POST UTME UI 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has a diameter of 10 cm. Find the area of the sector formed by a central angle of 60°.
A. \( \frac{1}{6} pi cdot 5^2 \)
B. \( \frac{1}{6} pi cdot 10^2 \)
C. \( \frac{1}{6} pi cdot 5^2 cdot \frac{3}{2} \)
D. \( \frac{1}{6} pi cdot 10^2 cdot \frac{3}{2} \)
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 3
Find the volume of the sphere \( V = \frac{4}{3} pi r^3 \) if the radius is 6 cm.
A. 904.778
B. 904.779
C. 904.780
D. 904.781
Question 4
Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).
A. 16
B. 32
C. 64
D. 128
Question 5
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the chain rule.
A. 6x + 2
B. 3x^2 + 2
C. 6x - 2
D. 3x^2 - 2
Question 6
A rec\tangular box has dimensions ( x ) cm by ( 2x ) cm by ( 3x ) cm. If its surface area is 264 cm², find the value of ( x ).
A. \( x = 4 \)
B. \( x = 6 \)
C. \( x = 8 \)
D. \( x = 10 \)
Question 7
Find the equation of the circle with center ( (3, 4) ) and radius 5.
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30
D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30
Question 8
Find the derivative of the function ( f(x) = 2x^3 - 3x^2 + x - 1 ) u\sing the power rule.
A. 6x^2 - 6x + 1
B. 2x^2 - 3x + 1
C. 6x^2 - 3x + 1
D. 2x^2 - 6x + 1
Question 9
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}
A. 0
B. 1
C. -1
D. 2
Question 10
A right-angled triangle has a hypotenuse of length 10 cm and one of the other sides is 6 cm. Find the length of the third side.
A. 8 cm
B. 6 cm
C. 4 cm
D. 2 cm
Question 11
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 = 3x - 2
D. y = 3x + 2
Question 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 13
In a random experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find the probability that both events occur.
A. 0.24
B. 0.48
C. 0.64
D. 0.76
Question 14
Evaluate the integral \int_0^1 x^2 \ln x \, dx.
A. \frac{1}{3} - \frac{1}{4}
B. \frac{1}{2} - \frac{1}{3}
C. \frac{1}{3} + \frac{1}{4}
D. \frac{1}{2} + \frac{1}{3}
Question 15
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 - 6x - 4y + 12 = 0
B. x^2 + y^2 - 8x - 2y + 16 = 0
C. x^2 + y^2 - 4x - 6y + 20 = 0
D. x^2 + y^2 - 2x - 4y + 8 = 0

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: