POST UTME CHRISTOPHER UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 9 \end{bmatrix}.
A. \begin{bmatrix} 1 \\ 3 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 4 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 9 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 12 \end{bmatrix}
Question 2
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the population.
A. 170.3 cm, 180.7 cm
B. 168.1 cm, 182.9 cm
C. 169.5 cm, 181.5 cm
D. 171.1 cm, 179.9 cm
Question 3
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. \frac{1}{10}
B. \frac{1}{5}
C. \frac{3}{10}
D. \frac{2}{5}
Question 4
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 5
Find the mean and s\tandard deviation of the data set: \{2, 4, 6, 8, 10\}.
A. \text{Mean: } 6, \text{S\tandard Deviation: } 2
B. \text{Mean: } 6, \text{S\tandard Deviation: } 4
C. \text{Mean: } 4, \text{S\tandard Deviation: } 2
D. \text{Mean: } 4, \text{S\tandard Deviation: } 4
Question 6
A set of numbers is defined as \( S = \{ x \in \mathbb{R} : x^2 - 4x + 3 = 0 \} \). Find the elements of the set.
A. \{ 1, 3 \}
B. \{ -1, -3 \}
C. \{ 1, -3 \}
D. \{ -1, 3 \}
Question 7
Solve the equation \sqrt{x + 2} = 3.
A. \boxed{x = 7}
B. x = 5
C. x = 9
D. x = 11
Question 8
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 9
Find the value of \log_{10} (1000).
A. \boxed{3}
B. 2
C. 4
D. 5
Question 10
Find the mean and s\tandard deviation of the data set ( { 2, 4, 6, 8, 10 } ).
A. \( \text{mean} = 6, \text{s\tandard deviation} = 2 \)
B. \( \text{mean} = 4, \text{s\tandard deviation} = 2 \)
C. \( \text{mean} = 8, \text{s\tandard deviation} = 2 \)
D. \( \text{mean} = 10, \text{s\tandard deviation} = 2 \)
Question 11
Let \( A = { 1, 2, 3, 4, 5 } \) and \( B = { 2, 4, 6, 8, 10 } \). Find ( A cap B ).
A. { 1, 2, 3, 4, 5 }
B. { 2, 4, 6, 8, 10 }
C. { 1, 2, 3, 4, 5, 6, 8, 10 }
D. { 2, 4 }
Question 12
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup (4, 6)
C. \( -3, -1 \) \cup (1, 3) \cup \( -6, -4 \)
D. \( -3, -1 \) \cup (1, 3) \cup (6, 8)
Question 13
Find the equation of the circle with center at ((2, 3)) and radius 4.
A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 4
C. \text{Equation: } \( x - 3 \)^2 + \( y - 2 \)^2 = 16
D. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 25
Question 14
Find the equation of the circle with center at (2, 3) and radius 4.
A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16
C. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 15
Find the sum of the first 5 terms of the geometric series \( 2x + 4x^2 + 8x^3 + ldots \).
A. 126x^5
B. 126x^4
C. 126x^3
D. 126x^2

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