# 2019 April(Z15) Math Question 1

Choice A

(r+b-g)(b+g)

=(4+2-(-5))(2+(-5))

=(4+2+5)(2-5)

=11(-3)

=-33

# 2019 April(Z15) Math Question 2

Choice J

$$2.5\times1+6\times n=22$$

# 2019 April(Z15) Math Question 3

Choice B

$$\angle CAB=\angle CBA=48°$$ $$\angle ACB=180°-48°-48°=84°$$

# 2019 April(Z15) Math Question 4

Choice H

$$20\div4=5$$ $$5\times5=25$$

# 2019 April(Z15) Math Question 5

Choice C

$$P(Not\ white)$$ $$=1-P(White)$$ $$=1-\frac{12}{21}$$ $$=\frac{9}{21}$$ $$=\frac{3}{7}$$

# 2019 April(Z15) Math Question 6

Choice G

$$=7-22$$ $$=-15$$

# 2019 April(Z15) Math Question 7

Choice A

$$39500-30000=9500$$ $$2500+370+400+4500+630+400=8800$$ $$9500-8800=700$$

# 2019 April(Z15) Math Question 8

Choice G

$$(165-42)\div3=123\div3=41$$

# 2019 April(Z15) Math Question 9

Choice A

$$5-\frac{3}{4}-2\frac{1}{2}$$ $$=\frac{20}{4}-\frac{3}{4}-\frac{10}{4}$$ $$=\frac{7}{4}$$ $$=1\frac{3}{4}$$

# 2019 April(Z15) Math Question 10

Choice F

$$\frac{25^{x}}{5^{2}}=5^{4}$$ $$\Rightarrow \frac{5^{2x}}{5^{2}}=5^{4}$$ $$\Rightarrow 2x-2=4$$ $$\Rightarrow 2x=6$$ $$\Rightarrow x=3$$

# 2019 April(Z15) Math Question 11

Choice B

$$f(x)=5\cdot 2^{x}$$ $$g(x)=10x$$ $$f(3)=5\cdot 2^{3}=5\cdot8=40$$ $$g(3)=10\cdot3=30$$ $$\Rightarrow f(3)-g(3)=40-30=10$$

# 2019 April(Z15) Math Question 12

Choice F

$$5\ bill:x$$ $$10\ bill:y$$ $$5x+10y=205---(1)$$ $$x+y=27---(2)$$ $$(1)-(2)\times5$$ $$\Rightarrow (5x+10y)-(5x+5y)=205-27\times5$$ $$\Rightarrow 5y=70$$ $$\Rightarrow y=14$$ $$\Rightarrow x=13$$

# 2019 April(Z15) Math Question 13

Choice A

$$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{3-2}{8-0}=\frac{1}{8}$$

# 2019 April(Z15) Math Question 14

Choice H

$$\sin^{2}(\theta)+\cos^{2}(\theta)=1$$ $$\Rightarrow \sin^{2}(\alpha)+\cos^{2}(\alpha)=1$$ $$\Rightarrow (\frac{15}{17})^{2}+\cos^{2}(\alpha)=1$$ $$\Rightarrow \frac{225}{289}+\cos^{2}(\alpha)=1$$ $$\Rightarrow \cos^{2}(\alpha)=\frac{64}{289}$$ $$\Rightarrow \cos(\alpha)=\sqrt{\frac{64}{289}}=\frac{8}{17}$$

Choice A

# 2019 April(Z15) Math Question 16

Choice J

$$(3x+5)=(4x-6)$$ $$\Rightarrow x=5+6=11$$ $$\Rightarrow (3x+5)=(4x-6)=38$$ $$\angle XYZ=180°-38°=142°$$

# 2019 April(Z15) Math Question 17

Choice E

$$Grade\ C\ or\ higher:10+26+18=54$$ $$\Rightarrow\frac{Grade\ C\ or\ higher}{Total}=\frac{54}{60}=\frac{9}{10}=0.9$$

# 2019 April(Z15) Math Question 18

Choice F

$$x^{2}-2x+n=0$$ $$x=4,$$ $$\Rightarrow 4^{2}-2\cdot4+n=0$$ $$\Rightarrow 16-8+n=0$$ $$\Rightarrow n=-8$$ $$x=-2,$$ $$\Rightarrow (-2)^{2}-2(-2)+n=0$$ $$\Rightarrow 4+4+n=0$$ $$\Rightarrow n=-8$$

# 2019 April(Z15) Math Question 19

Choice E

$$Circumference = π × diameter = 2 × π × radius.$$ $$2\pi r=12 \pi$$ $$\Rightarrow r=6$$ $$Area=\pi r^{2}=\pi 6^{2}=36\pi$$

# 2019 April(Z15) Math Question 20

Choice H

$$26-2=24$$ $$10-1=9$$ $$\Rightarrow24\times24\times24\times9\times9\times9$$

# 2019 April(Z15) Math Question 21

Choice E

$$3(a+b)-2(a-5b)$$ $$=3a+3b-2a+10b$$ $$=a+13b$$

# 2019 April(Z15) Math Question 22

Choice K

$$\Rightarrow\frac{8}{9}\times\frac{6}{7}$$

# 2019 April(Z15) Math Question 23

Choice D

$$\overline{AB}=\overline{BC}$$ $$\angle CBD=\angle ABD=\frac{1}{2}\angle ABC=40°$$ …

# 2019 April(Z15) Math Question 24

Choice K

$$\because\triangle ABC\sim\triangle DEF$$ $$\therefore 2:4=3:x$$ …

Choice C

# 2019 April(Z15) Math Question 33

Choice E

$$P(Heads\ up)=\frac{1}{2}$$ $$\Rightarrow \frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$$

Choice G

# 2019 April(Z15) Math Question 36

Choice F

$$A:\left\{0,1,2,3\right\}$$ $$B:\left\{1,3,5,7\right\}$$ $$F.\ f(x)=2x+1$$ $$f(0)=2\times0+1=1$$ …

# 2019 April(Z15) Math Question 37

Choice D

$$x=\frac{3}{4}+\frac{4}{3}=\frac{9+16}{12}=\frac{25}{12}$$ $$y=\frac{2}{3}+\frac{3}{2}=\frac{4+9}{6}=\frac{16}{6}=\frac{32}{12}$$ $$z=1+1=\frac{24}{12}$$ $$\Rightarrow \frac{32}{12}\gt\frac{25}{12}\gt\frac{24}{12}$$ …

# 2019 April(Z15) Math Question 38

Choice G

$$tan\ 76°=\frac{h}{18}$$ $$h=18\times tan\ 76°$$

# 2019 April(Z15) Math Question 39

Choice E

$$216=2^{3}\times 3^{3}$$ $$108=2^{2}\times 3^{3}$$ $$(A).[2,108]=108$$ …

# 2019 April(Z15) Math Question 40

Choice J

$$\Rightarrow y=3(x+7)^{2}-4$$

Choice E

# 2019 April(Z15) Math Question 44

Choice F

$$\sin\theta=\frac{maximum\ width}{maximum\ length}$$ $$=\frac{0.6}{1.2}=\frac{1}{2}$$

Take …

# 2019 April(Z15) Math Question 45

Choice A

$$1,2,2,2,3,3,3,3,4,4,4,5,5,6,7,8$$ $$Mode=3$$ $$Mean=\frac{1+2\times3+3\times4+4\times3+5\times2+6+7+8}{16}$$ $$=\frac{1+6+12+12+10+6+7+8}{16}$$ $$=\frac{62}{16}=3.875$$ …

Choice K

# 2019 April(Z15) Math Question 50

Choice G

$$380,204,032$$ $$F.\ 1\ and\ 10$$ …

Choice B

Choice K

# 2019 April(Z15) Math Question 59

Choice C

$$x^{2}-2x+17=0$$ $$\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$ \Rightarrow \frac{-(-2)\pm\sqrt{(-2)^{2}-4\times1\times17}}{2\times1} …

Choice G