POST UTME CHRISTOPHER UNIVERSITY 2025 Mathematics | Objective

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Question 1
A matrix ( A ) has the form \( \begin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \ \). Find the determinant of the matrix.
A. 1
B. -1
C. 2
D. 3
Question 2
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 3
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 4
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( -∞, -3 \) ∪ (2, ∞)
B. \( -∞, -3 \) ∪ (0, 2) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (0, 3)
D. \( -∞, -3 \) ∪ (2, 3)
Question 5
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 6
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 7
In a circle with center O and radius 5, what is the length of the arc intercepted by a central angle of 60 degrees?
A. 5
B. 10
C. 15
D. 20
Question 8
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.
A. 35
B. 40
C. 45
D. 50
Question 9
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
Question 10
Find the sum of the first 5 terms of the geometric series \( 2x^2, 4x^3, 8x^4, ... \).
A. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6
B. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 + 64x^7
C. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 + 64x^7 + 128x^8
D. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 + 64x^7 + 128x^8 + 256x^9
Question 11
Determine the value of ( x ) in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
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
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 14
A trigonometric function has the form ( f(x) = \sin(x) \). What is the value of the function at \( x = \frac{\pi}{4} \ \)?
A. \frac{1}{\sqrt{2}}
B. \frac{1}{2}
C. \frac{1}{3}
D. \frac{1}{4}
Question 15
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{8}{3}
B. \frac{16}{3}
C. \frac{4}{3}
D. \frac{2}{3}

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