POST UTME UI 2020 Mathematics | Objective

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Question 1
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 8, 12, 15, 10, and 5 units. Find the mean score of the class.
A. 10
B. 12
C. 15
D. 18
Question 2
Determine the number of terms in the series \( sum_{n=1}^{infty} \frac{1}{n\( n+1 \ \)} ) that satisfy \( \frac{1}{n\( n+1 \ \)} < \frac{1}{100} ).
A. 5
B. 10
C. 15
D. 20
Question 3
A polynomial is represented as \( x^2 + 5x + 6 \). Factor this polynomial.
A. \( x + 2 \)\( x + 3 \)
B. \( x + 1 \)\( x + 4 \)
C. \( x + 2 \)\( x + 2 \)
D. \( x + 3 \)\( x + 3 \)
Question 4
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 8, 12, 15, 10, and 5 units. Find the median score of the class.
A. 10
B. 12
C. 15
D. 18
Question 5
Solve for x in the equation: 2x^2 + 5x - 3 = 0
A. x = -1
B. x = 1
C. x = -3
D. x = 3
Question 6
Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. -\frac{2x}{\( x^2 + 1 \)^2} + \frac{2}{x^2 + 1}
C. \frac{2x}{\( x^2 + 1 \)^2}
D. \frac{2}{x^2 + 1}
Question 7
Solve the system of equations u\sing matrices: \[ \begin{array}{ccc} x + y + z & = & 6 2x + 3y + z & = & 11 x + 2y + 3z & = & 7 \end{array} \]
A. \begin{array}{ccc} x & = & 1 \ y & = & 2 \ z & = & 3 \end{array}
B. \begin{array}{ccc} x & = & 2 \ y & = & 1 \ z & = & 3 \end{array}
C. \begin{array}{ccc} x & = & 1 \ y & = & 3 \ z & = & 2 \end{array}
D. \begin{array}{ccc} x & = & 3 \ y & = & 2 \ z & = & 1 \end{array}
Question 8
A random variable X has a probability distribution given by \( P\( X = 1 \ \) = \frac{1}{3} ) and \( P\( X = 2 \ \) = \frac{2}{3} ). Find the probability that X is greater than 1.
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. 1
Question 9
Find the value of \( lim_{x \to 0} \frac{\sin x}{x} \) u\sing L'Hopital's rule.
A. 1
B. 0
C. -1
D. ∞
Question 10
Let X be a random variable with probability density function (pdf) given by ( f(x) = egin{cases} 2x & \text{if } 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 11
Find the sum of the infinite geometric series $\sum_{n=1}^\infty \frac{2}{3^n}$.
A. \frac{2}{3}
B. \frac{4}{9}
C. \frac{6}{9}
D. \frac{8}{9}
Question 12
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \pm \sqrt{2} \)
B. \( x = -2 \pm \sqrt{3} \)
C. \( x = -2 \pm \sqrt{4} \)
D. \( x = -2 \pm \sqrt{5} \)
Question 13
A vector ( mathbf{a} ) is defined by \( mathbf{a} = egin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \). Find the magnitude of ( mathbf{a} ).
A. 1
B. 2
C. 3
D. 4
Question 14
A number is represented in base 8 as 1234. Convert this number to base 10.
A. 512
B. 768
C. 1024
D. 1280
Question 15
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3

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