ACT Form 73G Math Answer Explanation


Choice B

$$|3(-2)+4|=|-6+4|=|-2|=2$$

Choice G

$$\frac{123.25}{\frac{55.25}{13}}=29$$

Choice B

$$\sqrt{\frac{m}{x-3}}=\sqrt{\frac{-16}{-1-3}}=\sqrt{4}=2$$

Choice H

$$ax-bx+cx=x(a-b+c)$$

2015 April(73G) Math Question 5

Word Problems Practice

- Cost

5. Hai has $100 available to buy USB drives to back up data for his business computers. Each USB drive has a price of $8, and Hai will pay a sales tax of 7% of the total price of the USB drives. What is the maximum number of USB drives Hai can buy?

Choice A

$$\frac{$100}{$8\times 107\%}=11.68\approx 11$$

Choice H

$$\sqrt{4^2+5^2}\approx6.4$$

Choice D

$$\frac{3150}{50}=63 \\$$ $$ \frac{3150}{70}=45 \\$$ $$ \frac{3150}{90}=35$$ Choice D.

Choice J

Let the number of small wreaths be x, thus the number of large wreath 2x: $$30\times 2x+20\times x=4\times 60 \\$$ $$ \Rightarrow x=3 \\$$ $$ \Rightarrow 2x=6$$

Choice E

The ratio ranges from 0 to 1.

Choice H

Distance = |(-7)-(-14)|=7

Choice E

$$3b-7=b+1 \\ $$ $$\Rightarrow2b=8 \\$$ $$ \Rightarrow b=4$$

Choice J

For Ben's:

Total charge = Number of miles

For Ronnie's:

Total charge = 0.5 Number of miles +40

Number of miles = 0.5 Number of miles +40

Number of miles = 80

2015 April(73G) Math Question 13

Angles Practice

- Circles

13. In the figure below, G is the center of the circle, LK is a diameter, H lies on the circle, J lies outside the circle on LK, and JM is tangent to the circle at M. Which of the following angles or minor arcs has the greatest degree measure?

Choice A

Apparently LM is greater than 90°, while the rest are either equal to or smaller than 90°.

2015 April(73G) Math Question 14

Probability Practice

- One Event

14. A bowl contains 6 red beads, 8 black beads, and a number of green beads. There are no other beads in the bowl. The probability of randomly choosing a black bead from the bowl is 1/3. How many green beads are in the bowl?

Choice H

$$\frac{8}{6+8+g}=\frac{1}{3} \\$$ $$\Rightarrow g =10$$

Choice C

$$\frac{x}{60}=\frac{28}{40} \\$$ $$\Rightarrow x=42$$

2015 April(73G) Math Question 16

Perimeter, Area, Volume Practice

- Mixed Shapes

16. Marcie will paint the shaded region (1 pentagonal wall) of the outside of the playhouse shown below. All given dimensions are in feet. Each 1-quart container of paint will cover 50 square feet, and only 1 coat of paint will be applied. How many 1-quart containers of paint will Marcie need in order to cover the 1 pentagonal wall of the playhouse?

Choice G

$$Area \ of \ shaded \ region=12\times 6+ \frac{12\times3}{2}=80 \ square \ feet$$ Since one 1-quart container of paint will cover 50 square feet, 2 will be needed.

Choice D

$$\frac{6.0\times10^{16}}{1.5\times 10^{8}}=4.0\times10^8 \ seconds$$

2015 April(73G) Math Question 18

Angles Practice

- Parallel Lines

18. In the figure below, AE and BD intersect at C, and AB || DE. Which of the following angles must have the same measure as BAC?

Choice K

Since AB and DE are parallel, $$\angle A=\angle E$$ Also, since: $$\angle BCA=\angle DCE$$ It follows that $$\angle BAC=\angle CED$$

Choice A

$$\frac{8+x}{2}=2 \\$$ $$ \Rightarrow x=-4\\ $$ $$\frac{-8+y}{2}=-4 \\ $$ $$\Rightarrow y=0$$

Choice J

Let the lesser integer be n: $$(2n+1)n=78 \\$$ $$ \Rightarrow n=6\\ $$ $$\Rightarrow 2n+1=13$$

2015 April(73G) Math Question 21

Probability Practice

- One Event

21. A set of numbers consists of all the odd integers that are greater than 1 and less than 21. What is the probability that a number picked at random from the set will be divisible by 3 ?

Choice A

The set of numbers are: …

Choice J

Let the number of points …

2015 April(73G) Math Question 23

Quadratic Equations Practice

- Factoring

23. For what 2 values of x is the equation x2 — 5x + 6 = 0 true?

Choice E

$$x^2-5x+6=0 \\$$ $$ \Rightarrow (x-2)(x-3)=0 …

Choice K

The colony is doubled 15/3=5 …

2015 April(73G) Math Question 25

Probability Practice

- Combinations

25. Audrey will take biology, algebra, and Spanish next year. Audrey will have 1 of the 3 teachers who teach biology, 1 of the 4 teachers who teach algebra, and I of the 2 teachers who teach Spanish. From among these 9 teachers, how many possibilities are there for Audrey's 3 teachers for the 3 classes?

Choice C

$$3\times4\times2=24$$

2015 April(73G) Math Question 26

Matrices Practice

- Addition & Subtraction

26. What value of x satisfies the matrix equation below?

Choice G

$$2x+1=9 \\$$ $$ \Rightarrow x=4$$

2015 April(73G) Math Question 27

Statistics Practice

- Mean, Median

27. Sophia's goal this past summer was to save an average of $5.00 per week for 10 weeks. She saved an average of $4.00 per week for the first 9 weeks and saved $12.00 for the 10th week. On average, how much more should Sophia have saved each week to reach her goal?

Choice B

$$5- \frac{4\times9 + 12}{10}=0.2$$

2015 April(73G) Math Question 28

Perimeter, Area, Volume Practice

- Mixed Shapes

28. The rectangular deck on Sachi's house has a width of 4 yards and a length of 6 yards. Sachi remodels the deck by increasing both the length and width by the same amount. The area of her new deck is twice the area of her original deck. What is the length, in yards, of Sachi's new deck?

Choice H

$$(4+d)(6+d)=2\times4\times6 \\ $$ $$\Rightarrow d=2\\$$ …

Choice C

$$\tan ?=\frac{8}{3}\\$$ $$\Rightarrow?=\tan ^{-1}(\frac{8}{3})$$

2015 April(73G) Math Question 30

Conics Practice

- Circles

30. The circle in the standard (x,y) coordinate plane below has center (-8.5,7.5) and has radius 5 coordinate units. Which of the following is an equation of this circle?

Choice J

The standard equation of a …

Choice D

$$Area=\pi r^2=\pi 5^2=25 \pi$$

Choice K

When a point is reflected …

2015 April(73G) Math Question 33

Angles Practice

- Collinear Points & Triangles

33. In a plane, the distinct lines AB and CD intersect at A, where A is between C and D. The measure of BAC is 54°. What is the measure of BAD ?

Choice E

73g

$$\angle BAD=180°-54°$$

2015 April(73G) Math Question 34

Trigonometry Practice

- Graphing Trig Functions

34. For an angle with measure a in a right triangle, sin a = 180/181 and tan a = 180/19. What is the value of cos a?

Choice F

$$\tan \alpha =\frac{\sin\alpha}{\cos\alpha} \\$$ $$ …

Choice E

I. n=19/3

II. n=4

III. …

Choice J

$$\frac{6x^{13}y^3}{2xy^{10}}=\frac{3x^{12}}{y^7}$$

Choice C

xy must be divisible by …

Choice G

$$2a=4c \\$$ $$ \Rightarrow a=2c$$

Choice D

By week w, Jan will …

Choice J

$$\Rightarrow q=4-p \\$$ $$ \Rightarrow …

Choice A

As can be seen from …

Choice J

$$\Rightarrow 7y=-8x+112 \\$$ $$ \Rightarrow …

2015 April(73G) Math Question 43

Perimeter, Area, Volume Practice

- Mixed Shapes

43. The circle below has a diameter of 8 centimeters. Which of the following is closest to the area, in square centimeters, of the square inscribed in the circle?

Choice B

$$d=\frac{8}{\sqrt{2}} \\$$ $$ \Rightarrow Area=d^2=(\frac{8}{\sqrt{2}})^2=32$$

2015 April(73G) Math Question 44

Angles Practice

- Circles

44. Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from B as from 0 forms a circle. The point (V3,0) is 1 point on the circle. What are the coordinates of the center of that circle?

Choice J

Since each point on the …

Choice A

$$\frac{3}{x}=12$$ $$ \Rightarrow x=\frac{1}{4} $$ …

2015 April(73G) Math Question 46

Word Problems Practice

- Temperature

46. Temperatures measured in degrees Fahrenheit (F) are related to temperatures measured in degrees Celsius (C) by the formula F =IC + 32. There is 1 value of x for which x degrees Fahrenheit equals x degrees Celsius. What is that value?

Choice G

$$C=\frac{9}{5}C+32 $$ $$\Rightarrow C=-40$$

Choice E

The equation is not defined …

2015 April(73G) Math Question 48

Perimeter, Area, Volume Practice

- Mixed Shapes

48. The figure shown below is composed of a rectangle and a semicircle. Points A and B are endpoints of both a side of the rectangle and a diameter of the semicircle. What is the perimeter, in feet, of the figure?

Choice G

$$\widehat{AB}=\frac{2\pi r}{2}=\pi r=3\pi \\$$ $$ …

2015 April(73G) Math Question 49

Perimeter, Area, Volume Practice

- Other Shapes

49. What is the area, in square inches, of the parallelogram shown below?

Choice B

Area = 10 x 5 …

Choice G

$$a_{5}=a_{2}\cdot k^3 \\$$ $$\Rightarrow 32=-4k^3 …

2015 April(73G) Math Question 51

Trigonometry Practice

- Graphing Trig Functions

51. What are the values of 0, between 0 and 2pi, when tan 0 = —1 ?

Choice C

73g

2015 April(73G) Math Question 52

Perimeter, Area, Volume Practice

- Other Shapes

52. A can of soda pop has the shape of a right circular cylinder with an inside height of 6 inches and an inside diameter of 2 inches. When you pour the soda pop from the full can into a cylindrical glass with an inside diameter of 3 inches, about how many inches high is the soda pop in the glass? (Note: The volume of a right circular cylinder is itr2h.)

Choice F

$$\pi (\frac{2}{2})^2\cdot 6=\pi (\frac{3}{2})^2\cdot h …

Choice C

$$(n - 2)\cdot s +s=ns-s$$

Choice F

$$\frac{1+100\times11}{100\times12}-1=-8.25\%$$

Choice E

$$\frac{8\times16}{2\times4}=16$$

Choice H

Apparently, the relationship between size …

Choice B

$$3^{x+1}=3^{3x-6} \\ $$ $$\Rightarrow x+1=3x-6 …

Choice F

73g

$$\Rightarrow AC=\frac{1}{2}, \ CO=\frac{\sqrt{3}}{2} \\ …

Choice A

(3, 45°+360°n) represent the same …

Choice K

$$\Rightarrow y=\frac{2-\frac{18}{x^2}}{1-\frac{5}{x}}$$ When x approaches …