## MATHEMATICS (2016) Study Mode

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Question 1
A
$$\frac{2x^3}{3}$$ - 2x + k
B
x3 + 2x + k
C
$$\frac{2x^3}{3}$$ + 2x + k
D
x3 - 2x + k
Explanation.
$$\int$$ $$\frac{2x^3 + 2x}{x}$$ = $$\int$$ $$\frac{2x^3}{x}$$ + $$\frac{2x}{x}$$ = $$\int$$ (2x2 + 2) dx

$$\frac{2x^2+1}{2 + 1}$$ + 2x + k

= $$\frac{2x^3}{3}$$+ 2x + k

Question 2
A
B
10
C
D
Explanation.
$$\frac{4 + y + 8 + 10}{4}$$ = 7

22 + y = 4 x 7
22 + y = 28
y = 28 - 22 = 6

Question 3
A

2( $$\frac{1}{3}$$X + 6 )

B

$$\frac{2}{3}$$ ( $$\frac{1}{3}$$X + 6)

C

$$\frac{2}{3}$$ ( $$\frac{1}{3}$$X + 6)2

D

$$\frac{1}{3}$$ ( $$\frac{1}{3}$$X + 6)2

Explanation.

Y = ( $$\frac{1}{3}$$X + 6)2

$$\frac{dy}{dx}$$ = 2( $$\frac{1}{3}$$X + 6) $$\frac{1}{3}$$

= $$\frac{2}{3}$$ ( $$\frac{1}{3}$$X + 6)

Question 4
A
45
B
10
C
35
D
30
Explanation.
80 - x + x + 60 - x + 20 = 150
160 - x = 150
x = 160 - 150 = 10

Question 5
A
B
$$\frac{3}{2}$$
C
$$\frac{2}{3}$$
D
Explanation.
T2 = $$\frac{8}{9}$$, T6 = 4$$\frac{1}{2}$$
ar = $$\frac{8}{9}$$
ar5 = $$\frac{9}{2}$$

$$\frac{ar}{ar^5}$$ = $$\frac{8}{9}$$ x $$\frac{2}{9}$$

$$\frac{1}{r^4}$$ = $$\frac{16}{81}$$

r = $$\sqrt[4]{18/16}$$ = $$\frac{3}{2}$$

Question 6
A

230o

B

55o

C

115o

D

65o

Explanation.
< OTQ = $$\frac{130}{2}$$
= 65o

Question 7
A
B
C
D
Explanation.
$$\frac{(n - 2) 180}{180}$$ = $$\frac{1080}{180}$$

(n - 2) = 6
n = 6 + 2 = 8

Question 8
A

82o

B

36o

C

72o

D

118o

Explanation.
< MPT = 180o - 118o = 62o

< PML = 62o ( Alternative angle)

y + 2y + 10o + 62o = 180o (Angles on a straight line)

3y = 180 - 72
$$\frac{3y}{3}$$ = $$\frac{108}{3}$$
y = 36o

< PMT = 2y + 10 = 2(36) + 10 = 82o

Question 9
A

110o

B

70o

C

95o

D

85o

Explanation.
< ROP = 95o (Exterior angle of cyclic quadrilateral)

Question 10
A

15

B

16

C

20

D

18

Explanation.

Number of students that plays only two games = 4 + 8 + 3  = 15