ACT Form Z15 Math Answer Explanation


Choice A

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

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

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

=11(-3)

=-33

Choice J

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

Choice B

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

Choice H

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

2019 April(Z15) Math Question 5

Probability Practice

- One Event

5. A bag contains exactly 21 solid-colored buttons ns:3 red 6 blue, and 12 white. What is the probability of randomly selecting I button that is NoT white?

Choice C

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

Choice G

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

Choice A

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

2019 April(Z15) Math Question 8

Word Problems Practice

- Distance, Speed, Time

8. When Jorge began a driving trip, his car's odometer read 42 miles. After Jorge drove for 3 hours, the odometer read 165 miles. Which of the following values is closest to Jorge's average driving speed, in miles per hour, during those 3 hours?

Choice G

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

Choice A

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

Choice F

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

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

Word Problems Practice

- 2 Variable Addition

12. Tanisha, a manager at a state park, counted the money in the cash register at the end of her shift, and then she deposited the money in the bank. When she went back to her office, she accidentally shredded the deposis ip. She remembered that there were only $5 and $10 bills. She also recalled that there were 27 bills totaling S205. How many $5 bills were in Tanisha's cash register at the end of her shift?

Choice F

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

Choice A

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

Choice H

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

2019 April(Z15) Math Question 16

Angles Practice

- Vertex Angles & Bisectors

16. In the figure below,  xw intersects vz at y,  the measure of ∠XYV  is(3x+5)°,  and the measure of
∠ZYW is(4x-6)°.  What is the measure of ∠XYZ?

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

Probability Practice

- One Event

17. The table below shows the letter grades 60 students earned on the final exam in American Literature. The highest possible grade is A:the lowest possible grade is F.
A student from this group will be chosen at random What is the probablity that the student's final exam grade is C or higher?

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

Quadratic Equations Practice

- Factoring

18. For what value of n does the quadratic equation x-2r+n=0 bave solutions of x=4 and x=-2?

Choice F

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

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

Probability Practice

- Combinations

20. The app plication for a license plate states that the license late number has 3 letters followed by a 3-digit number, for exampie, AEE123 The letters O and I and the digit 0 cannot be part of the license plate number.
Any of the other letters and digits may be used up to 3 times. Which of the following expressions represents how many different license plate numbers are possible?

Choice H

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

Choice E

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

Choice K

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

2019 April(Z15) Math Question 23

Angles Practice

- Collinear Points & Triangles

23. Marie is building a kite. In a drawing of her kite.
shown below BC, AD=DC, the measure of ∠ABC is80°, and the measure of ∠ADC is50°.What is the measure of ∠BAD?

Choice D

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

Choice K

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

Choice C

$$\because1\ foot =12\ inches$$ $$\therefore …

Choice F

z15

$$\Rightarrow 10:5=3:x$$ $$x=3\times\frac{1}{2}=1.5$$

Choice B

$$t=10,\ v=5$$ $$t=20,\ v=3$$ $$\frac{3-5}{20-10}=\frac{-2}{10}=-\frac{1}{5}$$

2019 April(Z15) Math Question 28

Word Problems Practice

- Distance, Speed, Time

28. Calen started his bike ride earlier than Shasta. During the first 15 seconds of Shasta s ride, Calen was traveling at a constant speed equal to 5 of Shasta's maximum speed during that same time period. How far, in meters, did Calen travel during the first 15 seconds of Shasta's ride?

Choice H

$$Shasta's\ maximum\ speed:\ 5$$ $$\frac{1}{2}\times5\times15=37.5$$

Choice D

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Choice J

$$\frac{2}{3}-\frac{5}{6}(\frac{2}{5}+\frac{1}{10})$$ $$=\frac{2}{3}-\frac{5}{6}(\frac{4}{10}+\frac{1}{10})$$ $$=\frac{2}{3}-\frac{5}{6}\times\frac{5}{10}$$ $$=\frac{2}{3}-\frac{5}{12}$$ $$=\frac{8}{12}-\frac{5}{12}$$ …

Choice E

$$(x+2)(2x+7)$$ $$=2x^{2}+7x+4x+14$$ $$=2x^{2}+11x+14$$

Choice H

$$F.\ 2\lt\sqrt{3}\lt4 $$ $$\Rightarrow 2=\sqrt{4} …

2019 April(Z15) Math Question 33

Probability Practice

- More than One Event

33. Two fair coins are repeatedly tossed simultaneously.
What is the probability that both coins land heads up on the 36th toss?

Choice E

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

2019 April(Z15) Math Question 34

Statistics Practice

- Mean, Median

34. Suppose a student's course grade is determined solely by that students scores on 8 tests, which are worth 100 points each. If Bane has an average of exactly 88 points on the first 6 tests, how many points must he average on the last 2 tests to earn exactly a 90-point course grade?

Choice G

$$\frac{88\times6+2x}{8}=90$$ $$\Rightarrow 528+2x =720$$ $$\Rightarrow …

Choice C

$$A.\ (62+(-\frac{1}{65}))\div2=31-\frac{1}{130}$$ $$B.\ 62\div(-\frac{1}{65})=-62\times65=4030$$ $$\checkmark …

Choice F

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

Choice D

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

Choice G

z15

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

Choice E

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

2019 April(Z15) Math Question 40

Conics Practice

- Parabola

40. In the standard (x,) coordinate plane, given Parabola A with equation y= 3x. Parabola B is the image of Parabola A after a shift of 7 coordinate units to the left and 4 coordinate units down. Parabola B has which of the following equations?

Choice J

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

Choice E

$$Less\ than\ $100$$ $$\Rightarrow(Less\ than\ …

Choice G

$$At\ least\ $150\ each\ week$$ …

2019 April(Z15) Math Question 43

Angles Practice

- Circles

43. A pollster will create a circle graph using the information in the table. One sector of the circle grap will represent the percent of adults in the sample who said they spend an average of $300 or more on food each week. What will be the measure of the central angle for that sector?

Choice C

$$$300\ or\ more:\ 0.1$$ $$\Rightarrow …

Choice F

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

Take …

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

$$Yolanda:\ y$$ $$Xavier:\ x$$ $$Zach:\ …

Choice D

$$1-(-2)=3$$ $$10-1=9$$ $$\sqrt{3^{2}+9^{2}}=\sqrt{9+81}=\sqrt{90}$$

Choice J

$$100=10\times10\times1$$ $$\Rightarrow 20\times20\times2=800$$

Choice D

$$\mid x-2 \mid\lt7$$ $$\Rightarrow -7\lt …

Choice G

$$380,204,032$$ $$F.\ 1\ and\ 10$$ …

2019 April(Z15) Math Question 51

Matrices Practice

- Multiplication

51. Given A=  , B=  , and C=  , if it is possible to calculate C+AB, which of the following matrices is the result?

Choice B

$$AB$$ $$=\begin{bmatrix}2(-3)+0(4)+3(1) & 2(1)+0(1)+3(2) \\(-1)(-3)+5(4)+(-2)1 …

Choice H

$$\frac{x+y}{y}$$ $$=\frac{x}{y}+\frac{y}{y}$$ $$=\frac{x}{y}+1$$

Clearly that …

Choice C

$$t=2\ hours,\ v_{2}=15$$ $$t=4\ hours,\ …

2019 April(Z15) Math Question 54

Probability Practice

- More than One Event

54. A fair spinner with 4 equally sized regions and an arrow has regions numbered 1,2,3 and 4 respectively,
and a second fair spinner with 5 equally sized regions and an arrow has regions numbered 1, 2, 3, 4 and 5.
respectively. The arrows are both spun at the same time, and the numbers the 2 arrows land on are multiplied together.  What is the probability that this product is an odd number?

Choice K

$$(1).\ 1,2,3,4 \rightarrow Odd:1,3$$ $$(2).\ …

Choice A

$$Area=630\ square\ feet$$ $$Depth=5\ ft$$ …

Choice K

$$3!=3\times2\times1$$ $$N!= N(N-1)(N-2)...1$$ $$\Rightarrow (a!)^{b}=[a(a-1)(a-2)...1]^{b}$$

2019 April(Z15) Math Question 57

Statistics Practice

- General Statistics

57. The standard normal probability distribution function
( =0 and o=l) is graphed in the standard(xy)
coordinate plane below. Which of the following percentages is closest to the percent of the data points that are within 2 standard deviations of the mean in any normal distribution?

Choice D

z15

2019 April(Z15) Math Question 58

Matrices Practice

- Determinants

58. For what value of b will the determinant of the matrix
[    ] have a value of 18?

Choice G

$$\begin{bmatrix}a & b \\c & …

2019 April(Z15) Math Question 59

Quadratic Equations Practice

- Factoring

59. What are the solutions to x-2x +17=0?

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

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