POST UTME FUTA 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function f(x) = \frac{\log\( x^2 \)}{x^2} u\sing the chain rule.
A. \frac{2}{x^3}
B. \frac{2\log(x)}{x^3}
C. \frac{2}{x^3} - \frac{2\log(x)}{x^3}
D. \frac{2\log(x)}{x^4}
Question 2
Find the determinant of the matrix \\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\end{bmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 3
Find the area under the curve y = \sin(x) from x = 0 to x = \frac{\pi}{2}.
A. 1
B. \frac{1}{2}
C. \frac{\pi}{2}
D. \frac{\pi}{4}
Question 4
Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 5
Find the sum of the first 10 terms of the geometric series: 2, 6, 18, 54, ...
A. 59049
B. 5904
C. 5904.5
D. 59049.5
Question 6
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. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 7
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 60 and 90.
A. 0.8413
B. 0.8419
C. 0.8423
D. 0.8431
Question 9
Find the vector product of the vectors \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} and \mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}.
A. \begin{pmatrix} -3 \ 6 \ -3 \end{pmatrix}
B. \begin{pmatrix} 3 \ -6 \ 3 \end{pmatrix}
C. \begin{pmatrix} 6 \ -3 \ 3 \end{pmatrix}
D. \begin{pmatrix} -6 \ 3 \ -3 \end{pmatrix}
Question 10
A circle has an equation of the form \( x-h \)^2 + \( y-k \)^2 = r^2. If the center of the circle is at (2,3) and the radius is 4 units, find the equation of the circle.
A. \( x-2 \)^2 + \( y-3 \)^2 = 16
B. \( x-3 \)^2 + \( y-2 \)^2 = 16
C. \( x-4 \)^2 + \( y-5 \)^2 = 16
D. \( x-5 \)^2 + \( y-4 \)^2 = 16
Question 11
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 12
Solve the inequality \( \frac{x+2}{x-1} > 0 \).
A. \( -∞, -2 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 13
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism?
A. 30
B. 40
C. 50
D. 60
Question 14
A histogram is constructed with a bin width of 2. If the total area of the histogram is 12, what is the value of the mean?
A. 4
B. 6
C. 8
D. 10
Question 15
A random variable X has a probability distribution given by P\( X=1 \)=0.4, P\( X=2 \)=0.3, P\( X=3 \)=0.2, P\( X=4 \)=0.1. Find the mean and variance of X.
A. mean=2.5, variance=1.2
B. mean=2.2, variance=1.1
C. mean=2.8, variance=1.5
D. mean=3.0, variance=1.8

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