POST UTME ABU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. 64
B. 80
C. 96
D. 112
Question 2
Find the equation of the circle pas\sing through the points $(1, 2)$ and $\( -2, 3 \)$.
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 3
A probability experiment consists of two indep\endent events $A$ and $B$. If $P(A) = 0.4$ and $P(B) = 0.6$, find the value of $P(A cap B)$.
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 4
A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 11, 12, 14, 16. What is the mean of the data set?
A. 7.5
B. 8.5
C. 9.5
D. 10.5
Question 5
A set of exam scores has a mean of 80 and a s\tandard deviation of 5. What is the z-score of a score of 90?
A. 0.8
B. 1.2
C. 1.6
D. 2.0
Question 6
A binary operation $ast$ is defined as $x ast y = xy + 1$. Find the value of $2 ast 3$.
A. 7
B. 8
C. 9
D. 10
Question 7
A quadratic equation $ax^2 + bx + c = 0$ has roots $x_1$ and $x_2$. If $x_1 + x_2 = 3$ and $x_1x_2 = 2$, find the value of $a + b + c$.
A. 5
B. 7
C. 9
D. 11
Question 8
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 9
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 2 cm. What is its volume?
A. 48
B. 64
C. 80
D. 96
Question 10
Find the derivative of the function f(x) = x^3 - 2x^2 + x - 1.
A. 3x^2 - 4x + 1
B. x^2 - 2x + 1
C. x^3 - 2x^2 + x - 1
D. x^2 + 2x - 1
Question 11
A random experiment has two possible outcomes: A and B. The probability of outcome A is ( P(A) = \frac{1}{3} ). What is the probability of outcome B?
A. 1/3
B. 2/3
C. 1/2
D. 4/5
Question 12
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 13
Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.
A. 1/2
B. -1/2
C. 1
D. -1
Question 14
Solve the system of equations $\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}$.
A. x = 1, y = 1
B. x = -1, y = 3
C. x = 1, y = 3
D. x = -1, y = 1
Question 15
Find the area under the curve \( y = \sin^2 x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{1}{3} \)
D. \( \frac{1}{6} \)

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