# Mathematics (2017) | Study Mode

Question 31
A
$$\frac{11!}{9!2!}$$
B
$$\frac{11!}{9!2!2!}$$
C
$$\frac{11!}{2!2!2!}$$
D
$$\frac{11!}{2!2!}$$
##### Explanation
MATHEMATICS is an eleven letter word = 11!

There are 2Ms and 2As and 2Es

Divide the number of repeating letters

= $$\frac{11!}{2!2!2!}$$

Question 32
A
$$\frac{8!}{2!}$$
B
$$\frac{8!}{3! 2!}$$
C
$$\frac{8!}{2! 2! 2!}$$
D
8!
##### Explanation
MACICITA is an eight letter word = 8!

Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I

? $$\frac{8!}{2! 2! 2!}$$

Question 33
A

47

B

42

C

54

D

46

##### Explanation
Y $$\frac{1}{2}$$

Y = 6, X = 7

Y = $$\frac{k}{x}$$ where k is constant

6 = $$\frac{k}{7}$$

k = 42

Question 34
A

123o

B

170o

C

117o

D

137o

##### Explanation
MN || PQ || RS

MN = PQ = RS (parallel lines)

Label the angle in the lines

a = i (corresponding angles are equal)

b = x (corresponding angles are equal)

If |MN| = |RS|

If a = i

and a = 63 = i

a + b = 180 (Adjacent interior angles are supplementary i.e add to 180)

? i + x = 180

63 + x = 180

x = 180 - 63

x = 1170

Question 35
A
2x + 2y = 9
B
2x + 3y = 8
C
2x + y = 9
D
x + 2y = 8
##### Explanation
The locus of a point p(x, y) such that pv = pw where v = (1, 1)

and w = (3, 5). This means that the point p moves so that its distance from v and w are equidistance

$$\sqrt{(x ? x_1)^2 + (y ? y_1)^2}$$ = $$\sqrt{(x ? x_2)^2 + (y ? y_2)^2}$$

$$\sqrt{(x -1)^2 + (y - 1)^2}$$ = $$\sqrt{(x - 3)^2 + (y - 5)^2}$$

square both sides
(x - 1)2 + (y - 1)2 = (x - 3)2 + (y - 5)2

x2 - 2x + 1 + y2 - 2y + 1 = x2 - 6x + 9 + y2 - 10y + 25

x2 + y2 -2x -2y + 2 = x2 + y2 - 6x - 10y + 34

Collecting like terms
x2 - x2 + y2 - y2 - 2x + 6x -2y + 10y = 34 - 2

4x + 8y = 32

Divide through by 4

x + 2y = 8

Question 36
A

$$\frac{x_3}{3}$$ - $$\frac{3x_2}{2}$$ - 5x + k

B

$$\frac{x_3}{3}$$ - $$\frac{3x_2}{2}$$ + 5x + k

C

$$\frac{x_3}{3}$$ + $$\frac{3x_2}{2}$$ - 5x + k

D

$$\frac{x_3}{3}$$ + $$\frac{3x_2}{2}$$ + 5x + k

##### Explanation

-xndx = $$\frac{x_{n + 1}}{n + 1}$$

-dx = x + k

where k is constant

-(x2 + 3x - 5)dx

-x2 dx + -3xdx - -5dx

$$\frac{2_{2 + 1}}{2 + 1}$$ + $$\frac{3x^{1 + 1}}{1 + 1}$$ - 5x + k

$$\frac{x_3}{3}$$ + $$\frac{3x_2}{2}$$ - 5x + k

Question 37
A

19cm

B

18cm

C

17cm

D

12cm

##### Explanation

Find the diagram
Sin 70o

x = 10 Sin 70o

= 9.3969

Hence, length of chord MN = 2x

= 2 $$\times$$ 9.3969

= 18.79

= 19cm (nearest cm)

Question 38
A

3

B

4

C

5

D

6

##### Explanation

m * n = $$\frac{m}{n}$$ - $$\frac{m}{n}$$

m = - 3

n = 4

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

= $$\frac{3(-3) - (- 4 \(\times$$ 4)}{12}\)

= $$\frac{- 9 + 16}{12}$$

= $$\frac{7}{12}$$

Question 39
A
(x + y + 6)(x + y -3)
B
(x - y - 6)(x - y + 3)
C
(x - y + 6)(x - y - 3)
D
(x + y - 6)(x + y + 3)
##### Explanation
x + 2xy + y + 3x + 3y - 18

x + 2xy + 3x + y + 3y -18

x + 2xy - 3x + 6x + y -3y + 6y -18

x + 2xy -3x + y -3y + 6x + 6y -18

x + xy -3x + xy + y - 3y + 6x + 6y -18

x(x + y - 3) + y(x + y - 3) + 6(x + y - 3)

= (x + y - 3)(x + y + 6)

= (x + y + 6)(x + y -3)

Question 40
A

s = $$\frac{nrp}{nr + m^2}$$

B

s = nr + $$\frac{m^2}{mrp}$$

C

s = $$\frac{nrp}{mr}$$ + m2

D

s = $$\frac{nrp}{nr}$$ + m2

##### Explanation

p = s + $$\frac{sm^2}{nr}$$

p = s + ( 1 + $$\frac{m^2}{nr}$$)

p = s (1 + $$\frac{nr + m^2}{nr}$$)

nr $$\times$$ p = s (nr + m2)

s = $$\frac{nrp}{nr + m^2}$$

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