Mathematics 2008 | Study Mode

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Question 31
A
x(x2-1)
B
3x(x2-1)
C
3x2-1
D
7x6-5x4
Explanation
\(y=\frac{x^7 - x^5}{x^4}\\
y = \frac{x^7}{x^4} \div \frac{x^5}{x^4}\\
y = x^3 - x \\
\frac{dy}{dx} = 3x^2 - 1\)

Correct option: C
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Question 32
A
x cos x
B
x sin x
C
-x cos x
D
-x sin x
Explanation
sin x - x cos x
dy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x

Correct option: B
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Question 33
A
-1/4
B
-1/2
C
1/4
D
1/2
Explanation
y = x(1+x)
= x + x2
dy/dx = 1 + 2x
As dy/dy 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4

Correct option: A
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Question 34
A
16
B
13
C
12
D
11
Explanation
\(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\\
= [2x^3 - x^2]_1^2\)
= [2(2)3 - (2)2] [2(1)3 - (1)2]
= [16-4] [2-1]
= 12 1
= 11

Correct option: D
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Question 35
A
zero
B
1
C
2
D
3
Explanation
\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\\
=sin\frac{\pi}{2} - sin\frac{-\pi}{2}\)
= sin90 sin-90
= sin90 sin270
= 1 (-1)
= 1+1
= 2

Correct option: C
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Question 36
A
15o
B
30o
C
45o
D
60o
Explanation
30 + 45 + 60 + 90 + 2x + x = 360o
225 + 3x = 360
3x = 360 - 225
3x = 135
x = 45o

Correct option: C
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Question 37
A
1/4
B
1/3
C
2/3
D
3/4
Explanation
Ratio of least to most = 3:12
= 3/12
= 1/4

Correct option: A
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Question 38
A
2t
B
2t-1
C
2/3t+1
D
2t-1/3
Explanation
\(Mean = \frac{t+2t-1+t-2+2t-14t+2t+2}{6}\\
Mean = \frac{12t-2}{6}\\
=\frac{2(6t-1)}{6}\\
=\frac{6t-1}{3}\\
=\frac{6t}{3}- \frac{1}{3}\\
=2t-\frac{1}{3}\)

Correct option: D
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Question 39
A
zero
B
1
C
2
D
4
Explanation
4, 4, 1, 0, 4, 4, 2, 0
Arrange in ascending order:
0, 0, 1, 1, 2, 4, 4, 4, 4
Position of median = N+1 / 2 = 9+1 / 2 = 5th
Median = 2

Correct option: C
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Question 40
A
3x+3
B
3x+1
C
2x+5
D
2x+1
Explanation
x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1
Range = 3x+2 - (x-3)
= 3x+2 - x - 3
= 2x + 5

Correct option: C

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