ACT Form C01 Math Answer Explanation


2020 July(C01) Math Question 1

Angles Practice

- Other Shapes

1. The parallelogram below has consecutive angles with measures x and 25. What is the value of x?

Choice E

c01

$$x+25°=180°$$ $$x=155°$$

2020 July(C01) Math Question 2

Statistics Practice

- Mean, Median

2. A retail sales associate's daily commission during I week was $30 on Monday and Tuesday and $70 on Wednesday, Thursday, and Friday. What was the associate's average daily commission for these 5 days?

Choice H

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

Choice B

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

Choice J

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

2020 July(C01) Math Question 5

Probability Practice

- One Event

A bag contains exactly 22 solid-colored buttons:4 red
6 blue, and 12 white. What is the probability of randomly selecting I button that is NOT white?

Choice A

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

Choice F

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

Choice B

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

Choice H

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

2020 July(C01) Math Question 9

Quadratic Equations Practice

- Factoring

9. What are the solutions to the quadratic equation
(2x+5)(3x-4)=0?

Choice C

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

Choice J

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

Choice C

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

Choice H

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

Choice E

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

Choice H

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

Choice D

c01

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

2020 July(C01) Math Question 16

Statistics Practice

- Mean, Median

16. Manuel estimates that s of a pizza is left. Stephen estimates that, is left. They are going to compromise for a joint estimate by using the number halfway between their 2 estimates, What is their joint estimate?

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

Statistics Practice

- Mean, Median

17. So far this basketball season. Sherita made 46 of her first 60 free throws, giving her a free-throw average of about 76.7%. What is the minimum number of free throws she would need to make from now on in order to have a free-throw average of at least 80?

Choice C

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

Choice G

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

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

Word Problems Practice

- Distance, Speed, Time

20. A truck traveling at 35 mph has a leaky radiator that is losing 4 fluid ounces per minute. How many miles will the truck travel before the radiator, which held
4so nuid ounces when it began to leak is empty?

Choice J

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

Choice B

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

Choice H

When the X value is …

2020 July(C01) Math Question 23

Angles Practice

- Other Shapes

23.In△ ABC shown below,m∠A=x°,m∠B=(2x)°, m∠C=(3x)°,AB= c inches,AC= b inches, and BC a inches. Which of the following inequalities correctly relates the side lengths of AABC Note:m∠ A denotes the measure of∠A. and AB denotes the length of AB. The triangle is NOT drawn to scale.)

Choice A

The larger the angle in …

Choice F

$$y=mx+b$$ $$5=m+b---(1)$$ $$7=17m+b---(2)$$ $$2=16m$$ $$\Rightarrow …

Choice C

$$The\ longer\ side=x+2$$ $$The\ Shorter\ …

2020 July(C01) Math Question 26

Word Problems Practice

- 2 Variable Addition

Use the following information to answer questions 26-28
winter Fun Ski Resort sells only 2 types of tickets--adult and student. On Monday. the resort sold 200 tickets I ticket to cach skier. Of those tickets. 25 were sold to first-time skiers. When Alyssa skis the resort's main, run her elevation, E feet, at any point on the run is modeled by the equation E= 300,000 where t is the number of seconds after she begins skiing at the start of the main run.

Choice F

We assume that x adult …

Choice E

NOT first-time skiers=200-25=175

$$\frac{175}{200}=\frac{x}{8}$$ $$\Rightarrow …

Choice H

$$E=\frac{300,000}{t+100}$$ $$t=0 \Rightarrow E=\frac{300,000}{100}=3,000$$

Choice E

Let another side of the …

2020 July(C01) Math Question 30

Matrices Practice

- Addition & Subtraction

30. The 2 x 2 matrices A and B below are related to matrix C by the equation C=2A-3B. What is matrix C?

Choice F

$$C=2A-3B$$ $$\Rightarrow C=2\begin{bmatrix}3 & 5 …

2020 July(C01) Math Question 31

Statistics Practice

- Mean, Median

31. Jen is doing an experiment to determine whether a high-protein food affects the ability of white mice to ind their way through a maze. The mice in the fi experimental group were given the high-protein food the mice in the control group were given regular food Jen then timed the mice as they found their way through the maze. The table below shows the results Mouse ExperimentalControl number group group I I min 46 see 2 min 13 sec
23452 min 2 sec I min 49 see
2 min 20 sec 2 min 28 sce I min SI
2 min 7 sec I min 4l sec I min 58 sec The average time the mice in the experimental group took to find their way through the maze was how many seconds less than the average time taken by the mice in the control group

Choice B

Experimental group:

1 min 46 …

2020 July(C01) Math Question 32

Probability Practice

- Combinations

32. In the United States, phone numbers begin with a
3-digit area code. Now, there are restrictions on some of the digits, but in the future as more and more area codes are needed. the restrictions may need to be lifted. If, and when. there are no restrictions and eacl of the 3 digits can be any integer from 0 through 9.
how many area codes will be possible?

Choice K

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

Choice C

c01

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

Angles Practice

- Other Shapes

Use the following information to answer questions 35-38
In parallelogram ABCD shown below, the diagonals intersect at E,m∠BDC=42°,m∠BDA=71°,and AB=l4n-5 inches
(Note:The figure is not drawn to scale; mZPQR denotes the measure of∠PQR.)

Choice D

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

Choice K

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

Choice E

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

Choice K

$$\because\ All\ three\ sides\ are\ …

2020 July(C01) Math Question 39

Quadratic Equations Practice

- FOIL

39.Which of the following expressions is equal to
(a+Vbla-2Vb)for all positive real numbers a and b

Choice B

$$=(a+\sqrt{b})a-(a+\sqrt{b})(2\sqrt{b})$$ $$=a^{2}+a\sqrt{b}-2a\sqrt{b}-2b$$ $$=a^{2}-a\sqrt{b}-2b$$

Choice H

$$\pi(30)+\pi(50)=80\pi$$ $$\frac{80\pi}{75}=\frac{80(3.14)}{75}=3.3493$$

Choice B

$$(\frac{4}{5})^{-\frac{3}{2}}=(\frac{5}{4})^{\frac{3}{2}}=\frac{5^{\frac{3}{2}}}{4^{\frac{3}{2}}}$$ $$=\frac{5^{1}\times5^{\frac{1}{2}}}{(2^{2})^{\frac{3}{2}}}$$ $$=\frac{5^{1}\times5^{\frac{1}{2}}}{8}=\frac{5\sqrt{5}}{8}$$

2020 July(C01) Math Question 42

Logarithms Practice

- Logarithm Expressions

42. What is the value of the positive real number x such that log,
=-2?

Choice F

$$\frac{1}{25}=5^{-2}$$ $$\log_{x}{5^{-2}}=-2$$ $$\Rightarrow x^{2}=5^{-2}$$ $$\Rightarrow …

Choice D

$$y=mx+b$$ $$(-4,-5)\rightarrow -5=-4m+b$$ $$(0,-3)\rightarrow -3=0m+b …

2020 July(C01) Math Question 44

Word Problems Practice

- Distance, Speed, Time

44. Rya and Sampath start running laps from the same starting line at the same time and in the same direction on a certain indoor track Rya completes one lap in 16 seconds, and Sampath completes the same lap in 28 seconds. Both continue running at their same respective rates and in the same direction for 10 minutes. What is the fewest number of seconds after starting that Rya and Sampath will again be at their starting line at the same time?

Choice G

$$16=4\times4$$ $$28=4\times7$$ $$[16,28]=4\times4\times7=112$$

Choice D

c01

$$p(c)=1600c-4c^{2}=-4c^{2}+1600c$$ $$=-4c(c-400)$$ $$\Rightarrow c=0,\ c=400$$ …

Choice H

$$a\lt b\lt c\lt d,$$ $$Let\ …

Choice A

$$The\ ratio\ of\ the\ area\ …

2020 July(C01) Math Question 48

Inequalities Practice

- Inequality Expressions

48. What is the set of all integer solutions for the inequality-l sx-V5<4?

Choice G

$$\sqrt{5}\approx2.23$$ $$-1\leq x-\sqrt{5}\leq 4$$ $$\Rightarrow …

Choice D

$$The\ maximum\ force=kSv^{2}$$ $$50=k(1)(40)^{2}=1600k$$ $$\Rightarrow …

Choice J

c01

$$4(10)+16(4)=40+64=104$$ $$104\times4=416$$ $$\frac{416}{12}=34.6$$ $$34.6\div0.6=57.7$$

Choice E

c01

$$\sin 20°=\frac{\overline{OA}}{\overline{OP}}=\frac{r}{r+x}=0.342$$ $$\Rightarrow(r+x)0.342=r$$ $$\Rightarrow(4.368+x)=\frac{4.368}{0.342}=12.77$$ $$\Rightarrow …

2020 July(C01) Math Question 52

Statistics Practice

- Mean, Median

52. The average of 10 test scores is r. When the highest score and lowest score are removed from the 10 scores the average is y Which of the following is an expression for the average of the highest score and lowest score

Choice J

The average of 10 test …

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

Probability Practice

- One Event

54. Each face of 2 cubes with faces numbered from I through 6 has a I chance of landing up when the
2 cubes are tossed. What is the probability that the sum of the numbers on the faces landing up will be less than 6?

Choice G

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

2020 July(C01) Math Question 55

Word Problems Practice

- Distance, Speed, Time

55. At 2:00 P.m., Louisa leaves Kansas City in her car traveling east on I-70 toward St Louis at an average spced of 68 mph. At precisely the same time, Antonio leaves St. Louis in his car traveling west on I-70
toward Kansas Cit y at an average speed of 57 mph The driving distance from St Louis to Kansas City is
10 miles. At what time, to the nearest minute, will they drive past each other on 1-70?

Choice D

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

2020 July(C01) Math Question 56

Angles Practice

- Collinear Points & Triangles

56. There are 10 points in a plane, and no 3 of the points are collinear. These 10 points, taken 2 points at a time determine how many distinct lines?

Choice J

c01

2020 July(C01) Math Question 57

Probability Practice

- Factorials

57. The expression n! (read as n factorial) is defined as the product of all positive integers up to and including n, whenever n is a positive integer. For example.
4!=1·2·3:4. Whenever n is a positive integer which of the following is equivalent to-m31?

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

Quadratic Equations Practice

- FOIL

59.When (x+ I) is expanded and like terms ar combined, what is the coefficient of r.

Choice E

c01

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

Choice K

c01

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