POST UTME SKYLINE UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the line pas\sing through the points [ (2, 3) ] and [ (4, 5) ].
A. y = 1x + 1
B. y = 2x + 2
C. y = 3x + 3
D. y = 4x + 4
Question 2
A set of numbers has a s\tandard deviation of 3. If the mean is 15, what is the range of the set?
A. 6
B. 12
C. 18
D. 24
Question 3
The mean of a set of numbers is 20. If one of the numbers is 5, what is the sum of the remaining numbers?
A. 15
B. 30
C. 45
D. 60
Question 4
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.
A. \( \frac{32}{3} \pi \ \)
B. \( \frac{64}{3} \pi \ \)
C. \( \frac{16}{3} \pi \ \)
D. \( \frac{128}{3} \pi \ \)
Question 5
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}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{2}{\( x^2 + 1 \)^2}
Question 6
Evaluate the definite integral \int_0^1 x^2 \sin x dx.
A. -1
B. 0
C. 1
D. 2
Question 7
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 32\pi cm^3
B. 64\pi cm^3
C. 96\pi cm^3
D. 128\pi cm^3
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, calculate the volume of water in the \tank.
A. 1200\pi
B. 1500\pi
C. 1800\pi
D. 2000\pi
Question 9
Solve for x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. \( x = -1 \ \)
B. \( x = 2 \ \)
C. \( x = -2 \ \)
D. \( x = 1 \ \)
Question 10
A right-angled triangle has a hypotenuse of length 10cm and one of the other sides has a length of 6cm. Calculate the length of the third side.
A. 8cm
B. 10cm
C. 12cm
D. 14cm
Question 11
A circle has a radius of 5 units. What is the area of the circle?
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 12
Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 0 \)
C. \( x = 0, y = 2 \)
D. \( x = 1, y = 2 \)
Question 13
Find the area under the curve \( y = x^2 + 1 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \frac{7}{3}
B. \frac{9}{2}
C. \frac{11}{3}
D. \frac{13}{3}
Question 14
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 15
A circle has a diameter of 10 cm. Find the area of the circle.
A. 78.5
B. 31.4
C. 314
D. 785

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