POST UTME WELLSPRING UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \boxed{\( x + 2 \)^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 2
A circle has a radius of 4 cm. Find its circumference.
A. ( 8pi ) cm
B. ( 16pi ) cm
C. ( 32pi ) cm
D. ( 64pi ) cm
Question 3
Solve the inequality $\frac{2x + 1}{x - 1} > 0$.
A. \( 1, \infty \)
B. \( -\infty, 1 \)
C. (1, 2)
D. \( 2, \infty \)
Question 4
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 10
B. -1
C. 7
D. -7
Question 5
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.
A. 30
B. 35
C. 40
D. 45
Question 6
A set of 10 points is chosen at random from a circle of radius 1. What is the probability that the dis\tance between the two closest points is greater than \( \frac{1}{2} \)?
A. 0
B. \frac{1}{2}
C. \frac{3}{4}
D. 1
Question 7
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 8
Solve the system of equations \[\begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases}\] u\sing matrices.
A. \boxed{\begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 3 \end{pmatrix}}
B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 2 \end{pmatrix}
C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 9
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 10
Evaluate the definite integral \( \int_0^1 x^2 \, dx \).
A. 1/3
B. 1/2
C. 2/3
D. 1
Question 11
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. 1/4
B. 1/2
C. 3/4
D. 1
Question 12
If ( f(x) = \frac{1}{x} ), find ( f'(x) ) u\sing the chain rule.
A. \( -\frac{1}{x^2} \)
B. \( \frac{1}{x^2} \)
C. \( -\frac{1}{x} \)
D. \( \frac{1}{x} \)
Question 13
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).
A. 3
B. 6
C. 9
D. 12
Question 14
A line passes through points $A(2,3)$ and $B(4,5)$. What is the equation of the line in slope-intercept form?
A. y = 1x + 1
B. y = 1x + 2
C. y = 1x + 3
D. y = 1x + 4
Question 15
A polynomial f(x) is defined as \( f(x) = x^3 + 2x^2 - 5x - 3 \). Find the value of f\( -1 \).
A. -1
B. 0
C. 1
D. 2

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