POST UTME ABU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).
A. ( 16 )
B. ( 20 )
C. ( 22 )
D. ( 24 )
Question 2
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 3
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 4
In the sequence ( 1, 2, 4, 8, 16, ... ), find the 7th term.
A. 32
B. 64
C. 128
D. 256
Question 5
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.
A. 8 cm
B. 6 cm
C. 8.6 cm
D. 9.8 cm
Question 6
Solve the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+2} \) for ( x ).
A. x = -1
B. x = 0
C. x = 1
D. x = 2
Question 7
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 8
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 9
Solve the system of equations \( x + y = 3 \) and \( xy = 2 \).
A. \( x = 2, y = 1 \)
B. \( x = 1, y = 2 \)
C. \( x = 2, y = -1 \)
D. \( x = -1, y = 2 \)
Question 10
Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.
A. ( 100pi ) cm³
B. ( 120pi ) cm³
C. ( 140pi ) cm³
D. ( 160pi ) cm³
Question 11
In the diagram below, the circle with center O has a radius of 6 units. The line segment AB is a chord of the circle. If the angle AOB measures 60 degrees, what is the length of AB?
A. 6
B. 8
C. 10
D. 12
Question 12
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 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) for ( x ).
A. x < -1
B. x > -1
C. x < 3
D. x > 3
Question 14
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ and $f_Y(y) = 3y^2$ for $0 < x < 1$ and $0 < y < 1$, respectively. Find the probability that $X + Y < 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 15
In the diagram below, the circle passes through points ( A(2, 3) ) and ( B(4, 5) ). Find the equation of the circle.
A. \( x^2 + y^2 - 4x + 2y + 4 = 0 \)
B. \( x^2 + y^2 - 4x - 2y + 4 = 0 \)
C. \( x^2 + y^2 + 4x - 2y + 4 = 0 \)
D. \( x^2 + y^2 - 4x + 2y - 4 = 0 \)

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