POST UTME IMS U 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 2
A quadratic equation has roots 2 and 3. What is the product of the roots?
A. \( -6 \)
B. \( -5 \)
C. \( -4 \)
D. \( -3 \)
Question 3
Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ) u\sing the chain rule.
A. f'(x) = 6x - 2
B. f'(x) = 6x + 2
C. f'(x) = 6x^2 - 2
D. f'(x) = 6x^2 + 2
Question 4
Evaluate the definite integral \( int_{0}^{1} x^2 dx \).
A. 1
B. 2
C. 3
D. 4
Question 5
Find the sum of the first 5 terms of the geometric series \( 2 + 6 + 18 + \ldots \).
A. \( 62 \ \)
B. \( 64 \ \)
C. \( 66 \ \)
D. \( 68 \ \)
Question 6
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 7
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{-x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{x}{\( x^2 + 1 \)^2} )
Question 8
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 9
Find the derivative of the function ( f(x) = \sin\( x^2 \) ) u\sing the chain rule.
A. f'(x) = 2x \cos\( x^2 \)
B. f'(x) = 2x \sin\( x^2 \)
C. f'(x) = x^2 \cos\( x^2 \)
D. f'(x) = x^2 \sin\( x^2 \)
Question 10
Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A. 5
B. 6
C. 7
D. 8
Question 11
Find the vector ( mathbf{a} ) given that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = egin{pmatrix} 2 \ 1 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 1 \ 2 \end{pmatrix} \).
A. \( egin{pmatrix} 3 \ 2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ 3 \end{pmatrix} \)
C. \( egin{pmatrix} 1 \ 1 \end{pmatrix} \)
D. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)
Question 12
In the diagram below, the circle has a radius of 4 cm. What is the length of the arc intercepted by the central angle of 60°?
A. ( 2pi ) cm
B. ( 4pi ) cm
C. ( 6pi ) cm
D. ( 8pi ) cm
Question 13
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8 cm
B. 6 cm
C. 4 cm
D. 2 cm
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
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)

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