POST UTME UNN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \(x^2 + 4x - 5 > 0\).
A. \(x < -5\) or \(x > 1\)
B. \(x < -1\) or \(x > 5\)
C. \(x < 1\) or \(x > 5\)
D. \(x < -5\) or \(x < 1\)
Question 2
In the diagram below, the circle with center O passes through points A, B, and C. If the radius of the circle is 10 cm, calculate the area of triangle ABC.
A. 50 cm^2
B. 75 cm^2
C. 100 cm^2
D. 125 cm^2
Question 3
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. \left\( 1, 1 \right \)
B. \left\( -1, -1 \right \)
C. \left\( 1, -1 \right \)
D. \left\( -1, 1 \right \)
Question 4
Find the value of x in the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 5
Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \), \( mathbf{v} cdot mathbf{j} = -4 \), and \( mathbf{v} cdot mathbf{k} = 5 \).
A. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} + 5mathbf{k} \)
B. \( mathbf{v} = 3mathbf{i} + 4mathbf{j} - 5mathbf{k} \)
C. \( mathbf{v} = -3mathbf{i} - 4mathbf{j} + 5mathbf{k} \)
D. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} - 5mathbf{k} \)
Question 6
Find the equation of the \tangent line to the curve \( y = x^2 + 2x - 3 \) at the point ( (1, 2) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = 2x - 2
D. y = 2x + 2
Question 7
Solve the system of equations: $\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$.
A. \begin{cases} x = 1 \ y = 2 \end{cases}
B. \begin{cases} x = 2 \ y = 1 \end{cases}
C. \begin{cases} x = 3 \ y = 4 \end{cases}
D. \begin{cases} x = 4 \ y = 3 \end{cases}
Question 8
Solve the inequality $|2x - 3| > 5$.
A. x < -1 \text{ or } x > 4
B. x < 1 \text{ or } x > 4
C. x < -1 \text{ or } x < 4
D. x > 1 \text{ or } x > 4
Question 9
A water \tank can hold 2400 liters of water. If 3/5 of the \tank is already filled, how many more liters of water can be added?
A. 1440 liters
B. 1600 liters
C. 1800 liters
D. 2000 liters
Question 10
If \(x^2 - 6x + 8 = 0\), solve for x.
A. \(x = 2\) or \(x = 4\)
B. \(x = 1\) or \(x = 8\)
C. \(x = 3\) or \(x = 5\)
D. \(x = 6\) or \(x = 9\)
Question 11
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the university students.
A. 170.5 cm, 179.5 cm
B. 172.5 cm, 177.5 cm
C. 174.5 cm, 175.5 cm
D. 176.5 cm, 173.5 cm
Question 12
Find the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 13
Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \( \frac{-1}{2}x^{-\frac{3}{2}} \)
B. \( \frac{1}{2}x^{-\frac{1}{2}} \)
C. \( -\frac{1}{2}x^{-\frac{3}{2}} \)
D. \( \frac{1}{2}x^{-\frac{3}{2}} \)
Question 14
Solve the equation \(2^x + 2^x = 100\).
A. \(x = 5\)
B. \(x = 6\)
C. \(x = 7\)
D. \(x = 8\)
Question 15
Determine the value of $\int_{0}^{\pi} \frac{\sin^2 x}{\sin^2 x + 1} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}

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