POST UTME KSU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 20
B. 30
C. 40
D. 50
Question 2
In a set of 10 integers, the mean is 20 and the median is 15. If the mode is 10, what is the sum of the two smallest numbers?
A. 40
B. 50
C. 60
D. 70
Question 3
A binary operation ( odot ) is defined as \( a odot b = a^2 + b^2 \). Find the value of ( 2 odot 3 ).
A. 13
B. 14
C. 15
D. 16
Question 4
Find the vector projection of the vector \mathbf{a} = 2\mathbf{i} + 3\mathbf{j} onto the vector \mathbf{b} = \mathbf{i} + \mathbf{j}.
A. \frac{5}{\sqrt{2}}\mathbf{i} + \frac{5}{\sqrt{2}}\mathbf{j}
B. \frac{5}{\sqrt{2}}\mathbf{i} - \frac{5}{\sqrt{2}}\mathbf{j}
C. \frac{5}{\sqrt{2}}\mathbf{i} + \frac{5}{\sqrt{2}}\mathbf{j}
D. \frac{5}{\sqrt{2}}\mathbf{i} - \frac{5}{\sqrt{2}}\mathbf{j}
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -1 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 6
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x < -3/2 or x > 1
C. x < -1 or x < 3/2
D. x < -3/2 or x > 1
Question 7
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.8413
B. 0.6915
C. 0.6827
D. 0.9772
Question 8
A polynomial function ( f(x) ) is defined as ( f(x) = x^3 - 2x^2 + 3x - 1 ). Find the value of \( f\( -1 \ \) ).
A. -2
B. -1
C. 0
D. 1
Question 9
A vector ( mathbf{a} ) is given by \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of ( mathbf{a} ).
A. 3.60555
B. 4.1231
C. 5.19615
D. 6.40312
Question 10
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. \( 5 \times 3 \times 2 \)
B. \( 5 \times 3 + 2 \)
C. \( 5 \times 3 + 2 \times 5 \)
D. \( 5 \times 3 \times 2 \times 5 \)
Question 11
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{-x}{\( x^2 + 1 \)^2}
D. \frac{x}{\( x^2 + 1 \)^2}
Question 12
Given that ( f(x) = \frac{1}{x^2 + 1} ), find the derivative of ( f(x) ) 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 13
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 14
Find the volume 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 15
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

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