POST UTME WELLSPRING UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the vector projection of vector \( \vec{a} = 2\hat{i} + 3\hat{j} \) onto vector \( \vec{b} = \hat{i} + \hat{j} \).
A. \frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}
B. \frac{5}{\sqrt{2}}\hat{i} - \frac{5}{\sqrt{2}}\hat{j}
C. \frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}
D. \frac{5}{\sqrt{2}}\hat{i} - \frac{5}{\sqrt{2}}\hat{j}
Question 3
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 2x - 1 about the x-axis.
A. \frac{\pi}{2}
B. \frac{\pi}{3}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 4
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 2.
A. \frac{28}{3}
B. \frac{32}{3}
C. \frac{36}{3}
D. \frac{40}{3}
Question 5
Find the equation of the circle with center \( -2, 3 \) and radius 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
Solve the system of linear equations u\sing matrices: \[ \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 3 \end{bmatrix} \]
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 3 \end{bmatrix}
Question 7
Find the area of the region bounded by the curves y = x^2 and y = 2x - 1.
A. \frac{1}{2}
B. \frac{3}{4}
C. \frac{5}{6}
D. \frac{7}{8}
Question 8
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 9
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 10
Solve for x in the equation \( \frac{1}{2}x^2 + 3x - 5 = 0 \).
A. -2
B. -1
C. 4
D. 5

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