ACT Form 72F Math Answer Explanation


2019 June(72F) Math Question 1

Choice E

$$\frac{4}{y}=0.4$$ $$\Rightarrow \frac{4}{y}\times y=0.4\times y$$ $$\Rightarrow 4=0.4y$$ $$\Rightarrow y=10$$


2019 June(72F) Math Question 2

Choice J

$$60\times1.24=74.4$$


2019 June(72F) Math Question 3

Choice C

$$$10\times40+$10\times(1\frac{1}{2})\times7$$ $$=$400+$105$$ $$=$505$$


2019 June(72F) Math Question 4

Choice J

$$3x^{9}\cdot 5x^{9}$$ $$=3\times5\times x^{9+9}$$ $$=15x^{18}$$


2019 June(72F) Math Question 5

Choice B

$$T=\pi r^{2}+\pi rs$$ $$T=\pi 3^{2}+\pi \times3\times5$$ $$=9\pi+15\pi$$ $$=24\pi$$


2019 June(72F) Math Question 6

Choice K

$$180°-45°-65°=70°$$


2019 June(72F) Math Question 7

Choice B

$$35=5\cdot7$$ $$28=2\cdot2\cdot7$$ $$8=2\cdot2\cdot2$$ $$2\cdot2\cdot2\cdot5\cdot7=280$$


2019 June(72F) Math Question 8

$$x=-2,5$$ $$f(x)=(x-5)(x+2)^{2}$$ $$f(-2)=0$$ $$f(5)=0$$


2019 June(72F) Math Question 9

Choice F

$$60\div(3+5+7)=60\div15=4$$ $$4\times7=28$$


2019 June(72F) Math Question 10

Choice F

$$f(9)=6$$ $$f(12)=8$$ $$F.\ f(x)=\frac{2}{3}n$$ $$f(9)=\frac{2}{3}\times9=6$$ $$f(12)=\frac{2}{3}\times12=8$$


2019 June(72F) Math Question 11

Choice C

$$(\frac{2+8}{2},\frac{5+11}{2})=(5,8)$$


2019 June(72F) Math Question 12

Choice F

$$1\times1\times\frac{1}{9}=\frac{1}{9}$$


2019 June(72F) Math Question 13

Choice C

$$=3x^{2}+x^{2}-4x-6x-5-7$$ $$=4x^{2}-10x-12$$


2019 June(72F) Math Question 14

Choice H

22 is even.

22 is not prime.


2019 June(72F) Math Question 15

Choice C

$$=\mid-42+32\mid=\mid-10\mid=10$$


2019 June(72F) Math Question 16

Choice G

$$11x+6y=3$$ $$y=\frac{-11}{6}x+3$$


2019 June(72F) Math Question 17

Choice A

$$g(2,4,3)$$ $$=4\times2\times4-3\times2\times (-3)^{2}$$ $$=32-54=-22$$


2019 June(72F) Math Question 18

Choice H

$$x°:360°=5000:45000$$ $$\Rightarrow x=40°$$


2019 June(72F) Math Question 19

Choice A

$$4000\div5=800$$


2019 June(72F) Math Question 20

$$3000:9000=1:3=\frac{1}{3}$$


2019 June(72F) Math Question 21

Choice E

$$4000+9000+5000+3000=21000 …


2019 June(72F) Math Question 22

$$(2x-10)+y=180 \Rightarrow 2x …


2019 June(72F) Math Question 23

Choice D

$$7-2=5$$ $$9-4=5$$ $$8-0 …


2019 June(72F) Math Question 24

Choice G

$$\tan C=\frac{8}{15}$$


2019 June(72F) Math Question 25

Choice B

$$3a-5b=22---(1)$$ $$a+3b …


2019 June(72F) Math Question 26

Choice F

$$3r+4p+50=545$$ $$\Rightarrow …


2019 June(72F) Math Question 27

Choice C

$$1st\ rectangle:\ 1\times2+4 …


2019 June(72F) Math Question 28

Choice F

$$2x^{3}+x^{2}-6x …


2019 June(72F) Math Question 29

Choice E

$$P(Not\ blue)$$ $$=1-P(Blue …


2019 June(72F) Math Question 30

Choice J

$$3x+1=5x-9$$ $$\Rightarrow 2x …


2019 June(72F) Math Question 31

Choice C

$$\cos L=\frac{a}{c …


2019 June(72F) Math Question 32

Choice K

$$(3.5+0.25n)(2500-100n)$$


2019 June(72F) Math Question 33

Choice B

$$2\pi r=20$$ $$r …


2019 June(72F) Math Question 34

Choice K

$$30°:60°:90°$$ $$\Rightarrow 1 …


2019 June(72F) Math Question 35

Choice C

$$45°:45°:90°$$ $$\Rightarrow 1 …


2019 June(72F) Math Question 36

Choice G

$$1\times4=4$$


2019 June(72F) Math Question 37

Choice D

$$450°=90°\times5$$


2019 June(72F) Math Question 38

Choice J


2019 June(72F) Math Question 39

Choice C

$$\sqrt[3]{3x-9}+10=13 …


2019 June(72F) Math Question 40

Choice J

$$=$2000(1+\frac{0.06 …


2019 June(72F) Math Question 41

Choice A

$$2\div7$$ $$=0.285714285714...$$ $$=0 …


2019 June(72F) Math Question 42

Choice K

$$\frac{60+65+70+75 …


2019 June(72F) Math Question 43

$$P=\frac{64G}{S}$$ $$\Rightarrow …


2019 June(72F) Math Question 44

Choice K

x quarters,

x+5 dimes …


2019 June(72F) Math Question 45

$$(3,9)\rightarrow(1,3 …


2019 June(72F) Math Question 46

Choice F

$$5^{2}+8^{2}=x …


2019 June(72F) Math Question 47

Choice E

$$x-20 \Rightarrow x+20$$ $$(x …


2019 June(72F) Math Question 48

Choice F

The range of temperatures is …


2019 June(72F) Math Question 49

Choice A

$$x+3=0$$ $$\Rightarrow x …


2019 June(72F) Math Question 50

Choice G

$$Circle\ area=\pi r^{2 …


2019 June(72F) Math Question 51

Choice D

$$\frac{3^{x}3^{4 …


2019 June(72F) Math Question 52

Choice J

All real numbers except 7.


2019 June(72F) Math Question 53

Choice D

By the Law of Sines …


2019 June(72F) Math Question 54

Choice G

$$F.\ f(x) > 0 \Rightarrow …


2019 June(72F) Math Question 55

Choice D

To minimize 2/(y-x),

we …


2019 June(72F) Math Question 56

Choice F

$$\Rightarrow (-r,s)$$


2019 June(72F) Math Question 57

Choice E

$$=\begin{bmatrix}2 & -5 \\-3 …


2019 June(72F) Math Question 58

Choice G

$$\overline{AE}=\overline{BE}$$ $$\overline …


2019 June(72F) Math Question 59

Choice D

$$ab\gt 0,$$ $$(-)(-)\gt 0 …


2019 June(72F) Math Question 60

Choice G

B is between D and …