POST UTME MADONNA UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 3
Find the value of x in the equation \( 2^x + 5^x = 3^x \).
A. 1
B. 2
C. 3
D. 4
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < -\frac{1}{2} \) or \( x > 3 \)
D. \( x < 1 \) or \( x > -\frac{3}{2} \)
Question 5
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 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 6
A vector ℓ has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of the vector.
A. x = 4, y = 3
B. x = 3, y = 4
C. x = 4, y = -3
D. x = -3, y = 4
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 8
B. 10
C. 12
D. 14
Question 8
Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A. 5
B. 6
C. 7
D. 10
Question 9
Solve the system of equations u\sing matrices:
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 10
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x<-1 or x>3/2
B. x<-2 or x>1
C. x<-3 or x>2
D. x<-4 or x>3
Question 12
Find the equation of the line pas\sing through the points $(2, 3)$ and $(4, 5)$.
A. y = \frac{1}{2}x + 1
B. y = \frac{1}{2}x - 1
C. y = 2x + 1
D. y = 2x - 1
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > -1
C. x < 1
D. x > 1
Question 14
Solve the system of equations: \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).
A. x = 1, y = 1
B. x = 2, y = 2
C. x = 3, y = 3
D. x = 4, y = 4
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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