POST UTME OAU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}.
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 20 )
B. ( 30 )
C. ( 40 )
D. ( 50 )
Question 3
A particle moves along the curve \( y = x^2 + 2x \) from \( x = 0 \) to \( x = 4 \). Find the work done by the force of gravity.
A. \( \frac{128}{3} \) Joules
B. \( \frac{256}{3} \) Joules
C. \( \frac{512}{3} \) Joules
D. \( \frac{1024}{3} \) Joules
Question 4
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x + 1
B. y = 2x - 1
C. y = x + 2
D. y = x - 2
Question 5
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. \( x^2 + y^2 + 4x - 8y + 12 = 0 \)
B. \( x^2 + y^2 - 4x + 8y + 12 = 0 \)
C. \( x^2 + y^2 + 8x - 4y + 12 = 0 \)
D. \( x^2 + y^2 - 8x + 4y + 12 = 0 \)
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{-2x^2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^2}{\( x^2 + 1 \)^2} )
Question 7
Find the value of ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
Find the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} u\sing the formula \( ar{x} = \frac{1}{n} sum_{i=1}^{n} x_i \).
A. 5
B. 6
C. 7
D. 8
Question 9
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 1, y = 1
D. x = 2, y = 2
Question 10
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < 1 \) or \( x > 3 \)
C. \( x < -1 \) or \( x < 3 \)
D. \( x < 1 \) or \( x < 3 \)
Question 11
A particle moves in a straight line with an initial velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its velocity after ( 3 ) seconds.
A. \( 13 , \text{m/s} \)
B. \( 15 , \text{m/s} \)
C. \( 17 , \text{m/s} \)
D. \( 19 , \text{m/s} \)
Question 12
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 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)
Question 14
A circle of radius 4 cm is inscribed in a square. Find the area of the region outside the circle but inside the square.
A. ( 48 pi ) square cm
B. ( 64 pi ) square cm
C. ( 96 pi ) square cm
D. ( 128 pi ) square cm
Question 15
A circle has a radius of 4 cm. Find the area of the sector that subt\ends an angle of 60° at the center.
A. 20
B. 30
C. 40
D. 50

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