POST UTME ABU 2021 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. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 2
Simplify the expression \( \frac{1}{2} \left\( \frac{1}{3} \right \ \)^{-2} \left\( \frac{1}{4} \right \)^{-1} \left\( \frac{1}{5} \right \)^{-3} \).
A. 120
B. 240
C. 360
D. 480
Question 3
Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$.
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 4
A sequence is defined as follows: $a_n = 2n + 1$. What is the sum of the first 5 terms of the sequence?
A. 25
B. 30
C. 35
D. 40
Question 5
A circle has a radius of 4 units. What is the area of the circle?
A. 50
B. 62
C. 75
D. 100
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 7
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 2
D. y = 3x + 2
Question 8
Find the vector $\mathbf{v}$ such that $\mathbf{v} \cdot \mathbf{i} = 3$, $\mathbf{v} \cdot \mathbf{j} = 4$, and $\mathbf{v} \cdot \mathbf{k} = 5$.
A. 3\mathbf{i} + 4\mathbf{j} + 5\mathbf{k}
B. 3\mathbf{i} + 4\mathbf{j} - 5\mathbf{k}
C. 3\mathbf{i} - 4\mathbf{j} + 5\mathbf{k}
D. 3\mathbf{i} - 4\mathbf{j} - 5\mathbf{k}
Question 9
Find the volume of the frustum of the cone with height \( h = 6 \) cm and radii of the bases \( r_1 = 4 \) cm and \( r_2 = 2 \) cm.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 10
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\( x-3\right \)^2 + \left\( y-2\right \)^2 = 16
C. \left\( x-4\right \)^2 + \left\( y-3\right \)^2 = 16
D. \left\( x-2\right \)^2 + \left\( y-4\right \)^2 = 16
Question 11
A set of data has a mean of 25 and a s\tandard deviation of 3. If the data set has 20 elements, what is the range of the data set?
A. 40
B. 50
C. 60
D. 70
Question 12
Solve the equation \( \sin^2 x + \cos^2 x = 1 \ \) for ( x ) in the interval \( [0, 2\pi] \).
A. 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}
B. \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}
C. \frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}
D. \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}
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
Solve the inequality \frac{x^2-4x-3}{x^2-4x+3}>0.
A. \left\( -\infty,-1\right)\cup\left\( 3,\infty\right \ \)
B. \left\( -\infty,1\right)\cup\left\( 3,\infty\right \ \)
C. \left\( -\infty,-1\right)\cup\left\( 1,\infty\right \ \)
D. \left\( -\infty,3\right)\cup\left\( 3,\infty\right \ \)
Question 15
A rec\tangular prism has a length of 8 units, a width of 5 units, and a height of 3 units. What is the volume of the prism?
A. 120
B. 140
C. 160
D. 180

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