# 2009 April(66F) Math Question 1

Choice E

$$12:4=x:12$$ $$4x=144$$ $$x=36$$

# 2009 April(66F) Math Question 2

Choice H

$$500-140=360$$ $$360\div40=9$$

# 2009 April(66F) Math Question 3

Choice A

$$\frac{x^{2}-1}{x+1}$$ $$=\frac{(-5)^{2}-1}{(-5)+1}$$ $$=\frac{24}{-4}$$ $$=-6$$

# 2009 April(66F) Math Question 4

Choice J

$$9.25-8.5=0.75$$ $$0.75\times27=20.25$$

# 2009 April(66F) Math Question 5

Choice C

$$P=\frac{1}{13-3}=\frac{1}{10}$$

# 2009 April(66F) Math Question 6

Choice H

$$(15+6)\times2=42$$

# 2009 April(66F) Math Question 7

Choice B

$$6\times142=852$$ $$2000-852=1148$$ $$1184\div8=143.5$$

# 2009 April(66F) Math Question 8

Choice J

$$\frac{8}{12}=\frac{10}{r}$$ $$8r=120$$ $$r=15$$

# 2009 April(66F) Math Question 9

Choice E

$$12(x-11)=-15$$ $$\Rightarrow 12x-132=-15$$ $$\Rightarrow 12x=117$$ $$\Rightarrow 4x=39$$ $$\Rightarrow x=\frac{39}{4}$$

Choice J

# 2009 April(66F) Math Question 11

Choice C

$$f(-2)=9(-2)^{2}+5(-2)-8$$ $$=9(4)-10-8$$ $$=36-18$$ $$=18$$

# 2009 April(66F) Math Question 12

Choice J

$$30=3\times10$$ $$20=2\times10$$ $$70=7\times10$$ $$[30,20,70]=2\times3\times7\times10=420$$

# 2009 April(66F) Math Question 13

Choice E

$$Originally\ wanted=\frac{x}{2}$$ $$(x\times2)\div\frac{x}{2}=4$$ $$\Rightarrow (x\times2)\div4=\frac{x}{2}$$

# 2009 April(66F) Math Question 14

Choice G

$$125\div5=25$$ $$25=5\times5$$ $$5\times12=60$$

# 2009 April(66F) Math Question 15

Choice E

$$\angle B=90°$$ $$\angle A+\angle B+\angle C=180°$$ $$\Rightarrow \angle A+\angle C=90°$$ $$\because \angle A\gt 43°$$ $$90-43=47$$ $$\therefore \angle C \lt 47°$$

# 2009 April(66F) Math Question 16

Choice G

$$I.$$ $$(2+1)^{4}+(6+3)^{2}\neq10$$ $$II.$$ $$(2-1)^{4}+(6-3)^{2}$$ $$=(1)^{4}+(3)^{2}$$ $$=1+9$$ $$=10$$ $$III.$$ $$(2\div1)^{4}+(6\div3)^{2}$$ $$=(1)^{4}+(2)^{2}$$ $$=1+4$$ $$=5$$ $$\neq 10$$

# 2009 April(66F) Math Question 17

Choice E

$$(0,5)\Rightarrow 5=2(0)+5$$ $$Only\ (E)\ is\ correct.$$

# 2009 April(66F) Math Question 18

Choice F

$$\Rightarrow (n+4)8=2n-10$$

# 2009 April(66F) Math Question 19

Choice A

Assuming that x years have passed...

$$\Rightarrow 20,000+800x=15,200+2,000x$$

# 2009 April(66F) Math Question 20

Choice J

$$5^{2}+12^{2}=13^{2}$$

# 2009 April(66F) Math Question 21

Choice E

$$=7x+21-6x+6$$ $$=x+27$$

# 2009 April(66F) Math Question 22

Choice G

$$x+y=32---(1)$$ $$x-y=12---(2)$$ $$(1)+(2)$$ $$\Rightarrow 2x=44$$ …

# 2009 April(66F) Math Question 23

- FOIL

Choice C

$$(2x-3)^{2}$$ $$=4x^{2}-12x+9$$ $$\Rightarrow a=4,b=-12,c=9$$ $$a+b+c=4-12+9=1$$

# 2009 April(66F) Math Question 24

Choice H

$$\Rightarrow 15\times15+5\times10$$ $$=225+50$$ $$=275$$

# 2009 April(66F) Math Question 25

Choice A

It can be seen from the table that f(x) moves in increments of 0.2, meaning f(x) is a linear function. It follows that f(4) = 0.2.

# 2009 April(66F) Math Question 26

Choice H

$$y=mx+b$$ $$6y=14x+5$$ $$y=\frac{14}{6}+\frac{5}{6}$$ $$m=\frac{14}{6}=\frac{7}{3}$$

# 2009 April(66F) Math Question 27

Choice C

$$x^{2}+x-12$$ $$=(x-3)(x+4)$$ $$\Rightarrow x=3,-4$$ $$3+(-4)=-1$$

# 2009 April(66F) Math Question 28

Choice J

$$3+5+7=15$$ $$\Rightarrow 15\times\frac{5}{3}=25$$

# 2009 April(66F) Math Question 29

Choice A

$$\Rightarrow -6,-5,-3,-2,1,2,4$$ $$The\ median:\ -2$$

# 2009 April(66F) Math Question 30

Choice G

$$x^{2}-23(x)=50$$ $$\Rightarrow x^{2}-23(x)-50=0$$ $$\Rightarrow (x-25)(x+2)=0$$ …

# 2009 April(66F) Math Question 31

Choice B

$$d=\frac{1}{2}at^{2}$$ $$80=\frac{1}{2}(20)t^{2}$$ $$80=10t^{2}$$ $$8=t^{2}$$ $$t\approx2.82$$

# 2009 April(66F) Math Question 32

Choice F

$$\frac{abc^{2}d}{bcd}=ac$$ $$\frac{a^{2}bc^{3}d}{abc^{2}d}=ac$$ $$\Rightarrow a^{2}bc^{3}d(ac)=a^{3}bc^{4}d$$

# 2009 April(66F) Math Question 33

Choice D

$$\Rightarrow \frac{2+5+6}{20}$$ $$=\frac{13}{20}$$

# 2009 April(66F) Math Question 34

Choice J

$$\Rightarrow \frac{4}{20}=\frac{2}{10}$$ $$\frac{2}{10}\times360°=72°$$

# 2009 April(66F) Math Question 35

Choice B

$$=\frac{0(2)+1(5)+2(6)+3(4)+4(2)+5(1)}{20}$$ $$=\frac{0+5+12+12+8+5}{20}$$ $$=\frac{42}{20}$$ $$=2.1$$

# 2009 April(66F) Math Question 36

Choice F

$$\Rightarrow\frac{(x+7)(x+1)}{(x+7)(x-3)}\times\frac{x-3}{x+1}$$ $$\Rightarrow 1$$

# 2009 April(66F) Math Question 37

Choice E

$$\sin 72°=\frac{x}{144}$$ $$x=144\sin 72°$$

# 2009 April(66F) Math Question 38

Choice G

$$\Rightarrow(\frac{-8+2}{2},\frac{-3+3}{2})$$ $$=(\frac{-6}{2},\frac{0}{2})$$ $$=(-3,0)$$ $$\Rightarrow x=-3$$

# 2009 April(66F) Math Question 39

Choice B

$$\Rightarrow\sqrt{(-6-(-2))^{2}+(-7-(-3))^{2}}$$ $$=\sqrt{16+16}$$ $$=\sqrt{32}$$ $$\approx 5.65$$ …

# 2009 April(66F) Math Question 40

Choice K

"The sum of two rational …

Choice B

# 2009 April(66F) Math Question 45

Choice E

$$\triangle 45°-45°-90°=1:1:\sqrt{2}$$ $$\triangle 30°-60°-90°=1:\sqrt{3}:2$$ $$H=\frac{100}{\sqrt{2}}+20\sqrt{3}+30$$ …

# 2009 April(66F) Math Question 46

Choice H

The equation of a circle …

# 2009 April(66F) Math Question 47

Choice A

$$2a\times(6-2a^{2})$$ $$=12a-4a^{3}$$

Choice F

Choice B

# 2009 April(66F) Math Question 54

Choice K

$$3:4:5$$ $$=24:32:40$$ $$The\ height=32$$

Choice C

# 2009 April(66F) Math Question 58

Choice K

$$24^{2}+7^{2}=25^{2}$$ $$\Rightarrow \sin \phi=\frac{7}{25}$$

Choice B