Mathematics 2008 | Study Mode

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Question 71
A
\(\frac{2}{3}\)
B
-\(\frac{2}{3}\)
C
-\(\frac{3}{2}\)
D
\(\frac{4}{3}\)
Explanation
3x + 2y + 1 = 0

y = mx + c

2y = -3x - 1

y = -\(\frac{3}{2}\) x -\(\frac{1}{2}\)

m = -\(\frac{3}{2}\)

Correct option: C
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Question 72
A
5
B
23
C
20
D
50
Explanation
L\(\begin{pmatrix} x_1 & y_1 \\ -1 & -6 \end{pmatrix}\) m L\(\begin{pmatrix} x_2 & y_2 \\ -3 & -5 \end{pmatrix}\)

D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

D = \(\sqrt{(-3 - (-1)^2 + (-5 -(-6)^2}\)

D = \(\sqrt{(-3 + 1)^2 + (-5 + 6)^2}\)

D = \(\sqrt{(-2)^2 + 1^2}\)

D = \(\sqrt{4 + 1}\)

D = \(\sqrt{5}\)

Correct option: A
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Question 73
A
\(\frac{3}{4}\)
B
\(\frac{3}{5}\)
C
\(\frac{2}{4}\)
D
\(\frac{1}{4}\)
Explanation
sin \(\theta\) = \(\frac{3}{5}\), find tan \(\theta\)

sin \(\theta\) = \(\frac{opp}{hyp}\) = \(\frac{3}{5}\)

52 = x2 + 32

25 = x2 + 9

x2 = 16

x = \(\sqrt{16}\)

x = 4

tan = \(\frac{3}{4}\)

Correct option: A
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Question 74
A
184m
B
185m
C
186m
D
187m
Explanation
Tan 20o = \(\frac{68m}{x}\)

x tan 20o = 68

x = \(\frac{68}{tan 20}\) = \(\frac{68}{0.364}\)

x = 186.8

= 187m

Correct option: D
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Question 75
A
(x2 - 1)
B
3x(x2 - 1)
C
3X2 - 1
D
7X6 - 5X4
Explanation
y = \(\frac{x^7 - x^5}{x^4}\) = \(\frac{x^7 - x^5}{x^4}\)

Y = X3 - X

\(\frac{dy}{dx}\) = 3x3 - 1 - x1 - 1

= 3x2 - xo


\(\frac{dy}{dx}\) = 3x2 - 1

Correct option: C
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Question 76
A
x cos x
B
x sin x
C
-x cos x
D
-x sin x
Explanation
y = sin x - x cos x

let; U = -x

\(\frac{dy}{dx}\) = -1

V = cos x

\(\frac{dx}{dx}\) = -5x

-x (-sin x) + cos x (-1)

x sin x - cos x

\(\frac{dy}{dx}\) = x sin x + cos x - cos x

\(\frac{dy}{dx}\) = x sin x

Correct option: B
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Question 77
A
-\(\frac{1}{4}\)
B
-\(\frac{1}{2}\)
C
\(\frac{1}{4}\)
D
\(\frac{1}{2}\)
Explanation
y = x(1 + x)

y = x + x2

\(\frac{dy}{dx}\) = 1 + 2x

at minimum \(\frac{dy}{dx}\) = 0

therefore, 1 + 2x = 0 \(\to\) 2x = -1

x = -\(\frac{1}{2}\)

Correct option: B
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Question 78
A
16
B
13
C
12
D
11
Explanation
\(\int ^{2}_{1}\)(6x2 - 2x)dx

= [\(\frac{6x^3}{3} - \frac{2x^2}{2}\)]2

= [2x3 - x2]2

= (2(2)3 - 4 - 2 + 1

= 16 - 4 - 2 + 1

= 17 - 6

= 11

Correct option: D
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Question 79
A
7
B
1
C
2
D
3
Explanation
\(\int ^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\)cosx

\([sin x]^{\frac{\pi}{2}}_{\frac{\pi}{2}}\)

= sin\(\frac{\pi}{2}\)- (-sin \(\frac{\pi}{2}\))

= sin \(\frac{\pi}{2}\) + sin \(\frac{\pi}{2}\)

= 2 sin \(\frac{\pi}{2}\)

= 2 sin 1.5714

= 2(0.2704)

= 0.5

= 1

Correct option: B
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Question 80
A
15o
B
30o
C
45o
D
60o
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: C

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