POST UTME DELSU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let \( S = \{1, 2, 3, 4, 5\} \) and \( T = \{2, 4, 6, 8, 10\} \). Find the symmetric difference of ( S ) and ( T ).
A. {1, 3, 5, 6, 8, 10}
B. {1, 3, 5}
C. {2, 4, 6, 8, 10}
D. {1, 2, 3, 4, 5}
Question 2
Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.
A. 6x + 2
B. 6x + 3
C. 6x - 2
D. 6x - 3
Question 3
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}{\( x^2 + 1 \)^3} )
C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^3} )
Question 4
Solve the inequality \( \frac{x-2}{x+1} < 0 \) u\sing interval notation.
A. \( -∞,-1 \) ∪ (1, ∞)
B. \( -∞,-1 \) ∪ (2, ∞)
C. \( -∞,1 \) ∪ (2, ∞)
D. \( -∞,1 \) ∪ (2, ∞)
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{x}{\( 1 - x^2 \)^{3/2}}
B. f'(x) = \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 - x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 - x^2 \)^{3/2}}
Question 6
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 1240
B. 1245
C. 1250
D. 1255
Question 7
If $x^2 + 4x + 4 = 0$, find the value of $x$.
A. -2
B. -1
C. 1
D. 2
Question 8
In a geometric sequence with first term $a$ and common ratio $r$, the sum of the first $n$ terms is given by the formula $S_n = \frac{a\( 1 - r^n \)}{1 - r}$. If $a = 2$, $r = \frac{1}{2}$, and $n = 5$, find the value of $S_n$.
A. 15
B. 16
C. 17
D. 18
Question 9
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 10
A company produces 300 units of a product per day. If the production rate is increased by 20%, find the new production rate.
A. 360 units/day
B. 400 units/day
C. 420 units/day
D. 440 units/day
Question 11
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ... \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 22 )
B. ( 24 )
C. ( 26 )
D. ( 28 )
Question 13
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 128
C. 256
D. 512
Question 14
Find the volume of the frustum of a cone with height 10cm, lower base radius 6cm, and upper base radius 4cm.
A. 200\pi cm^3
B. 300\pi cm^3
C. 400\pi cm^3
D. 500\pi cm^3
Question 15
Determine the value of x in the equation \( \frac{1}{x} + \frac{1}{2x} = \frac{3}{4x} \).
A. 1
B. 2
C. 3
D. 4

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