POST UTME MADONNA UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, 3 \) \cup \( 3, \infty \)
C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, 3 \) \cup \( 3, \infty \)
D. \( -3, -1 \) \cup (1, 3)
Question 2
Find the value of \( \frac{1}{2} \sin 2x + \frac{1}{4} \cos 2x \) when \( x = \frac{\pi}{6} \).
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{1}{8}
D. \frac{1}{16}
Question 3
Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}.
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 4
Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
C. 24
D. 48
Question 5
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 59048
B. 59049
C. 59050
D. 59051
Question 6
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{16}{3} pi \)
C. \( \frac{64}{3} pi \)
D. \( \frac{128}{3} pi \)
Question 7
Find the area under the curve \[y = \frac{1}{x^2 + 1}\] from x = 0 to x = 1.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{6}
D. \frac{\pi}{3}
Question 8
Let \( a \) and \( b \) be the roots of the quadratic equation \( x^2 + 2x + 3 = 0 \). Find the value of \( a^2 + b^2 \).
A. \( 4 \)
B. \( 5 \)
C. \( 6 \)
D. \( 7 \)
Question 9
Solve the system of equations: \begin{align*} x + y &= 2 \ 2x - 3y &= - 1 \end{align*}
A. \begin{pmatrix} 1 \ 1 \end{pmatrix}
B. \begin{pmatrix} -1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 2 \ -1 \end{pmatrix}
D. \begin{pmatrix} -2 \ 1 \end{pmatrix}
Question 10
Find the area of the circle with radius 4.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 11
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.2
B. 0.24
C. 0.28
D. 0.32
Question 12
Find the equation of the plane pas\sing through the points (1, 2, 3), (2, 3, 4), and (3, 4, 5).
A. \( x - y + z - 6 = 0 \)
B. \( x + y - z + 6 = 0 \)
C. \( x - y + z + 6 = 0 \)
D. \( x + y + z + 6 = 0 \)
Question 13
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 all students in the university.
A. 170.1 cm, 180.9 cm
B. 168.5 cm, 182.5 cm
C. 169.5 cm, 181.5 cm
D. 171.5 cm, 179.5 cm
Question 14
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. \frac{1}{3}
B. \frac{1}{6}
C. \frac{2}{3}
D. \frac{5}{6}
Question 15
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000

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