ACT Form B02 Math Answer Explanation


2019 June(B02) Math Question 1

Word Problems Practice

- Cost

1. A calculator has a regular price of $59.95 before taxes It goes on sale at 20% below the regular price. Before taxes are added, what is the sale price of the calculator? calculator?

Choice D

$$$59.95\approx$60$$ $$\frac{20}{100}\times$60=$12$$ $$$60 - $12 = $48$$ $$$48\approx.$47.96$$

Choice F

$$(r + b - g)(b + g) = [6 + 4 -(-9)][(4+(-9)] = 19\times(-5)= -95$$

Choice E

$$\angle ACB = 180°- \angle ABC - \angle BAC = 180° - 108° - 42° = 30°$$ $$\angle ACD = 180° - \angle ACB = 180° - 30° = 150°$$

Choice H

$$X=(17-10)\cdot\frac{5}{3}=\frac{35}{3}$$

Choice C

b02

$$9^{2}+2^{2}=C^{2}$$ $$81+4=85=C^{2}$$ $$C=\sqrt{85}$$

2019 June(B02) Math Question 6

Probability Practice

- One Event

6. A bag contains exactly 18 solid-colored buttons: 3 red,
5 blue; and 10 white. What is the probability of
randomly selecting 1 button that is NOT white?

Choice H

White : 10

Not-white : 3 red + 5 blue = 8

The probability of randomly selecting 1 button that is NOT white

$$= \frac{8}{10+8}=\frac{8}{18}=\frac{4}{9}$$

2019 June(B02) Math Question 7

Statistics Practice

- Mean, Median

7. What is the sum of 3 consecutive odd integers whose
mean is 27?

Choice C

Sum of 3 consecutive odd integers

$$= 27\times3 = 81$$

Choice K

1: 1+0=1

4: 2+2=4

6: 4+2=6

7: 5+2=7

8 is NOT a possible sum of those 2 numbers

Choice B

$$\widetilde{13}=6.6 miles$$ $$\widetilde{23}=4.5 miles$$ $$\widetilde{25}=9.7 miles$$ $$\widetilde{12}=\widetilde{13}-\widetilde{23}=6.6-4.5=2.1 miles$$ $$\widetilde{15}=\widetilde{12}+\widetilde{25}=2.1+9.7=11.8 miles$$

Choice H

b02

The perimeter of the hexagon:

$$6\times10=60$$

Choice D

N: the maximum number of bats that can be produced by the company

$$ $3,500+$2\times N =$15000 $$ $$ $2\times N = $11500 $$ $$N=5750 $$

Choice G

$$3x+2=4$$ $$\Rightarrow 3x=2$$ $$\Rightarrow x=\frac{2}{3}$$ $$2y+6=5$$ $$\Rightarrow 2y=-1$$ $$\Rightarrow y=\frac{-1}{2}$$ $$x+y=\frac{2}{3}+\frac{-1}{2}=\frac{4}{6}+\frac{-3}{6}=\frac{1}{6}$$

Choice C

$$\require{cancel} $$ $$\frac{ 15x ^{2}+25x}{5x}=\frac{\cancel{5}(3x^{2}+5x)}{\cancel{5}x}=\frac{3x^\cancel{2}+5\cancel{x}}{\cancel{x}}=3x+5$$

Choice K

$$ {\displaystyle \left\vert -5\right\vert^{2} =25}$$ $$\Rightarrow\frac{\displaystyle \left\vert -5\right\vert^{2}+(-1)}{(16\div4)\times2-5}=\frac{25-1}{4\times2-5}=\frac{24}{8-5}=\frac{24}{3}=8$$

Choice D

This special savings account will double every 5 years.

$$ \because 40\ years = 5\ years\times 8 $$

Therefore, this account will double 8 times.

$$ $2000\times 2^{8}=$2000\times256=$512000 $$

Choice F

2 hours ~ 4 hours:

the number of hours the amount of water in the pond remained constant.

Choice B

lf it rains in Franklin City on a particular day, the probability that it will rain there the following day is 0.70.

Therefore,

if it rains on a Monday,

the probability that it will NOT rain there the following day is

1 - 0.70 = 0.30

Choice G

$$5x=9y+18$$ $$\Rightarrow 9y=5x-18$$ $$\Rightarrow y=\frac{5}{9}-2$$

Choice B

b02

$$Slope=\frac{y-y_{0}}{x-x_{0}}$$ $$\Rightarrow \frac{4-0}{0-2}=-2$$ $$\Rightarrow y=-2x+4$$

2019 June(B02) Math Question 20

Angles Practice

- Parallel Lines

20. In the figure below, line m is perpendicular to line n, and
line p is parallel to line q. Lines m, n, and p intersect at a
single point Some angle measures are given. What is
the value of x ?

2019 June(B02) Math Question 21

Probability Practice

- More than One Event

21. A bag contains 10 solid-colored marbles of the same
size: 3 red, 2 green,.1 yellow, and 4 blue. Which of the
following expressions gives the probability of drawing,
at random and without replacement, a blue marble on
the 1st draw, a green marble on the 2nd draw, and a
blue marble on the 3rd draw?

Choice D

b02

The 1st draw: a blue …

2019 June(B02) Math Question 22

Probability Practice

- One Event

22. A physical education teacher recorded the distances, in
inches, that her students jumped during a long jump
lesson. The distances of 1 jump by each of the students
are represented in the stem-and-leaf plot below.

Choice K

b02

At least 60 inches ⇒ …

Choice C

$$f(x)=5-3x $$ $$\left\{-1,0,2\right\} $$ $$f(-1)=5-3(-1)=8$$ …

Choice F

$$100 cubic feet =15\times 1\frac{1}{3}\times …

Choice C

b02

Choice H

b02

$$\frac{h}{15}=\sin56°$$ $$h=15 \sin56°$$

Choice C

The amount of iodine-131 remaining …

Choice F

$$\sqrt[4]{256x^{16}}=(256x^{16})^{\frac{1}{4}}$$ $$=256^{\frac{1}{4}}\times (x^{16})^{\frac{1}{4}}$$ $$=(16^{2})^{\frac{1}{4}}\times x^{4}$$ …

Choice C

b02

The formula for the circumference …

Choice G

b02

$$Area= 8\times18-4\times x^{2} =144-x^{2}$$

Choice E

b02

A(-5,1-10)=A(-5,-9)

Choice J

b02

$$\tan\theta=\frac{20}{40}$$ $$\Rightarrow\theta=\tan^{-1}\frac{20}{40}$$

Choice D

b02

$$ Area = \frac{1}{2}\times6\times6=18 $$

Choice G

b02

Choice A

$$\because y=mx+b$$ $$A(0,6)\Rightarrow6=0+b\Rightarrow b=6$$ $$B(6,0)\Rightarrow0=m\cdot6+6\Rightarrow …

Choice K

$$\frac{9}{5}=1.8 $$ $$1.\overline{8}=1.88888... $$ $$1.08=1.08$$ …

2019 June(B02) Math Question 37

Statistics Practice

- Mean, Median

37. Andre's Floral Shop asked each of 20 customers to
give a rating of the shop's service. The table below
, summarizes the 20 customer ratings.
Which of the following values is closest to the mean of
the 20 customer ratings?

Choice A

$$\frac{6\times3+8\times2+2\times1+4\times0}{20}$$ $$=\frac{18+16+2+0}{20}$$ $$=\frac{36}{20}$$ $$=\frac{9}{5}=1.8$$

Choice G

$$(F)14+(\frac{-1}{40})=14-(\frac{1}{40})$$ $$(G)14-(\frac{-1}{40})=14+\frac{1}{40}$$ $$(H)14\div(\frac{-1}{40})=14\times(-40)=-560$$ $$(J)14\times(\frac{-1}{40})=\frac{-14}{40}$$ $$(K)\frac{14+\frac{-1}{40}}{2}=7+\frac{-1}{80}$$

Choice E

$$H=0.75\times(200-A)$$

2019 June(B02) Math Question 40

Word Problems Practice

- Temperature

40. The equation t = -0.0066a + 15 models the noon
temperature, t degrees Celsius,  a meters above sea
level, on a certain day on Laurel Mountain. According
to. this equation, what would be the noon temperature
for that certain day on Laurel Mountain at sea level?

Choice J

t=-0.0066a+15

t : degrees Celsius …

Choice C

b02

$$The\ formula\ for\ the\ area\ …

2019 June(B02) Math Question 42

Conics Practice

- Circles

42. Which of the following equations is that of a circle that
is in the standard (x,y) coordinate plane, has center
(1,--4), and has a radius of 5 coordinate units?

Choice J

$$(x-h)^{2}+(y-k)^{2}=r^{2}$$ $$(h,k)=(1,-4)$$ $$r=5$$ $$\Rightarrow (x-1)^{2}+(y+4)^{2}=5^{2}$$

Choice D

$$5= 1\times5 \Rightarrow1,5$$ $$6=1\times6, 2\times3 …

Choice K

$$49^{a}= (7^{2})^{a}=7 $$ $$\Rightarrow a=\frac{1}{2}$$ …

Choice A

b02

$$(A)16\times16=256,\ 16\times4=64$$ $$(B)17\times17=289,\ 17\times4=68\gt64$$ $$(C)14\times16=224\lt256,\ …

Choice J

$$\frac{3}{5}-(\frac{-1}{3})$$ $$=\frac{9}{15}+\frac{5}{15}=\frac{14}{15}$$ $$\frac{14}{15}=1-\frac{1}{15} \Rightarrow \frac{14}{15} …

Choice B

$$a_{1}=10 $$ $$a_{n}=a_{n-1}+5 $$ $$\Rightarrow …

2019 June(B02) Math Question 48

Probability Practice

- More than One Event

48. The probabilities that each of 2 independent events
will occur are given in the table below.

Choice F

$$P(A\ and\ B)=P(A)\times P(B) $$ …

2019 June(B02) Math Question 49

Quadratic Equations Practice

- Factoring

49. What is the solution set of the equation
x4 +21x 2 -100=0?

Choice E

$$x^{4}+21x^{2}-100=0 $$ $$Let\ x^{2}=a, $$ …

Choice F

b02

$$\sin37°=\frac{1000}{d}$$ $$\Rightarrow d=\frac{1000}{\sin37°}$$

Choice E

$5000 in 1 day

Tickets …

2019 June(B02) Math Question 52

Word Problems Practice

- Distance, Speed, Time

52. Jarrod went on Tour A, and his trip. covered a distance
of 6 miles. Bhumi went on Tour C, and her trip covered
a distance of 9 miles. Which of the following values is
the difference, in miles per hour, of the average speeds
of their balloons during their tours?

Choice G

$$Speed=\frac{Distance}{Time}$$ $$6\ miles\div \frac{45}{60}\ hours …

Choice A

b02

$$\frac{perimeter}{4}=\frac{130+x+y}{4}$$ $$\frac{x}{\sin47°}=\frac{130}{\sin91°}=\frac{y}{\sin42°}$$ $$x=\frac{130\sin47°}{\sin91°}$$ $$y=\frac{130\sin42°}{\sin91°}$$ $$\Rightarrow\frac{perimeter}{4}=\frac{130+\frac{130\sin47°}{\sin91°}+\frac{130\sin42°}{\sin91°}}{4}$$

Choice G

$$21=3\times7 $$ $$22=2\times11 $$ $$23=23 …

2019 June(B02) Math Question 55

Inequalities Practice

- Intersection of Lines

55. ·The graph of y= x+1, y= x-3 and x2 + y2= 9 are
shown in the standard (x,y) coordinate plane below.
The, shaded region is the solution set to one o{ the
following systems of inequalities. Which system is it?

Choice A

b02

Choice J

b02

$$g(x)=-[f(x)-3]$$ $$g(4)=-[f(4)-3]$$ $$f(4)=-1$$ $$\Rightarrow g(4)=-[(-1)-3]=4$$

Choice D

$$\require{cancel} $$ $$\frac{a}{b}=\frac{6}{1}\Rightarrow a=6b $$ …

2019 June(B02) Math Question 58

Statistics Practice

- Mean, Median

58. The frequency histogram below shows the distribution '
of the heights, in inches, of 11 basketball players.

Using the data from the frequency histogram, what is
the sum of the mean the median of this distribution?

Choice F

b02

$$Median=70 $$ $$Mean=\frac{66\times3+68\times2+70+73+74+76+77\times2}{11}=71 $$ $$Median+Mean=141$$

Choice A

Definition of y-intercept: the y-coordinate …

2019 June(B02) Math Question 60

Matrices Practice

- Multiplication

60. What is the matrix product [2 4 ] [a b] ? _

Choice K

b02