# 2009 December(68A) Math Question 1

Choice D

$$=\mid3\mid-\mid-3\mid$$ $$=3-3$$ $$=0$$

# 2009 December(68A) Math Question 2

Choice G

$$y=2x+1=3$$ $$2x+1=3$$ $$x=1$$

# 2009 December(68A) Math Question 3

Choice A

$$=80\times16+n\times22$$

# 2009 December(68A) Math Question 4

Choice J

$$=50\times1.5=75$$

# 2009 December(68A) Math Question 5

Choice E

Draw the blue one twice, …

# 2009 December(68A) Math Question 6

Choice J

$$3\ pieces=x,\ y,\ z$$ $$x=2y=2(2z)=4z$$ $$y=2z$$ $$\Rightarrow x+y+z=4z+2z+z=21$$ $$\Rightarrow 7z=21$$ $$\Rightarrow z=3$$ $$x=4z=12$$

# 2009 December(68A) Math Question 7

Choice C

$$(8+3)2=22$$

Choice F

# 2009 December(68A) Math Question 9

Choice C

$$\triangle BCD is a 6-8-10 triangle.$$ $$\overline{BD}=10$$ $$\underline{AB}=\overline{BD}=\overline{AD}=10$$

# 2009 December(68A) Math Question 10

Choice F

The yellow area accounts for 1/2 of the area, so the probability is 1/2.

# 2009 December(68A) Math Question 11

Choice A

$$2(3x+5)=6x+10$$ $$=6\ squares+10\ circles$$

# 2009 December(68A) Math Question 12

Choice H

$$y=mx+b$$ $$5x-y-9=0$$ $$\Rightarrow -y=9-5x$$ $$\Rightarrow y=5x-9y$$

# 2009 December(68A) Math Question 13

Choice D

$$\Rightarrow\frac{S+T}{2}$$ $$=\frac{(4,10)+(6,-2)}{2}$$ $$=\frac{(10,8)}{2}$$ $$=(5,4)$$

# 2009 December(68A) Math Question 14

Choice K

$$\frac{3}{5}\times\frac{1}{2}=\frac{3}{10}$$

# 2009 December(68A) Math Question 15

Choice C

$$\frac{1}{a}=2$$ $$\frac{1}{b}=3$$ $$\frac{1}{2}(\frac{1}{a}+\frac{1}{b})$$ $$=\frac{1}{2}(2+3)$$ $$=\frac{5}{2}$$

# 2009 December(68A) Math Question 16

- Cost

Choice J

$$30\times0.85\times0.9\times1.06=24.327\approx24.34$$

# 2009 December(68A) Math Question 17

Choice E

$$a=c$$ $$b=d$$ $$a+b=180°$$ $$c+d=180°$$ $$a+b+c+d=360°$$

# 2009 December(68A) Math Question 18

Choice G

$$5000\div50=100$$

# 2009 December(68A) Math Question 19

Choice E

$$(x+2)(x-1)$$ $$=x^{2}-x+2x-2$$ $$=x^{2}+x-2$$

# 2009 December(68A) Math Question 20

Choice G

$$A=1000(1+0.05)^{2}$$ $$=1000(1.1025)$$ $$=1102.5\approx 1103$$

# 2009 December(68A) Math Question 21

Choice C

$$20\ mins=\frac{1}{3}\ hr$$ $$50\times\frac{1}{3}=16.666\approx17$$

# 2009 December(68A) Math Question 22

Choice H

$$1=100¢$$ $$0.40\times x+0.25\times(20-x)=6.95$$ $$0.4x+5-0.25x=6.95$$ $$0.15x=1.95$$ …

# 2009 December(68A) Math Question 23

Choice B

$$3x-2y=6$$ $$-2y=6-3x$$ $$2y=3x-6$$ $$y=\frac{3}{2}x-3$$ $$y=mx+b$$ …

# 2009 December(68A) Math Question 24

Choice G

$$\sin 6°=0.1045=\frac{?}{4}$$ $$?=0.1045\times4=0.418$$

Choice E

# 2009 December(68A) Math Question 27

Choice B

$$16(16-6)(\frac{1}{2})=80$$

Choice K

# 2009 December(68A) Math Question 31

Choice C

$$\Rightarrow \overline{AB}=4\overline{GH}$$

# 2009 December(68A) Math Question 32

Choice F

$$2\frac{1}{3}\times\frac{1}{2}=1\frac{1}{6}$$

# 2009 December(68A) Math Question 33

Choice B

$$6+1\times x=3+1\frac{1}{2}x$$ $$3=\frac{1}{2}x$$ $$x=6$$

# 2009 December(68A) Math Question 34

Choice K

$$\Rightarrow x^{3}-4x^{2}-x^{2}+5x+3x+6$$ $$\Rightarrow x^{3}-5x^{2}+8x+6$$

# 2009 December(68A) Math Question 35

Choice A

$$\tan \theta=\frac{0.5}{1}$$ $$\Rightarrow \tan \theta=\frac{1}{2}$$ …

Choice G

# 2009 December(68A) Math Question 37

Choice C

$$\pi r^{2}=16\pi$$

Choice K

Choice B

Choice F

# 2009 December(68A) Math Question 41

Choice D

$$r=\frac{10}{2}=5$$ $$\pi r^{2}h=\pi 5^{2}h=1000$$ $$h=1000\div25\div\pi=\frac{40}{\pi}\approx\frac{40}{3.14}=12.73$$

# 2009 December(68A) Math Question 42

Choice J

$$1-\frac{1}{12}\times3=\frac{9}{12}=\frac{3}{4}$$ $$\frac{3}{4}\times\frac{1}{5}=\frac{3}{20}$$

# 2009 December(68A) Math Question 43

Choice A

$$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$ $$=\frac{-(-5)\pm\sqrt{(-5)^{2}-4(1)(3)}}{2(1)}$$ $$=\frac{5\pm\sqrt{25-4(1)(3)}}{2(1)}$$

Choice F

# 2009 December(68A) Math Question 47

Choice D

$$(10+18)\times 3\times\frac{1}{2}=42$$

# 2009 December(68A) Math Question 48

Choice G

$$C=99\times h$$ $$m=0.99$$

# 2009 December(68A) Math Question 49

Choice D

$$4,10,25$$ $$10\div4=2.5$$ $$25\div10=2.5$$ $$25\times2.5=62.5$$

# 2009 December(68A) Math Question 50

Choice J

$$64=x^{3}$$ $$x=4$$ $$Total\ surface\ area=4\times4\times6=96$$

# 2009 December(68A) Math Question 51

Choice C

$$2\pi r=2 \pi(4)=8\pi$$ $$\frac{7 \pi}{8\pi}=\frac{315}{360}$$ …

# 2009 December(68A) Math Question 52

Choice K

The equation for a circle …

Choice D

Choice E