POST UTME IGBINEDION UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a right triangle with legs of length 3 and 4, find the area of the triangle.
A. 6
B. 12
C. 18
D. 24
Question 2
A polynomial function is defined as $f(x) = 2x^3 - 5x^2 + 7x - 3$. What is the value of $f\( -1 \)$?
A. -2
B. -1
C. 1
D. 3
Question 3
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 4
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 5
A circle has a radius of 5 cm. What is the area of the circle in square centimeters?
A. 25π
B. 50π
C. 75π
D. 100π
Question 6
In a geometric sequence with first term 3 and common ratio 2, find the sum of the first five terms.
A. 1231
B. 2047
C. 4095
D. 8191
Question 7
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 8
A s\tandard six-sided die is rolled. What is the probability that the number on the die is a multiple of 3?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 9
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 10
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 5 & 7 \end{bmatrix} \).
A. 1
B. -1
C. 13
D. 21
Question 11
A function f(x) is defined as f(x) = 2x^2 + 3x - 1. What is the value of f\( -2 \)?
A. -11
B. -9
C. -7
D. -5
Question 12
Find the vector \( \vec{a} \ \) such that \( \vec{a} \cdot \vec{b} = 12 \ \) and \( \vec{a} \cdot \vec{c} = 9 \ \), where \( \vec{b} = \begin{bmatrix} 2 \ 3 \end{bmatrix} \ \) and \( \vec{c} = \begin{bmatrix} 4 \ 5 \end{bmatrix} \ \).
A. \begin{bmatrix} 3 \ 2 \end{bmatrix}
B. \begin{bmatrix} 4 \ 3 \end{bmatrix}
C. \begin{bmatrix} 5 \ 4 \end{bmatrix}
D. \begin{bmatrix} 6 \ 5 \end{bmatrix}
Question 13
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 all students in the university.
A. 170.5 cm, 179.5 cm
B. 172.5 cm, 177.5 cm
C. 173.5 cm, 176.5 cm
D. 174.5 cm, 175.5 cm
Question 14
A random variable X has a probability distribution given by \[P\( X = x \) = \begin{cases} 0.2 & x = 1 \ 0.3 & x = 2 \ 0.5 & x = 3 \ 0.1 & x = 4 \ 0.1 & x = 5 \ \end{cases}\] Find the probability that X is greater than 3.
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 15
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}

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