POST UTME ABU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 - 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 - 3 \times 4 + 2 \)
Question 2
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( -∞, -3 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (3, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, 3)
Question 3
Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. ( 16 pi )
B. ( 32 pi )
C. ( 64 pi )
D. ( 128 pi )
Question 4
A circle passes through the points (1, 2) and (3, 4). Find the equation of the circle.
A. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)
B. \( x^2 + y^2 - 4x - 6y + 5 = 0 \)
C. \( x^2 + y^2 - 4x - 6y + 7 = 0 \)
D. \( x^2 + y^2 - 4x - 6y + 11 = 0 \)
Question 5
A company produces x units of a product, where the \cost function is given by C(x) = 2x^2 + 10x + 5. Find the marginal \cost when x = 5.
A. 40
B. 50
C. 60
D. 70
Question 6
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ... .
A. ( 55 )
B. ( 65 )
C. ( 75 )
D. ( 85 )
Question 7
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. x^2 + y^2 + 4x - 6y + 13 = 0
B. x^2 + y^2 - 4x + 6y + 13 = 0
C. x^2 + y^2 + 4x + 6y + 13 = 0
D. x^2 + y^2 - 4x - 6y + 13 = 0
Question 8
Find the value of \( \sin(2x) \) when \( \cos(x) = \frac{1}{2} \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{1}{4}
D. \frac{1}{5}
Question 9
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 10
A set A contains 5 elements and a set B contains 3 elements. Find the number of elements in the union of sets A and B.
A. \( 5 + 3 - 2 \)
B. \( 5 + 3 + 2 \)
C. ( 5 cdot 3 )
D. \( 5 cdot 3 + 2 \)
Question 11
Simplify the expression \( \sqrt{\frac{16x^2y^2}{25}} \) and express it in the form \( ax^by^c \).
A. \frac{4x}{5y}
B. \frac{4xy}{5}
C. \frac{4x^2y}{5}
D. \frac{4xy^2}{5}
Question 12
Solve the inequality \( \frac{x}{2} + 3 > 5 \).
A. x > 2
B. x < 2
C. x ≥ 2
D. x ≤ 2
Question 13
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{64}{3} pi \)
C. \( \frac{128}{3} pi \)
D. \( \frac{256}{3} pi \)
Question 14
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 15
A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) from the positive x-axis. Find the unit vector in the direction of ( mathbf{a} ).
A. \( egin{pmatrix} \frac{5}{\sqrt{3}} \ \frac{5}{\sqrt{3}} \end{pmatrix} \)
B. \( egin{pmatrix} \frac{5}{\sqrt{2}} \ \frac{5}{\sqrt{2}} \end{pmatrix} \)
C. \( egin{pmatrix} \frac{5}{\sqrt{3}} \ -\frac{5}{\sqrt{3}} \end{pmatrix} \)
D. \( egin{pmatrix} \frac{5}{\sqrt{2}} \ -\frac{5}{\sqrt{2}} \end{pmatrix} \)

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