# 2019 April(B04) Math Question 1

Choice E

$$3x-7=5x-13$$ $$\Rightarrow(3x−7)-3x+13=(5x-13)-3x+13$$ $$\Rightarrow6=2x$$ $$\Rightarrow x=3$$

# 2019 April(B04) Math Question 2

- Cost

Choice H

$$1\sim40\ hours:14/hour$$ $$Over\ 40\ hours:14\times 1\frac{1}{2}=21/hour$$ $$\Rightarrow14\times40+21\times8=560+168=728$$

# 2019 April(B04) Math Question 3

Choice B

The rate of leaking water is 4 gallons per minute.

$$\because The\ rate\ of\ leaking\ water\ is\ 4\ gallons\ per\ minute.$$ $$After\ t\ minutes \Rightarrow 4 \times t$$ $$\Rightarrow G(t)=200-4t$$

# 2019 April(B04) Math Question 4

Choice F

$$(x^{5}y^{3}z^{2})(x^{4}y^{3}z^{6})$$ $$=x^{(5+4)}y^{(3+3)}z^{(2+6)}$$ $$=x^{9}y^{6}z^{8}$$

# 2019 April(B04) Math Question 5

Choice D

$$-12,24,-48,96,-192,...$$ $$-12\times-2=24$$ $$24\times-2=-48$$ $$-48\times-2=96$$ $$96\times-2=-192$$ $$-192\times-2=384$$

# 2019 April(B04) Math Question 6

Choice K

$$\require{cancel}$$ $$50 \times\frac{miles}{hour} = 50 \times\frac{miles}{60 minutes}=\frac{5}{6}\times\frac{miles}{minute}$$ $$\Rightarrow120\ miles\div(\frac{5}{6}\times\frac{miles}{minute})=120\ \cancel{miles}\times(\frac{6}{5}\times\frac{minute}{\cancel{miles}})=144\ minutes$$

# 2019 April(B04) Math Question 7

Choice B

$$6-\frac{1}{2}-1\frac{3}{4}=\frac{24}{4}-\frac{2}{4}-\frac{7}{4}$$ $$=\frac{24-2-7}{4}=\frac{15}{4}=3\frac{3}{4}$$

# 2019 April(B04) Math Question 8

Choice G

$$x^{2}+40^{2}=50^{2}$$ $$\Rightarrow x^{2}=2500-1600=900$$ $$\Rightarrow x=30$$

# 2019 April(B04) Math Question 9

Choice D

8% of the spaces are reserved for handicapped parking. That means 92% NOT served for handicapped parking.

$$450\times \frac{92}{100}=414$$

Of those parkinf spaces NOT reserved for handicapped parking, 18 are suitable for compact cars only.

$$\Rightarrow 414-18=396$$

# 2019 April(B04) Math Question 10

Choice J

raw1=1,raw2=1+2,raw3=1+2(2),raw4=1+2(3),...,raw7=1+2(6)=13

$$\Rightarrow (1+13)7\frac{1}{2}=49$$

# 2019 April(B04) Math Question 11

Choice C

$$\frac{a}{b^{2}}+\frac{c}{2}$$ $$=\frac{3}{5^{2}}+\frac{8}{2}$$ $$=\frac{3}{25}+4=\frac{103}{25}$$

# 2019 April(B04) Math Question 12

Choice G

$$21\Rightarrow3\times7$$ $$12\Rightarrow3\times4=3\times2\times2=3\times2^{2}$$ $$8\Rightarrow2\times2\times2=2^{3}$$ $$\Rightarrow 2^{3}\times 3\times7=168$$

# 2019 April(B04) Math Question 13

Choice C

$$1440=180\times(n-2)$$ $$\Rightarrow\frac{1440}{180}=n-2$$ $$\Rightarrow 8=n-2$$ $$\Rightarrow n=10$$

# 2019 April(B04) Math Question 14

Choice F

$$Let\ \overline{CG}\equiv\overline{AE}=x$$ $$24\times2=(x+6)(x+4)$$ $$\Rightarrow 48=x^{2}+10x+24$$ $$\Rightarrow x(x+10)=24$$ $$\Rightarrow x=2$$

Choice C

# 2019 April(B04) Math Question 16

Choice H

$$x^{2}+3x-54=0$$ $$\Rightarrow (x+9)(x-6)=0$$ $$\Rightarrow x=-9,6$$ $$\Rightarrow -9+6=-3$$

# 2019 April(B04) Math Question 17

Choice E

$$36=r^{2}$$ $$\Rightarrow r=\sqrt{36}=6$$ $$6\times4=24$$

Choice H

# 2019 April(B04) Math Question 19

Choice A

$$\require{cancel}$$ $$5.13\times10^{5}\times\frac{3}{100}$$ $$=5.13\times1000\cancel{00}\times\frac{3}{\cancel{100}}$$ $$=5.13\times1000\times3$$ $$=15390$$

# 2019 April(B04) Math Question 20

Choice K

$$\tan\theta=\frac{x}{10}$$ $$\Rightarrow x=\frac{\tan35°}{10}=\frac{1}{10}\tan35°$$

# 2019 April(B04) Math Question 21

Choice B

$$\left[40,24\right]=8\times5\times3=120$$ $$120\div40=3$$

3,12,15,24 are multiples …

Choice K

# 2019 April(B04) Math Question 26

Choice J

$$(120+128)\div2=124$$

# 2019 April(B04) Math Question 27

Choice A

$$\frac{1\ word\ films}{After\ 1965}=\frac{2}{4}$$

# 2019 April(B04) Math Question 28

Choice G

The new version is 20% …

# 2019 April(B04) Math Question 29

Choice A

Tapaz=143 minutes

Frenzy= x minutes …

Choice K

# 2019 April(B04) Math Question 35

Choice D

$$(kx+m)(rx+n)$$ $$=krx^{2}+knx+mrx+mn$$ $$=krx^{2}+(kn+mr)x+mn$$

# 2019 April(B04) Math Question 36

Choice J

$$(F)\frac{15}{101}\lt\frac{15}{100}$$ $$(G)\frac{150}{999}\lt\frac{150}{1000}(=\frac{15}{100})$$ $$(H)0.15=\frac{15}{100}$$ $$(J)0.\overline{15}=0.151515...\gt\frac{15}{100}$$ $$(K)0.\overline{151}=0.151151...(\lt0.151515...)$$ …

# 2019 April(B04) Math Question 37

Choice D

$$2+2+2=6$$ $$12-6=6$$ $$270\div6=45$$

# 2019 April(B04) Math Question 38

Choice H

$$f(x)=x^{2}+2, g(x)=x+3$$ $$f(g(x))=f(x+3)$$ $$=(x+3)^{2}+2$$ $$=(x+3)(x+3)+2$$ …

Choice C

Choice J