# Mathematics 2008 | Study Mode

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 = -$$\frac{3}{2}$$

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 = $$\sqrt{5}$$

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 = $$\frac{3}{4}$$

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

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

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

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 = -$$\frac{1}{2}$$

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

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

Question 80
A
15o
B
30o
C
45o
D
60o