# 2020 July(C01) Math Question 1

Choice E

$$x+25°=180°$$ $$x=155°$$

# 2020 July(C01) Math Question 2

Choice H

$$\frac{(30+30+70+70+70)}{5}=\frac{270}{5}=54$$

# 2020 July(C01) Math Question 3

Choice B

$$45=1\times3\times3\times5$$ $$50=1\times2\times5\times5$$ $$84=1\times2\times2\times3\times7$$ $$The\ greastest\ common\ factor=1$$

# 2020 July(C01) Math Question 4

Choice J

$$\Rightarrow 2x-24+x=36$$ $$\Rightarrow 3x=36+24$$ $$\Rightarrow 3x=60$$ $$\Rightarrow x=20$$

# 2020 July(C01) Math Question 5

Choice A

$$Total=22$$ $$Not\ white=22-12=10$$ $$P(Not\ white)=\frac{Not\ white}{Total}=\frac{10}{22}=\frac{5}{11}$$

# 2020 July(C01) Math Question 6

Choice F

$$\frac{1}{2}:12=5:x$$ $$12\times5=\frac{1}{2}x$$ $$60=\frac{1}{2}x$$ $$x=120$$

# 2020 July(C01) Math Question 7

Choice B

$$45-42=3$$ $$42-39=3$$ $$39-36=3$$ $$45-3\times6=45-18=27$$

# 2020 July(C01) Math Question 8

Choice H

$$\Rightarrow T=5+2M$$

# 2020 July(C01) Math Question 9

Choice C

$$\Rightarrow 2x+5=0\ or\ 3x-4=0$$ $$\Rightarrow x=-\frac{5}{2}\ or\ x=\frac{4}{3}$$

# 2020 July(C01) Math Question 10

Choice J

$$8\times6=48$$ $$48\div2=24$$

# 2020 July(C01) Math Question 11

Choice C

$$\frac{2}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{60}$$ $$=\frac{40}{60}+\frac{10}{60}+\frac{6}{60}+\frac{1}{60}$$ $$=\frac{40+10+6+1}{60}$$ $$=\frac{57}{60}$$ $$1-\frac{57}{60}=\frac{3}{60}=\frac{1}{20}$$

# 2020 July(C01) Math Question 12

Choice H

$$7^{2}=49$$ $$8^{2}=64$$ $$\sqrt{61}\lt\sqrt{64}$$ $$\Rightarrow \sqrt{61}\lt8$$

# 2020 July(C01) Math Question 13

Choice E

$$\sin C=\frac{2}{3}=\frac{6}{?}$$ $$?=9$$

# 2020 July(C01) Math Question 14

Choice H

$$n=1,\ 1=2n-1,\ 1=3n-2,\ 1=4n-3,\ 1=5n-4,\ 1=6n-5$$ $$n=2,\ 5\neq4-1,\ 5\neq6-2,\ 5=8-3,\ 5\neq10-4,\ 5\neq12-5$$ $$Only\ 4n-3\ is correct.$$

# 2020 July(C01) Math Question 15

Choice D

$$8+6+12+14+20+20=80$$

# 2020 July(C01) Math Question 16

Choice F

$$(\frac{2}{3}+\frac{3}{4})\div2$$ $$=(\frac{8}{12}+\frac{9}{12})\div2$$ $$=\frac{17}{12}\div2$$ $$=\frac{17}{24}$$

# 2020 July(C01) Math Question 17

Choice C

$$\frac{46+x}{60+x}=0.8$$ $$\Rightarrow 0.8\times(60+x)=46+x$$ $$\Rightarrow 48+0.8x=46+x$$ $$\Rightarrow 0.2x=2$$ $$\Rightarrow x=10$$

# 2020 July(C01) Math Question 18

Choice G

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

# 2020 July(C01) Math Question 19

Choice A

Let the 9th number be 91 which is greater than 90.

$$The\ mean\ of\ Set\ A=(62+76+76+80+82+87+94+96)\div8=\frac{653}{8}=81.625$$ $$The\ median\ of\ Set\ A=(80+82)\div2=81$$ $$The\ mean\ of\ Set\ B=\frac{653+91}{9}\approx82.66$$ $$The\ median\ of\ Set\ B=82$$ $$\Rightarrow 82.66\gt 81.625$$ $$\Rightarrow 82\gt 81$$

The mean and the median of Set B will each be greater than the mean and the median of Set A.

# 2020 July(C01) Math Question 20

Choice J

$$\frac{480}{4}=120\ mins=2\ hrs$$ $$\Rightarrow 35\times2=70$$

# 2020 July(C01) Math Question 21

Choice B

$$\Rightarrow \frac{((-5)+3),(8+(-1))}{2}=(-1,\frac{7}{2})$$

# 2020 July(C01) Math Question 22

Choice H

When the X value is …

# 2020 July(C01) Math Question 23

Choice A

The larger the angle in …

Choice F

# 2020 July(C01) Math Question 26

Choice F

We assume that x adult …

# 2020 July(C01) Math Question 27

Choice E

NOT first-time skiers=200-25=175

# 2020 July(C01) Math Question 31

Choice B

Experimental group:

1 min 46 …

# 2020 July(C01) Math Question 32

Choice K

$$0,1,2,3,4,5,6,7,8,9\rightarrow 10\ numbers$$ $$10\times10\times10=1000$$

Choice C

# 2020 July(C01) Math Question 34

Choice J

$$3=1\times3$$ $$7=1\times7$$ $$9=1\times3\times3$$ $$\Rightarrow[3,7,9]=1\times3\times3\times7=63$$

# 2020 July(C01) Math Question 35

Choice D

$$\because\ ABCD\ is\ a\ parallelogram.$$ …

# 2020 July(C01) Math Question 36

Choice K

$$\because\ ABCD\ is\ a\ parallelogram.$$ …

# 2020 July(C01) Math Question 37

Choice E

$$\frac{2+30}{2}=16$$ $$\frac{10+3}{2}=\frac{13}{2}$$ $$\Rightarrow\ E(16,\frac{13}{2})$$

Choice K

Choice D

Choice A

Choice D

# 2020 July(C01) Math Question 52

Choice J

The average of 10 test …

# 2020 July(C01) Math Question 53

Choice E

$$27^{n^{2}}=9^{5n-4}$$ $$\Rightarrow (3^{3})^{n^{2}}=(3^{2})^{5n-4}$$ $$\Rightarrow 3^{3(n^{2})}=3^{2(5n-4)}$$ …

# 2020 July(C01) Math Question 54

Choice G

$$Less\ than\ 6:$$ $$(1,1),(1,2),(1,3),(1,4),$$ …

# 2020 July(C01) Math Question 55

Choice D

$$68\times x=240-57\times x$$ $$68x=240-57x$$ $$125x=240$$ …

Choice J

# 2020 July(C01) Math Question 57

Choice A

$$\frac{(n+1)!6!}{n!3!}$$ $$=\frac{(n+1)!(6\cdot5\cdot4\cdot3\cdot2\cdot1)}{n!(3\cdot2\cdot1)}$$ $$=\frac{(n+1)!(6\cdot5\cdot4)}{n!}$$ $$=\frac{n!(n+1)(6\cdot5\cdot4)}{n!}$$ $$=(n+1)(6\cdot5\cdot4)$$ …

Choice G

I.

1,2,3,4

24,25,26,27

24, 25, …

# 2020 July(C01) Math Question 59

- FOIL

Choice E

$$(x+1)^{4}$$ $$=(x+1)^{2}(x+1)^{2}$$ $$=(x^{2}+2x+1)(x^{2}+2x+1)$$ $$x^{2}(1)+2x(2x)+1(x^{2})$$ $$=2x^{2}+4x^{2}$$ …

# 2020 July(C01) Math Question 60

Choice K

$$c^{2}=60^{2}+25^{2}-2(60)(25)\cos 110°$$ $$c=\sqrt{60^{2}+25^{2}-2(60)(25)\cos 110°}$$