POST UTME IGBINEDION UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function \[f(x) = \frac{\log\( x^2 \)}{x^2 + 1}\] u\sing the chain rule.
A. \[f'(x) = \frac{2x}{x^2 + 1} - \frac{2x \log\( x^2 \)}{\( x^2 + 1 \)^2}\]
B. \[f'(x) = \frac{2x}{x^2 + 1} + \frac{2x \log\( x^2 \)}{\( x^2 + 1 \)^2}\]
C. \[f'(x) = \frac{2x}{x^2 + 1} - \frac{2x}{\( x^2 + 1 \)^2}\]
D. \[f'(x) = \frac{2x}{x^2 + 1} + \frac{2x}{\( x^2 + 1 \)^2}\]
Question 2
Find the value of ( x ) in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 3
A survey of 100 students found that 60% of them preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the number of students who preferred Mathematics but not Science?
A. 12
B. 15
C. 18
D. 20
Question 4
Find the magnitude of the vector \( \vec{a} = 2 \hat{i} + 3 \hat{j} \).
A. \boxed{\sqrt{13}}
B. \sqrt{5}
C. \sqrt{2}
D. \sqrt{1}
Question 5
Solve the system of linear equations \[\begin{align*} x + y + z &= 6 \ 2x + 3y + z &= 11 \ x + 2y + 3z &= 7 \ \end{align*}\] u\sing matrices.
A. \[\begin{align*} x &= 1 \ y &= 2 \ z &= 3 \ \end{align*}\]
B. \[\begin{align*} x &= 2 \ y &= 1 \ z &= 3 \ \end{align*}\]
C. \[\begin{align*} x &= 3 \ y &= 1 \ z &= 2 \ \end{align*}\]
D. \[\begin{align*} x &= 1 \ y &= 3 \ z &= 2 \ \end{align*}\]
Question 6
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?
A. 4
B. 6
C. 8
D. 10
Question 7
Solve the trigonometric equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \) for \( 0 \leq x \leq 2 \pi \).
A. \boxed{x = \frac{\pi}{6}, \frac{5\pi}{6}}
B. x = \frac{\pi}{3}, \frac{2\pi}{3}
C. x = \frac{\pi}{4}, \frac{3\pi}{4}
D. x = \frac{\pi}{2}, \frac{3\pi}{2}
Question 8
In a trapezoid, the length of the shorter base is 8 cm, and the length of the longer base is 12 cm. If the height of the trapezoid is 6 cm, what is the area of the trapezoid in square centimeters?
A. 40
B. 48
C. 60
D. 72
Question 9
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 10
A circle has a radius of 5 cm. Find the area of the circle.
A. 25
B. 50
C. 75
D. 100
Question 11
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 12
Let \( S = \{ 1, 2, 3, \ldots, n \} \). Find the sum of the first n terms of the arithmetic sequence with first term 1 and common difference 2.
A. \boxed{\frac{n}{2} [2 + \( n - 1 \)2]}
B. \frac{n}{2} [1 + \( n - 1 \)2]
C. \frac{n}{2} [2 + \( n - 1 \)1]
D. \frac{n}{2} [1 + \( n - 1 \)1]
Question 13
Solve the system of equations \( egin{cases} x + y = 2 \ x - 2y = -3 \end{cases} \) u\sing matrices.
A. \( x = 1, y = 1 \)
B. \( x = 1, y = -1 \)
C. \( x = -1, y = 1 \)
D. \( x = -1, y = -1 \)
Question 14
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x - 3} ) u\sing the quotient rule.
A. \frac{-10x + 15}{\( 2x^2 + 5x - 3 \)^2}
B. \frac{10x - 15}{\( 2x^2 + 5x - 3 \)^2}
C. \frac{20x^2 - 10x + 15}{\( 2x^2 + 5x - 3 \)^2}
D. \frac{-20x^2 + 10x - 15}{\( 2x^2 + 5x - 3 \)^2}
Question 15
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 50 and 70.
A. \boxed{0.9545}
B. 0.8413
C. 0.6915
D. 0.5

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