POST UTME WELLSPRING UNIVERSITY 2023 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. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 2
Solve for y in the equation \( \frac{dy}{dx} = \frac{2x}{y} \) where y(1) = 2.
A. y = 2x^2
B. y = x^2
C. y = 2x
D. y = x
Question 3
Find the equation of the line pas\sing through the points ((2,3)) and ((4,5)) in the coordinate plane. Use the slope-intercept form \( y=mx+b \).
A. y=1x+1
B. y=2x-1
C. y=3x+2
D. y=4x-3
Question 4
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 60
B. 70
C. 80
D. 90
Question 5
Let ( f(x) = 2x^3 - 5x^2 + x - 1 ). Find the value of ( f(2) ).
A. 1
B. 3
C. 5
D. 7
Question 6
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 greater than 85.
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 7
Let \( A = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix} \) and \( B = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \). Find the value of \( AB^2 \).
A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}
B. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}
C. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}
D. \begin{pmatrix} 7 & 8 \ 11 & 16 \end{pmatrix}
Question 8
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 9
Let ( f(x) = 2x^3 - 5x^2 + x - 1 ). Find the value of \( f\( -2 \ \) ).
A. -9
B. -7
C. -5
D. -3
Question 10
A random variable X has a probability distribution given by \( P\( X = 1 \ \) = \frac{1}{2} ) and \( P\( X = 2 \ \) = \frac{1}{2} ). Find the expected value of X.
A. 1
B. 1.5
C. 2
D. 2.5
Question 11
Find the vector projection of vector \mathbf{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} onto vector \mathbf{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}.
A. \boxed{\begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}}
B. \begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}
C. \begin{pmatrix} \frac{13}{14} \ \frac{15}{14} \ \frac{17}{14} \end{pmatrix}
D. \begin{pmatrix} \frac{15}{14} \ \frac{17}{14} \ \frac{19}{14} \end{pmatrix}
Question 12
Let ( f(x) = \frac{x^2 - 4}{x^2 - 9} ). Find the value of \( lim_{x \to 3} f\( x \ \) ).
A. 1
B. 2
C. 3
D. 4
Question 13
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=20
C. \( x-2 \)^2+\( y-3 \)^2=24
D. \( x-2 \)^2+\( y-3 \)^2=28
Question 14
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.
A. 1.5
B. 2
C. 2.5
D. 3
Question 15
Let \( A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \) and \( B = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix} \). Find the value of \( A^2 \).
A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}
B. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}
C. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}
D. \begin{pmatrix} 7 & 8 \ 11 & 16 \end{pmatrix}

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