POST UTME PAN-ATLANTIC UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.
A. 3x^2 - 4x + 3
B. 3x^2 - 2x + 1
C. 2x^2 - 4x + 3
D. x^2 - 2x + 1
Question 2
Find the area under the curve of ( f(x) = 2x^2 + 3x - 1 ) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 15
D. 18
Question 3
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 4
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 5
Solve the quadratic equation: \( x^2 + 4x + 4 = 0 \).
A. \begin{bmatrix} -2 \ 2 \end{bmatrix}
B. \begin{bmatrix} -1 \ 1 \end{bmatrix}
C. \begin{bmatrix} 1 \ -1 \end{bmatrix}
D. \begin{bmatrix} 2 \ -2 \end{bmatrix}
Question 6
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 7
Find the area of the triangle with vertices (0, 0), (2, 0), and (0, 3).
A. 3
B. 6
C. 9
D. 12
Question 8
Find the value of k such that the equation \( x^2 + kx + 16 = 0 \) has equal roots.
A. 8
B. -8
C. 4
D. -4
Question 9
Find the mean and s\tandard deviation of the data set: 2, 4, 6, 8, 10.
A. \text{Mean} = 6, \text{S\tandard Deviation} = 2
B. \text{Mean} = 5, \text{S\tandard Deviation} = 1
C. \text{Mean} = 4, \text{S\tandard Deviation} = 3
D. \text{Mean} = 3, \text{S\tandard Deviation} = 4
Question 10
Solve the inequality \( \frac{x}{2} + 1 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 12
A histogram is constructed from the following data: 2, 4, 5, 7, 8, 9, 10. What is the class width of the histogram?
A. 1
B. 2
C. 3
D. 4
Question 13
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms.
A. 15
B. 20
C. 25
D. 30
Question 14
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. x < 1 or x > 3
B. x < 3 or x > 1
C. x < 1 or x < 3
D. x > 1 or x > 3
Question 15
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

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