# 2019 December(C03) Math Question 1

Choice C

$$f(x,y)=3x^{2}-4y$$ $$f(3,2)=3\times3^{2}-4\times2=27-8=19$$

# 2019 December(C03) Math Question 2

Choice H

$$\angle ACB=180°-35°-95°=50°$$ $$\angle ACD=180°-50°=130°$$

Choice E

# 2019 December(C03) Math Question 4

Choice H

$$\frac{7000}{100}\times0.75+20$$ $$=70\times0.75+20$$ $$=52.5+20$$ $$=72.5$$

# 2019 December(C03) Math Question 5

Choice E

$$f(x)=4x^{2}-11x$$ $$f(-5)=4\times(-5)^{2}-11\times(-5)$$ $$=4\times25-(-55)$$ $$=100+55=155$$

# 2019 December(C03) Math Question 6

Choice G

Taho works 40 hours+10 hours.

$$40\ hours\Rightarrow 11\times 40=440$$ $$10\ hours\Rightarrow 11(1\frac{1}{2})\times 10=16.5\times 10=165$$ $$440+165=605$$

# 2019 December(C03) Math Question 7

Choice E

$$8\ juniors+4\ seniors\Rightarrow 7\ juniors+4\ seniors$$ $$P(Seniors)=\frac{4}{7+4}=\frac{4}{11}$$

# 2019 December(C03) Math Question 8

Choice F

$$-12°F-24°F=-36°F$$

# 2019 December(C03) Math Question 9

Choice C

$$35\times6+0.425\times350$$ $$=210+148.75$$ $$=358.75$$

# 2019 December(C03) Math Question 10

Choice H

$$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{3-4}{1-(-6)}=\frac{-1}{7}$$

# 2019 December(C03) Math Question 11

Choice B

$$P=\frac{Regular\ coffee\ without\ milk}{Total}$$ $$=\frac{10}{36}=\frac{5}{18}$$

# 2019 December(C03) Math Question 12

Choice J

$$3x-5\lt2x+1$$ $$\Rightarrow 3x-5-2x+5\lt2x+1-2x+5$$ $$\Rightarrow x\lt6$$

# 2019 December(C03) Math Question 13

Choice B

$$4(x+2)+3(2x-1)$$ $$=4x+8+6x-3$$ $$=10x+5$$ $$=5(2x+1)$$

# 2019 December(C03) Math Question 14

Choice G

$$1.36\times 10^{4}\times\frac{4}{100}$$ $$=1.36\times4\times10^{2}$$ $$=136\times4$$ $$=544$$

# 2019 December(C03) Math Question 15

Choice B

$$7\times11\times5\times1\times2=770$$

Choice F

# 2019 December(C03) Math Question 17

Choice B

$$\frac{(-6,9)+(2,5)}{2}$$ $$=\frac{(-6+2,9+5)}{2}$$ $$=\frac{(-4,14)}{2}$$ $$=(-2,7)$$

# 2019 December(C03) Math Question 18

Choice K

$$\require{cancel}$$ $$\frac{x^{2}+2x}{x+2}=2$$ $$\Rightarrow x^{2}+2x=2(x+2)$$ $$\Rightarrow x\cancel{(x+2)}=2\cancel{(x+2)}$$ $$\Rightarrow x=2$$

# 2019 December(C03) Math Question 19

Choice D

$$830+1650+2320+200=5000$$ $$5000\div4=1250$$

# 2019 December(C03) Math Question 20

Choice G

$$x:\ attend\ regular\ showing$$ $$y:\ attend\ matinees$$ $$x+y=5000$$ $$\Rightarrow y=5000-x$$ $$9.5x+(5000-x)7=44000$$ $$\Rightarrow 9.5x+35000-7x=44000$$ $$\Rightarrow 2.5x=9000$$ $$\Rightarrow x=3600$$ $$\Rightarrow y=5000-3600=1400$$

# 2019 December(C03) Math Question 21

Choice A

$$\frac{2750}{5000}=0.55$$ $$\frac{1225}{5000}=0.245$$ $$\frac{625}{5000}=0.125$$ $$\frac{400}{5000}=0.08$$

# 2019 December(C03) Math Question 22

Choice G

$$9\times6=54$$ $$3\times7=21$$ $$54+21=75$$

Choice C

Choice D

# 2019 December(C03) Math Question 37

- FOIL

Choice E

$$\require{cancel}$$ $$\frac{x^{2}-x-6}{x^{2}-9}$$ $$=\frac{\cancel{(x-3)}(x+2)}{\cancel{(x-3)}(x+3)}$$ $$=\frac{x+2}{x+3}$$

# 2019 December(C03) Math Question 38

Choice H

$$\frac{9\times12+4}{2}=\frac{112}{2}=56$$ $$12\times4=48$$ $$56=48+8$$

# 2019 December(C03) Math Question 39

Choice A

$$\frac{1}{2}+\frac{1}{3}\cdot\frac{1}{4}\div\frac{1}{5}=\frac{x}{y}$$ $$\Rightarrow\frac{1}{2}+\frac{1}{3}\cdot\frac{1}{4}\cdot5=\frac{x}{y}$$ $$\Rightarrow\frac{1}{2}+\frac{5}{12}=\frac{x}{y}$$ $$\Rightarrow\frac{6}{12}+\frac{5}{12}=\frac{11}{12}$$ $$\Rightarrow11+12=23$$

# 2019 December(C03) Math Question 40

Choice H

$$0.\overline{3178}=0.3178317831783178...$$ $$358\div4=89...2$$

# 2019 December(C03) Math Question 41

Choice C

$$60\times0.1=6$$ $$60\times0.3=18$$ $$60\times0.6=36$$ $$\frac{6\times3+18\times2+36\times1}{6}$$ $$=\frac{18+36+36}{6}$$ …

Choice G

200/2400=8.33%

# 2019 December(C03) Math Question 43

Choice A

$$600\times50+200\times5+400\times10$$

# 2019 December(C03) Math Question 44

Choice J

$$10000(1+0.02)^{t}$$

Choice D

Choice H

# 2019 December(C03) Math Question 50

Choice F

$$\require{cancel}$$ $$1-\frac{1}{9}=\frac{8}{9}$$ $$\frac{\frac{1}{9}}{\frac{8}{9}}=\frac{1}{\cancel{9}}\times\frac{\cancel{9}}{8}=\frac{1}{8}$$

# 2019 December(C03) Math Question 51

Choice B

$$\frac{120\times0.05+80\times0.15}{200}$$ $$=\frac{6+12}{200}$$ $$=\frac{18}{200}$$ $$=\frac{9}{100}$$

# 2019 December(C03) Math Question 52

Choice F

$$\tan\theta=\frac{7}{50}$$ $$\theta=\tan^{-1}\frac{7}{50}$$

# 2019 December(C03) Math Question 53

Choice A

$$\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$$ $$\frac{(x-2)^{2}}{a^{2}}-\frac{(y-2)^{2}}{b^{2}}=1$$ $$(A)\frac{(x-2)^{2}}{1}-\frac{3(y-2)^{2}}{4}=1$$ $$(0,0)\Rightarrow \frac{(0-2)^{2}}{1}-\frac{3(0-2)^{2}}{4}=1$$ …

# 2019 December(C03) Math Question 54

Choice K

$$c^{2}=a^{2}+b^{2}-2ab\cos C$$ $$c^{2}=\sqrt{250^{2}+700^{2}-2\times250\times700\times\cos 155°}$$

# 2019 December(C03) Math Question 55

Choice A

$$a\gt b\gt c, b\gt0$$ $$(1)a=3,b=2,c=1$$ …

Choice J