POST UTME UI 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 95% of the scores lie within 2 s\tandard deviations of the mean, what is the minimum score that 95% of the students scored?
A. 40
B. 50
C. 60
D. 70
Question 2
A circle has a diameter of 10cm. Find the area of the circle.
A. 25\pi cm^2
B. 50\pi cm^2
C. 75\pi cm^2
D. 100\pi cm^2
Question 3
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \( P\( X > 0.5 \ \) = \frac{1}{2} )
B. \( P\( X > 0.5 \ \) = \frac{1}{4} )
C. \( P\( X > 0.5 \ \) = \frac{3}{4} )
D. \( P\( X > 0.5 \ \) = \frac{1}{3} )
Question 4
A random variable X has a probability distribution given by the following table:
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 5
Solve the system of equations u\sing matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= -1 \end{align*}
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ -1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 6
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism in cubic centimeters?
A. 20
B. 30
C. 40
D. 50
Question 7
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?
A. 0.9544
B. 0.9772
C. 0.9987
D. 0.9999
Question 8
In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both Mathematics and Science. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 9
A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of the vector.
A. x = 4, y = 3
B. x = 3, y = 4
C. x = 2, y = 5
D. x = 5, y = 2
Question 10
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 3 \end{bmatrix}
Question 11
Find the equation of the circle with center ( (3, 4) ) and radius 5.
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 9 )
D. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 9 )
Question 12
Find the mean and s\tandard deviation of the random variable X with probability mass function \begin{align*} p(x) = \begin{cases} \frac{1}{3} & \text{if } x = 1 \frac{1}{2} & \text{if } x = 2 \frac{1}{6} & \text{if } x = 3 \end{cases} \end{align*}.
A. \text{Mean: } 1.5, \text{ S\tandard Deviation: } 1.1
B. \text{Mean: } 2, \text{ S\tandard Deviation: } 1.2
C. \text{Mean: } 1, \text{ S\tandard Deviation: } 1.3
D. \text{Mean: } 2.5, \text{ S\tandard Deviation: } 1.4
Question 13
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 256\pi cm^3
B. 512\pi cm^3
C. 768\pi cm^3
D. 1024\pi cm^3
Question 14
Find the matrix product AB, where A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} and B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}.
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
C. \begin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix}
D. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}
Question 15
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{8}
D. \frac{5}{8}

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