ACT Form C02 Math Answer Explanation


Choice B

$$60=2\times2\times3\times5$$ $$84=2\times2\times3\times7$$ $$126=2\times3\times3\times7$$ $$(64,84,126)=2\times3=6$$

Choice J

$$=(4)(3)(n^{7})(n^{5})$$ $$=12(n^{7+5})$$ $$=12(n^{12})$$

2020 June(C02) Math Question 3

Word Problems Practice

- Cost

3. Devon bought running shoes at a price that was t off the original price of $88. He paid a sales tax of 7% on the discounted price and gave the clerk four $20 bills How much change should he receive

Choice C

$$$88\times\frac{3}{4}=$66$$ $$($20\times4)-($66\times1.07)$$ $$=$80-$70.62$$ $$=$9.38$$

2020 June(C02) Math Question 4

Word Problems Practice

- 2 Variable Addition

4. Brandon is having a bake sale at school to raise S140.00 to donate to the local animal shelter. He sells brownies for $1. 00 each and cookies for $0.50 each Given that Brandon sells 82 brownies, and all sales go to the donation, how many cookies does he need to sell to reach his goal?

Choice J

$$82\times$1+x\times$0.5=$140$$ $$\Rightarrow 0.5x=140-82=58$$ $$\Rightarrow x=116$$

2020 June(C02) Math Question 5

Angles Practice

- Vertex Angles & Bisectors

5. In the figure below, AB is congruent to BC, and AE intersects BF at C. What is the measure of ZB?

Choice D

c02

$$\because \overline{AB}=\overline{BC}$$ $$\therefore \angle BAC=\angle BCA=38°$$ $$\Rightarrow \angle B=180°-38°-38°=104°$$

2020 June(C02) Math Question 6

Statistics Practice

- Mean, Median

6. Patty, Carla, Shada, and Ling ran a race. The bar graph below gives each girl's running time, in seconds. How many of the girls ran the race in less time than the average of the 4 running times?

Choice G

$$(81+84+62+94)\div4=80.25$$

Only one girl ran the race in less time than the average of the 4 running times.

2020 June(C02) Math Question 7

Statistics Practice

- Mean, Median

7. Between 9:00 a, m. and 10:20 a. m. 18 000 visitors entered the Family Fun Amusement Park, Between
9:00 a. m. and 10:20 a. m, an average of how many visitors per minute entered the park?

Choice D

From 9:00 a.m. to 10:20 a.m., a total of 80 minutes.

$$\frac{18000}{80}=225$$

2020 June(C02) Math Question 8

Graphing Properties Practice

- Vectors

8. Given that u and v are vectors such that u=(-1. 3)and v=(5, 8), what is the component form of the vector u+v?

Choice H

$$\Rightarrow (-1+5,3+8)=(4,11)$$

Choice B

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

Choice G

$$r=-3(4)+2$$ $$r=-12+2$$ $$r=-10$$

Choice A

$$f(x)=mx+b$$ $$6=m(8)+b---(1)$$ $$9=m(12)+b---(2)$$ $$(2)-(1)$$ $$\Rightarrow 3=4m$$ $$\Rightarrow m=\frac{3}{4}$$ $$f(x)=\frac{3}{4}x+b$$ $$6=6+b$$ $$b=0$$ $$f(n)=\frac{3}{4}n$$

Choice G

$$f(-5)=-4(-5)^{2}=-4(25)=-100$$

Choice B

$$=4(-1)^{3}-2(-1)^{2}$$ $$=-4-2$$ $$=-6$$

Choice H

c02

$$9\times6+4\times11$$ $$=54+44$$ $$=98$$

Choice C

c02

The slope is negative and intersects the Y axis at a position where Y is greater than 0, so the Y axis intercept is positive.

Choice G

$$4x+2=-10$$ $$\Rightarrow 4x=-12$$ $$\Rightarrow x=-3$$ …

Choice B

c02

According to the picture provided, it can be observed that the maximum value of this function, that is, the maximum value of Y is 3.

2020 June(C02) Math Question 18

Statistics Practice

- Mean, Median

18. Renata took 9 quizzes in German class. Her scores, in order, were 6.7.7.6.8.7.8. 10, and 9. She discovered a scoring error on the 9th quiz, and her score on that quiz was corrected to 10. Which of the following measures of central tendency changed as a result of the correction?
I. Mean IL. Median III. Mode

Choice F

The mean is the average of the numbers.

The Median is the "middle" of a sorted list of numbers.

The mode is the number that is repeated more often than any other.

$$6,7,7,6,8,7,8,10,9$$

Rearrange the 9 scores in order.

$$\rightarrow 6,6,7,7,7,8,8,9,10$$ $$Mean=(6+6+7+7+7+8+8+9+10)\div9=68\div9\approx7.55$$ $$Median=7$$ $$Mode=7$$

After correcting the 9th score to 10.

$$\rightarrow 6,6,7,7,7,8,8,10,10$$ $$Mean=(68+1)\div9\approx7.66$$ $$Median=7$$ $$Mode=7$$

Only the mean is changed.

Choice E

Parallel lines have the same slope and will never intersect.

$$y=\frac{2}{3}x+4$$ $$\Rightarrow Slope=\frac{2}{3}$$

Only the E option has the same slope.

Choice H

$$\tan \theta=\frac{Opposite}{Adjacent}$$ $$\tan B=\frac{1}{\sqrt{2}}$$

Choice E

c02

It's very clear after drawing …

Choice J

1 foot is equal to …

Choice E

1 foot is equal to …

Choice H

c02

$$2^{2}=1^{2}+x^{2}$$ $$\Rightarrow x=\sqrt{3}$$ $$1:\sqrt{3}:2$$

It …

Choice E

$$x\times x+(x-2)(x-2)$$ $$=x^{2}+x^{2}-4x+4$$ $$=2x^{2}-4x+4$$

Choice H

$$\frac{5}{2}x+\frac{3}{4}y=-\frac{1}{2}$$ $$\Rightarrow 4\times\frac{5}{2}x+4\times\frac{3}{4}y=4\times(-\frac{1}{2})$$ $$\Rightarrow 10x+3y=-2$$ …

Choice D

$$0.5+34.2(0.05)$$ $$=0.5+1.71$$ $$=2.21$$

Choice F

$$5.75\div0.5=11.5$$

Choice D

$$x+y=116---(1)$$ $$0.03x+0.05y=4.34---(2)$$ $$(1)\times5-(2)\times100$$ $$(5x+5y)-(3x+5y)=580-434$$ $$2x=146$$ …

Choice J

$$V=\pi r^{2}h$$ $$V=3.14(6)^{2}(5)=565.2$$ $$565.2\times2,205=1,246,266$$

It's …

2020 June(C02) Math Question 31

Word Problems Practice

- 2 Variable Addition

31. Admission to a carnival is s4 for children and $6 for adults. A group of 21 people pays $90 for admission to the carnival. What is the ratio of the number of children to the number of adults in this group

Choice C

$$Children: x$$ $$Adults: y$$ $$x+y=21---(1)$$ …

Choice K

$$(\frac{2x^{3}y^{-5}z^{8}}{8x^{-2}y^{6}z^{3}})^{-2}$$ $$=(\frac{2}{8})(\frac{x^{3}y^{-5}z^{8}}{x^{-2}y^{6}z^{3}})^{-2}$$ $$=(\frac{1}{4})(x^{3-(-2)}y^{-5-6}z^{8-3})^{-2}$$ $$=(2^{-2})(x^{5}y^{-11}z^{5})^{-2}$$ $$=(2^{(-2)(-2)})(x^{5(-2)}y^{(-11)(-2)}z^{5(-2)})$$ …

Choice D

$$g(-1)=(-1)^{2}-1=1-1=0$$ $$f(g(-1))=f(0)=2(0)+3=3$$

2020 June(C02) Math Question 34

Probability Practice

- Combinations

34. In a window display at a flower shop, there are 3 spots for I plant each. To fill these 3 spots, Adam has
7 plants to select from m, each of a different type Selecting from the 7 plants, Adam can make how many possible display arrangements with I plant in each spot?
(Note:The positions of the unselected plants do not matter.

Choice J

Choose a pot from the …

Choice B

Area of a trapezoid is …

Choice H

First calculate the area of …

Choice A

$$The\ large\ rectangle=ab$$ $$The\ shaded\ …

2020 June(C02) Math Question 38

Probability Practice

- Combinations

38. A company prints contest codes on its fun-size bags of candy. Each 6-character code consists of the letter A followed by the letter H followed by 4 of the digits o through 9. The digits may repeat. Which of the following expressions gives the number of different
6-character codes that are possible?

Choice F

$$Code\rightarrow A-H-Number-Number-Number-Number$$ $$Number:(1,2,3,4,5,6,7,8,9,0)$$ $$\Rightarrow 1(1)(10)(10)(10)(10)$$

2020 June(C02) Math Question 39

Statistics Practice

- Mean, Median

39. The mean of the daily high temperatures for a 5-day period in a certain city was recorded as being 4.0F was later determined that the high temperature for I of these 5 days was recorded incorrectly. If that day's high temperature was 2 F higher than originall recorded. what is the difference between. the incorrectly recorded mean and the correct mean?

Choice A

$$2\div5=0.4$$

2020 June(C02) Math Question 40

Probability Practice

- One Event

40. A box contains 6 objects. Of those, 3 are disks (2 blue and I red) and 3 are triangles(I blue, I red, and I yellow)。 If the probability of drawing each object is the same, what is the probability that an object drawn from the box is a blue object or a triangle?

Choice K

The box cotains 6 objects. …

2020 June(C02) Math Question 41

Logarithms Practice

- Logarithm Expressions

41. When log4 x=-3, what is x

Choice A

$$\log_{4}{x}=-3$$ $$\Rightarrow \log_{4}{4^{-3}}=-3$$ $$\Rightarrow x=4^{-3}=\frac{1}{64}$$

Choice J

c02

$$41-50\rightarrow 2$$ $$51-60\rightarrow 3$$ $$61-70\rightarrow …

Choice D

c02

The Median is the "middle" …

Choice F

$$4\times2=8$$ $$8-3=5$$

Choice B

$$x-1=x-1$$ $$-(x-1)=x-1$$ $$-x+1=x-1$$ $$\Rightarrow x=1$$ …

Choice F

We require that the value …

2020 June(C02) Math Question 47

Conics Practice

- Ellipse

47. Which of the following equations determines the ellipse shown in the standard (x, y) coordinate plane below?

Choice C

c02

$$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ $$\Rightarrow \frac{x^{2}}{5^{2}}+\frac{y^{2}}{3^{2}}=1$$ $$\Rightarrow 9x^{2}+52y^{2}=1\times9\times25$$ …

2020 June(C02) Math Question 48

Quadratic Equations Practice

- Factoring

48. Given that x=-2 is a solution to x'+bx-6=0,which of the following polynomials is a factor of x+bx-6?

Choice F

$$(-2)^{2}+(-2)b-6=0$$ $$\Rightarrow 4-2b-6=0$$ $$\Rightarrow -2=2b$$ …

Choice C

c02

$$\Rightarrow 1:7$$

Choice G

$$12\div2=6$$ $$1+2+3=6$$ $$\mid-3\mid+\mid-2\mid+\mid-1\mid+\mid0\mid+\mid1\mid+\mid2\mid+ \mid3\mid$$ $$=3+2+1+0+1+2+3$$ …

Choice C

c02

$$f(g(x))$$ $$=\sqrt{(x-3)^{3}}+1$$

If x < 3, you would be taking the square root of a negative number, so x ≥ 3.

Choice G

$$(0,0)$$ $$\rightarrow(0+4,0)=(4,0)$$ $$\rightarrow(4,0-1)=(4,-1)$$ $$\rightarrow(4+2,-1)=(6,-1)$$ $$\rightarrow(6,-1-6)=(6,-7)$$ …

Choice B

A Rational Number can be …

Choice K

Let X be -0.5 and …

Choice E

c02

$$8:00\ a.m.\ \rightarrow \sin \theta=\frac{2}{6}$$ …

Choice K

$$\frac{2-i}{-3+i}$$ $$=\frac{(2-i)(-3-i)}{(-3+i)(-3-i)}$$ $$=\frac{-6-2i+3i+i^{2}}{(-3)^{2}-(i)^{2}}$$ $$=\frac{-6+i-1}{9-(-1)}$$ $$=\frac{(-7+i)}{10}$$ …

2020 June(C02) Math Question 57

Angles Practice

- Other Shapes

57. The degree measures of the interior angles of a certain pentagon are in the ratio 2:3:4:4:5. What is the measure of the largest interior angle of this pentagon?

Choice E

The sum of the internal …

Choice K

c02

The absolute value sign is …

2020 June(C02) Math Question 59

Word Problems Practice

- Cost

59. The sale price of a jacket is 10%o off the original price The clearance price of the jacket is 30% off the sale price. The clearance price is what percent off the original price?

Choice D

$$The\ clearance\ price$$ $$=The\ sale\ …

Choice F

$$2\pi r=2 \pi\times2=4\pi$$ $$\frac{4\pi}{4}=\pi$$