POST UTME UNIPORT 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. \( x = -10 \)
B. \( x = 6 \)
C. \( x = -\frac{3}{2} \)
D. \( x = 2 \)
Question 2
In the circuit below, find the current ( I ) in the resistor \( R_2 \).
A. 1
B. 2
C. 3
D. 4
Question 3
Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies in the interval (-2, 0].
A. 0.8647
B. 0.6321
C. 0.1353
D. 0.5
Question 4
In the coordinate plane, 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 5
Two events, A and B, are indep\endent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events occur.
A. 0.2
B. 0.24
C. 0.28
D. 0.32
Question 6
Solve the inequality $\frac{x}{x-1} > 0$.
A. x < 0 or x > 1
B. x < 1
C. x > 1
D. x = 1
Question 7
A matrix ( A ) is defined by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the value of ( det(A) ).
A. 0
B. 2
C. 4
D. 6
Question 8
A polynomial ( P(x) ) is defined by ( P(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( P(2) ).
A. 0
B. 2
C. 4
D. 6
Question 9
A set of data has a mean of 25 and a s\tandard deviation of 3. If two data points are randomly selected from this set, what is the probability that their sum is greater than 50?
A. 0.1353
B. 0.8647
C. 0.6321
D. 0.5
Question 10
A set of exam scores has a mean of 70 and a s\tandard deviation of 10. Find the z-score of a score of 80.
A. 0.5
B. 1
C. 1.5
D. 2
Question 11
Let ( S ) be the set of all real numbers ( x ) such that \( x^2 - 6x + 8 = 0 \). Find the value of \( sum_{x in S} x \).
A. 4
B. -2
C. 6
D. 8
Question 12
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. 2
D. -4
Question 13
In the number base 8, what is the value of the expression \( 5 \times 6 + 7 \)?
A. 37
B. 43
C. 47
D. 53
Question 14
A set of 5 numbers has a mean of 10. Find the sum of the numbers.
A. ( 50 )
B. ( 60 )
C. ( 70 )
D. ( 80 )
Question 15
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. 1
B. 2
C. 3
D. 4

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