( x^2 - 4 \)^2}
B. \frac{-2x}{\( x^2 - 4 \)^2}
C. \frac{x}{\( x^2 - 4 \)^2}
D. \frac{-x}{\( x^2 - 4 \)^2}

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