POST UTME CHRISTOPHER UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.
A. 6
B. 8
C. 10
D. 12
Question 2
Determine the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 4
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 4095
B. 4096
C. 4097
D. 4098
Question 5
A sequence is defined recursively as \( a_n = 2a_{n-1} + 1 \) with \( a_1 = 3 \). Find the sum of the first 5 terms of the sequence.
A. 123
B. 1235
C. 1237
D. 1239
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < 1 or x > 3
C. x < -3 or x > 1/2
D. x < 3 or x > 1
Question 7
A matrix ( A ) is given by \( A = \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \ \). Find the determinant of \( A^2 \).
A. 1
B. 3
C. 5
D. 7
Question 8
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).
A. 0
B. \begin{pmatrix} \frac{4}{13} \\ \frac{6}{13} \end{pmatrix}
C. \begin{pmatrix} \frac{2}{13} \\ \frac{3}{13} \end{pmatrix}
D. \begin{pmatrix} \frac{1}{13} \\ \frac{-2}{13} \end{pmatrix}
Question 9
Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).
A. 6
B. 12
C. 18
D. 24
Question 10
Evaluate the definite integral \( int_{0}^{1} x^2 ln\( x \ \) , dx ) u\sing integration by parts.
A. \frac{1}{4}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{1}{6}
Question 11
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the center of the circle is at ( (3, 4) ) and the radius is 5, what is the equation of the circle?
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25 \)
B. \( x + 3 \)^2 + \( y + 4 \)^2 = 25 \)
C. \( x - 3 \)^2 + \( y + 4 \)^2 = 25 \)
D. \( x + 3 \)^2 + \( y - 4 \)^2 = 25 \)
Question 12
Solve the inequality \( x^2 - 4x + 4 \geq 0 \).
A. x \leq 2
B. x \geq 2
C. x < 2
D. x > 2
Question 13
Determine the value of ( x ) in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 14
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 2
B. -3
C. -2
D. 1
Question 15
A probability experiment consists of rolling a fair six-sided die. Find the probability that the number rolled is greater than 4.
A. 1/6
B. 1/3
C. 1/2
D. 2/3

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