POST UTME KSU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 10
B. 12
C. 14
D. 16
Question 2
A particle moves along the x-axis with its position given by the equation ( x(t) = 3t^3 - 2t^2 + t ), where ( t ) is time in seconds. Find the acceleration of the particle at time \( t = 1 \) second.
A. 3 m/s^2
B. 6 m/s^2
C. 9 m/s^2
D. 12 m/s^2
Question 3
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 4
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 5
A company has two warehouses, A and B, which store the same product. Warehouse A has a capacity of 500 units, while warehouse B has a capacity of 300 units. If the company wants to store a total of 800 units, how many units should be stored in each warehouse?
A. Warehouse A: 400 units, Warehouse B: 400 units
B. Warehouse A: 500 units, Warehouse B: 300 units
C. Warehouse A: 300 units, Warehouse B: 500 units
D. Warehouse A: 200 units, Warehouse B: 600 units
Question 6
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 7
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 8
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. y = 2x + 1
B. y = 2x - 1
C. y = -2x + 1
D. y = -2x - 1
Question 9
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 10
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the points ( (1, 2) ) and ( (3, 4) ), find the center of the circle.
A. (2, 3)
B. (3, 2)
C. (4, 5)
D. (5, 4)
Question 11
A company produces two products, A and B. Product A requires 2 hours of labor and 1 hour of machine time to produce 100 units, while product B requires 1 hour of labor and 2 hours of machine time to produce 150 units. If the company has 120 hours of labor and 180 hours of machine time available, how many units of product A and product B should the company produce to maximize profit?
A. 200 units of A and 300 units of B
B. 300 units of A and 200 units of B
C. 400 units of A and 100 units of B
D. 100 units of A and 400 units of B
Question 12
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
C. 18
D. 24
Question 13
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 14
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 15
Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).
A. x = 1
B. x = 2
C. x = 3
D. x = 4

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