POST UTME OAU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 3
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 4
Solve the equation \( 2^x + 3^x = 5^x \) for ( x ).
A. 1
B. 2
C. 3
D. 4
Question 5
In the diagram below, the graph of \( y = x^2 + 2x + 1 \) intersects the x-axis at two points. Find the sum of the x-coordinates of these points.
A. -1
B. -2
C. -3
D. -4
Question 6
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 7
Find the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{5}{6} \).
A. 1
B. 2
C. 3
D. 4
Question 8
A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, find the volume of water in the \tank.
A. 1200
B. 2400
C. 3600
D. 4800
Question 9
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 10
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 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
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 13
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 80?
A. 0.25
B. 0.33
C. 0.5
D. 0.67
Question 14
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
Question 15
A circle has a radius of 5 cm. Find the area of the circle.
A. 10π cm²
B. 20π cm²
C. 25π cm²
D. 50π cm²

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