POST UTME UNIPORT 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \( \vec{a} \) has components \( a_x = 2 \) and \( a_y = 3 \). Find the magnitude of the vector.
A. 5
B. 10
C. 15
D. 20
Question 2
A polynomial function is defined as ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of \( f\( -1 \ \) ).
A. -2
B. -1
C. 0
D. 1
Question 3
The mean of a set of numbers is 25. If the sum of the numbers is 150, how many numbers are in the set?
A. 4
B. 6
C. 8
D. 10
Question 4
A set of 5 numbers has a mean of 10 and a median of 8. Find the sum of the numbers.
A. 50
B. 60
C. 70
D. 80
Question 5
Solve the inequality \frac{x-2}{x+1}>0.
A. x<-1 or x>2
B. x<-1 or x<2
C. x>1 or x>2
D. x<-1 or x<2
Question 6
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 72\pi cm^3
D. 96\pi cm^3
Question 7
A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a score range. The heights of the bars are 2, 3, 4, 5, and 6. Find the mean of the scores.
A. 4.2
B. 4.4
C. 4.6
D. 4.8
Question 8
A random experiment has two possible outcomes: heads or tails. If the probability of getting heads is \( \frac{1}{3} \), find the probability of getting tails.
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{1}{4}
Question 9
Find the sum of the first 10 terms of the geometric series $\sum_{n=1}^{10} \frac{2}{3^n}$.
A. \frac{63}{32}
B. \frac{63}{64}
C. \frac{63}{128}
D. \frac{63}{256}
Question 10
A set ( S ) contains the elements ( 1, 2, 3, 4, 5, 6 ). Find the number of subsets of ( S ) that contain exactly two elements.
A. 6
B. 12
C. 20
D. 30
Question 11
Solve for x in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 12
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. -1
C. 2
D. 3
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 14
A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find the volume of the prism u\sing the formula V = lwh.
A. 100 cm^3
B. 120 cm^3
C. 150 cm^3
D. 200 cm^3
Question 15
Find the value of \( \sin\( 2x \ \) ) given that \( \sin\( x \ \) = \frac{1}{2} ).
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{\sqrt{5}}{2}
D. \frac{\sqrt{7}}{2}

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