POST UTME REDEEMERS UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 14 cm
D. 16 cm
Question 2
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ), given that \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4}{5} \)
B. \( \frac{3}{5} \)
C. \( \frac{2}{5} \)
D. \( \frac{1}{5} \)
Question 3
Find the probability that the sum of the numbers on the faces of two fair six-sided dice is 7.
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{36}
D. \frac{5}{36}
Question 4
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 59049
B. 59048
C. 59050
D. 59051
Question 5
Evaluate the definite integral \( \int_{0}^{1} x^2 \, dx \).
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{1}{4}
Question 6
Solve the inequality $|x - 2| > 3$.
A. \( -\infty, -1 \) \cup \( 4, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 4, \infty \)
D. \( -\infty, 1 \) \cup \( 2, \infty \)
Question 7
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 8
Find the determinant of the matrix \[ \begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 9
Find the area under the curve of \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. 0.7854
B. 0.4636
C. 0.5723
D. 0.6931
Question 10
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 11
A histogram of the heights of students in a class is shown below. If the total number of students is 50, find the mean height of the students.
A. 160
B. 170
C. 180
D. 190
Question 12
A quadratic equation has roots $\alpha$ and $\beta$ such that $\alpha + \beta = 3$ and $\alpha \beta = 2$. Find the equation of the quadratic.
A. x^2 - 3x + 2 = 0
B. x^2 - 3x - 2 = 0
C. x^2 + 3x + 2 = 0
D. x^2 + 3x - 2 = 0
Question 13
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{3}{4}
D. \frac{3}{5}
Question 14
Find the equation of the line pas\sing through the points $\( -2, 3 \)$ and $\( 1, -2 \)$.
A. y = -\frac{5}{3}x + \frac{13}{3}
B. y = \frac{5}{3}x - \frac{13}{3}
C. y = -\frac{3}{5}x + \frac{13}{5}
D. y = \frac{3}{5}x - \frac{13}{5}
Question 15
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms.
A. 15
B. 20
C. 25
D. 30

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