POST UTME KSU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the triangle with vertices ( A(2,3) ), ( B(4,5) ), and ( C(6,3) ).
A. 10
B. 15
C. 20
D. 25
Question 2
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 3
Find the area under the curve y = x^2 + 2x - 3 from x = 1 to x = 3.
A. 20
B. 22
C. 24
D. 26
Question 4
Simplify the expression \( \sqrt{\frac{16}{25}} \) and express it in the form \( \frac{a}{b} \).
A. \( \frac{4}{5} \)
B. \( \frac{3}{5} \)
C. \( \frac{2}{5} \)
D. \( \frac{1}{5} \)
Question 5
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?
A. 150
B. 200
C. 250
D. 300
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. -2
B. 2
C. -1
D. 1
Question 7
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the points ( (2, 3) ) and ( (4, 5) ), find the radius of the circle.
A. 1
B. 2
C. 3
D. 4
Question 8
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 32
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 64
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 128
Question 9
Find the volume of the sphere with radius 4.
A. 32π
B. 64π
C. 128π
D. 256π
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 11
Solve the system of equations: \( \begin{cases} x + y = 4 \ x - 2y = -3 \end{cases} \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 12
A company has two factories, A and B, which produce the same product. Factory A produces 200 units per day, while factory B produces 150 units per day. If the company wants to produce a total of 500 units per day, how many days will it take to produce this amount?
A. 2 days
B. 3 days
C. 4 days
D. 5 days
Question 13
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 14
A particle moves along the x-axis with its position given by the equation ( x(t) = 2t^2 - 5t + 3 ), where ( t ) is time in seconds. Find the velocity of the particle at time \( t = 2 \) seconds.
A. -1 m/s
B. 1 m/s
C. 2 m/s
D. 3 m/s
Question 15
Find the determinant of the matrix: \begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}.
A. 0
B. 1
C. 2
D. 3

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