ACT Form A09 Math Answer Explanation


Choice A

$$slope = \frac{3-(-6)}{5-(-2)}>0$$

Choice J

(3 - 4i) + (5 + 3i) = 8 - I

Choice C

$$\frac{630}{x}=\frac{2}{7} $$ $$ x=\frac{630\times7}{2}=2205$$

2018 April(A09) Math Question 4

Angles Practice

- Collinear Points & Triangles

4. Three line segments intersect as shown in the figure below, forming angles with measures of 150°, 40°, and x°, respectively. What is the value of x ?

Choice K

a09

x = 40 + (180-150) = 70

Choice C

a09

$$p=\frac{4\times4}{6\times13}\approx 0.21$$

Choice H

$$9x-y-5=0 \\$$ $$\Rightarrow 9x-5=y \\$$ $$\Rightarrow y=9x-5$$

Choice A

$$XY=5k\\$$ $$YZ=9k \\$$ $$\Rightarrow XZ=14k\\$$ $$\Rightarrow \frac{XY}{XZ}=\frac{5k}{9k}=\frac{5}{9}$$

2018 April(A09) Math Question 8

Inequalities Practice

- Inequality Expressions

8. The solution set of 2x + 4 —8 is the set of all real values of .v such that:

Choice G

$$2x+4\geq -8 \\$$ $$\Rightarrow 2x\geq -8-4 \\$$ $$\Rightarrow x\geq \frac{-8-4}{2}\\$$ $$\Rightarrow x\geq -6$$

Choice E

$$(a^3)^{21}=a^{3\times21}=a^{63}$$

Choice G

$$f(-3)=3(-3)^2+7(-3)-8=-2$$

Choice D

$$2a+(a+3)=93\\$$ $$a=30\\$$ $$a+3=33$$

Choice G

$$a_1=10 \\$$ $$d=2 \\$$ $$a_n=10+2(n-1)=2n+8 \\$$ $$S_n=\frac {a_1+a_n}{2}\cdot n=\frac {10+2n+8}{2}\cdot n=220 \\$$ $$n=11$$

Choice B

$$\frac {9+x}{2}=3 \\$$ $$\frac {-11+y}{2}=-7 \\$$ $$\Rightarrow x=-3 ,\ y=-3$$

2018 April(A09) Math Question 14

Word Problems Practice

- 2 Variable Addition

14. A community theater group performed at 5 local schools. For each school, the table below shows the total number of tickets sold and the total dollar amount collected from ticket sales. At School A, only 2 types of tickets were sold: premium tickets for $10 each and value tickets for $6 each. How many value tickets were sold at School A ?

Choice J

$$t+v=200\\$$ $$10t+6v=1400\\$$ $$\Rightarrow t=50,\ v=150$$

Choice E

$$10\% \times 1800+200=380$$

Choice K

$$median=250 \\$$ $$mean=\frac {200+250+300+150+275}{5}=235 \\$$ $$\Rightarrow median - mean = 250-235=15$$

Choice E

$$Area = \frac{10\times24}{2}=120 \ dm^2$$

2018 April(A09) Math Question 18

Statistics Practice

- Mean, Median

18. The mean of a list of 7 numbers is 85. The first 6 numbers on the list are 82, 93, 68, 93, 70, and 98. What is the 7th number on the list?

Choice J

$$Mean = \frac{82+93+68+93+70+x}{7}=85 \\$$ $$\Rightarrow x=91$$

Choice A

$$\sin A = \frac{7}{25}$$

Choice G

a09

The longer length of the smaller rectangle (S2) = 12-5=7

$$Total\ area = S1+S2=10 \times 5 + 3 \times 7=71$$

Choice A

x+(x+3)+(x+5)=26 => x=6

2018 April(A09) Math Question 22

Word Problems Practice

- Distance, Speed, Time

22. A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assuming the truck continues at 35 mph and its radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty?

Choice J

$$t=\frac{480}{4}=120 \ minutes = 2 …

Choice A

v+c+s=42

c=v+11

v=s+2

=> c=s+13 …

Choice G

$$BC=\sqrt{AC^2-AB^2}=\sqrt{10^2-8^2}=6\\$$ $$BD=\frac{BC}{2}=3\\$$ $$\Rightarrow AD=\sqrt{BD^2+AB^2}=\sqrt{3^2+8^2}=\sqrt{73}$$

Choice C

$$x=\frac{(-2)+(-1)+(-2)+1+4}{5}=0 \\$$ $$y=\frac{4+1+(-2)+(-1)+(-2)}{5}=0 $$

Choice H

$$10, -5, \frac{5}{2}, -\frac{5}{4}, \frac{5}{8}, …

2018 April(A09) Math Question 27

Word Problems Practice

- 1 Variable Equations

27. Alani works 8 hours per day 5 days each week at a custom embroidery shop. Each day Alani is paid either $1.00 per shirt that she stitches or $10.00 per hour, whichever daily amount is higher. Alani stitched the following numbers of shirts: 60 on Monday, 52 on Tuesday, 85 on Wednesday, 80 on Thursday, and 90 on Friday. What is Alani’s total pay for these 5 days?

Choice C

Monday:

The daily amount for …

2018 April(A09) Math Question 28

Quadratic Equations Practice

- Factoring

28. Which of the following most precisely describes the roots of the equation 5×2 + 7x + 2 = 0 ?

Choice H

To find the roots of …

Choice D

a09

$$BC=\sqrt{AB^2+AC^2}=13$$

Total distance of the …

Choice G

The number of students NOT …

Choice D

$$\sqrt{x}+3=6 \\$$ $$\Rightarrow \sqrt{x}=3 \\$$ …

Choice H

$$\sin A = \frac{3}{4}=\frac{BC}{AB}=\frac{12}{AB} \\$$ …

2018 April(A09) Math Question 33

Logarithms Practice

- Logarithm Expressions

33. What integer does 3(log2 16) equal?

Choice A

$$3(\log_2 16)=3(\log_2 2^4)=3(4)=12$$

2018 April(A09) Math Question 34

Probability Practice

- One Event

34. A bag contains several marbles. On 3 successive draws with replacement, a red marble is drawn from the bag each time. Which of the following statements must be: true about the marbles in the bag?

Choice F

F. is apparently true, because …

Choice B

Total distance travelled in 1 …

Choice G

$$\frac{5 \ seconds}{2.25 \ minutes …

Choice E

a09

$$The\ slope \approx \frac{200\ ft}{50\ …

Choice J

$$10^5(0.5\times10^2+2.5\times10+6)=10^5(50+25+6)=81\times10^5=8.1\times10^6 \\$$ $$\Rightarrow 8\times10^6<8.1\times10^6 …

Choice D

A. { 10, 10, 10, …

2018 April(A09) Math Question 40

Perimeter, Area, Volume Practice

- Mixed Shapes

40. Pablo has a deck and pool in his backyard. The deck’s shape is a rectangle with a semicircle removed and is shown shaded in the figure below. The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top of the deck with stain. To decide how much stain to purchase, he needs to find the area of the top of the deck. To the nearest square foot, what is the area of the top of the deck?

Choice K

a09

Diameter of the circle = …

Choice B

a09

a=30-3-3=24 feet

b=40-3-3=34 feet

Therefore, …

Choice F

$$g(f(x))=\frac{1}{4-f(x)}=\frac{1}{4-x^2}$$ Choice F.

Choice C

$$C=2 \pi r=2 \pi \sqrt{2} …

Choice F

a09

The graph of the function …

2018 April(A09) Math Question 45

Conics Practice

- Parabola

45. Which of the following is an equation of a parabola that passes through the 3 points labeled in the standard (x,y) coordinate plane below?

Choice A

Only Choice A satisfies that …

Choice H

When x become really large, …

2018 April(A09) Math Question 47

Probability Practice

- More than One Event

47. Yulan will use a bag of 30 solid-colored marbles for a game in which each player randomly draws marbles from the bag. The number of marbles of each color is shown in the table below.

Choice B

The probability of drawing a …

Choice K

The expression is undefined whenever …

Choice E

$$\frac{\frac{2}{5}+\frac{8}{7}}{2}=\frac{27}{35}$$

Choice H

$$3^{x^2-x-2}=1=3^0\\$$ $$x^2-x-2=0\\$$ $$(x-2)(x+1)=0\\$$ $$\Rightarrow x=2,-1$$

2018 April(A09) Math Question 51

Conics Practice

- Ellipse

51. The ellipse shown in the standard (x,y) coordinate plane below has equation 93)2 + `-Y 255,2 = 1. Which of the

Choice D

a09

The major radius p is …

2018 April(A09) Math Question 52

Probability Practice

- One Event

52. A basket contains 10 solid-colored balls–2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered 1 and 2 (each number is used once), the red balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will he red or have a 3 printed on it?

Choice J

a09

$$p=\frac{3+1}{10}=\frac{4}{10}$$

Choice B

a09

$$Area \ of \triangle ABC …

Choice J

$$\frac{59\%\times66}{15}\times5=12.98$$ Choice J.

2018 April(A09) Math Question 55

Perimeter, Area, Volume Practice

- Mixed Shapes

55. In the diagram below, B, F, and H are on AC, AE, and BF, respectively, and GH I BE. The area of square ABGF is -12-t the area of square ACDE. What percent of the area of ACDE does the shaded portion represent?

Choice D

a09

Area of shaded portion = …

Choice F

The median will stay the …

2018 April(A09) Math Question 57

Matrices Practice

- Multiplication

57. Valley High School and Mountain High School have decided that selected students will attend a daytime theatrical performance that costs $5 for each teacher and $3 for each student. One teacher and 10 students from Valley High will attend, and 2 teachers and 25 students from Mountain High will attend. Which of the following matrix products represents the ticket costs. in dollars, for each high school?

Choice A

The ticket cost is $$5\times1+3\times10$$ …

Choice F

$$I. n\downarrow+(n+1)=(n+1)\downarrow$$ $$(1+2+3+...+n)+(n+1)=1+2+3+...+n+(n+1)=(n+1)\downarrow\\$$ Therefore, I. …

Choice E

a09

$$(x-4)(x-4)\times2=72\\$$ $$x=10 \\$$ $$\Rightarrow 10 …

2018 April(A09) Math Question 60

Quadratic Equations Practice

- Factoring

60. Which of the following quadratic equations has the complex number (1 + V-1) as a solution?

Choice K

Let's start with K. To …