POST UTME KSU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
A probability experiment consists of rolling a fair six-sided die. What is the probability that the number rolled is greater than 4?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 4
A binary operation \( * \) on the set of real numbers is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).
A. 13
B. 25
C. 37
D. 49
Question 5
A circle with radius 4 cm is inscribed in a square. Find the area of the square.
A. 16\pi
B. 32\pi
C. 48\pi
D. 64\pi
Question 6
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) + 5 )
B. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) - 5 )
C. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) + 1 )
D. \( 2\( 1 + 2 + 3 + 4 + 5 \ \) - 1 )
Question 7
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 8
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \( y = \frac{2}{2} x + \frac{1}{2} \)
B. \( y = \frac{1}{2} x + \frac{3}{2} \)
C. \( y = 2x + 1 \)
D. \( y = x + 2 \)
Question 9
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 10
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 11
Find the mean deviation about the mean of the data set: 2, 4, 6, 8, 10.
A. 2
B. 4
C. 6
D. 8
Question 12
A curve is defined by the equation \( y = \frac{1}{x} \). Find the derivative of the curve.
A. \( -\frac{1}{x^2} \)
B. \( \frac{1}{x^2} \)
C. \( -\frac{1}{x} \)
D. \( \frac{1}{x} \)
Question 13
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 14
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.
A. \( \frac{64}{5} pi \)
B. \( \frac{32}{3} pi \)
C. \( \frac{16}{3} pi \)
D. \( \frac{8}{3} pi \)
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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