ACT Form 73E Math Answer Explanation


Choice C

$$|5-x|=|5-9|=|-4|=4$$

Choice J

$$Width =\frac12\cdot Length = \frac12\cdot 12 =6 \\ $$ $$\Rightarrow Perimeter = 6+6+12+12=36$$

Choice A

$$(9m-4n)-(2n+5m)=9m-4n-2n-5m=4m-6n$$

Choice F

$$0.\overline{3}(Choice\ F)=0.333333...> 0.3333(Choice\ K)$$

2016 April(73E) Math Question 5

Word Problems Practice

- 2 Variable Addition

5. At a grocery store, Jo Ellen received $1.60 when she returned her cans, glass bottles, and plastic bottles. Jo Ellen received $0.05 for each can, $0.10 for each glass bottle, and $0.05 for each plastic bottle. She knew she had returned 6 cans and 8 glass bottles. How many plastic bottles did Jo Ellen return to the store?

Choice C

Let x be the number of plastic bottles Jo Ellen return to the store: $$$0.05\times6+$0.1\times8+$0.05\cdot x=$1.6 \\$$ $$\Rightarrow x = 10$$

2016 April(73E) Math Question 6

Word Problems Practice

- Temperature

6. Pablo recorded the noon temperature, in degrees Celsius, on 4 consecutive days as part of a science project. On the 1st day, the noon temperature was —4°C. On the 4th day, the noon temperature was 12°C. What was the change in the noon temperature from the 1st day to the 4th day?

Choice K

$$change=12°C-(-4°C)=12+4=16$$

Choice A

$$Sienna's\ pay = $75+25\% \times Total \ weekly \ sales = $75+25\% \times w=0.25w+75 $$

2016 April(73E) Math Question 8

Matrices Practice

- Addition & Subtraction

8. Which of the following augmented matrices represents the system of linear equations below? 3x + 5y = 20 2x— y= 9

Choice G

73e

A system of equations can be represented by an augmented matrix.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

Choice E

$$g(-3)=2(-3)^2-3(-3)+4=31$$

2016 April(73E) Math Question 10

Angles Practice

- Collinear Points & Triangles

10. The figure below shows lines AB and DC, line segments AT and BC, and 2 angle measures. What is the measure of ACB ?

2016 April(73E) Math Question 11

Word Problems Practice

- 1 Variable Equations

11. Marietta purchased a car that had a purchase price of $10,400, which included all other costs and tax. She paid $2,000 as a down payment and got a loan for the rest of the purchase price. Marietta paid off the loan by making 48 payments of $225 each. The total of all her payments, including the down payment, was how much more than the car's purchase price?

Choice B

$$ $2000+$225\times 48 - $10400=$2400 $$

Choice J

$$Area =(x+2)(2x-1)=2x^2-x+4x-2=2x^2+3x-2$$

Choice B

$$p=120000(1.1)^2=145200\approx 145000$$

Choice G

$$I. \ y(height)=h_{0}-\frac{1}{2}gx^2 \\$$ $$II. \ y=kx \\$$ $$III. y=a\cdot t\cdot t=at^2$$

Choice E

The flatter the line, the smaller the slope.

2016 April(73E) Math Question 16

Statistics Practice

- Mean, Median

16. Jamal earned scores of 70, 75, 85, and 94 points on the first 4 history projects, and he has 1 more project to complete. What is the minimum score Jamal needs to earn on the 5th project so that the mean of his scores on all 5 projects is at least 2 points more than the mean of the scores he earned on the first 4 projects?

Choice J

$$Mean \ of \ the \ first \ 4 \ projects = \frac{70+75+85+94}{4}=81 \\$$ $$ Mean \ of \ the \ 5 \ projects = \frac{70+75+85+94+x}{5}\geq 81+2=83 \\ $$ $$\Rightarrow x \geq 91$$

2016 April(73E) Math Question 18

Statistics Practice

- Mean, Median

18. What is the median of the list of numbers below? 6, 3, 5, 7, 12, 9, 5, 5, 11

Choice G

From the smallest to the largest: $$3, 5, 5, 5, \underline{6}, 7, 9, 11, 12$$

2016 April(73E) Math Question 19

Probability Practice

- More than One Event

19. A batch of 100 defective computer chips consisting of 2 types (I and II) and made by 2 companies (A and B) was selected, and it was determined how many of each type of chip was made by each company. The results are displayed in the table below.

Choice A

73e

$$P=\frac{30}{100}$$

Choice H

$$x=\sqrt{13^2-5^2}=12 \\$$ $$ \Rightarrow pitch = \frac{5}{12}$$

Choice D

When x = 2, the …

Choice J

73e

$$AD=AB+BD=(AC-BC)+BD=12-3+12=21$$

2016 April(73E) Math Question 23

Word Problems Practice

- Cost

23. Keanu bought a new laptop computer and paid a discount price that was 20% less than the $1,000 list price. He also paid tax on the laptop equal to 6% of the discount price. What is the total amount Keanu paid for the laptop computer?

Choice C

$$Total \ amouunt = $1000 …

2016 April(73E) Math Question 24

Angles Practice

- Parallel Lines

24. In Middletown, Main Street and Market Street are parallel to each other. Patrick Street intersects Market Street to form a 76° angle at the northeast corner, as shown in the figure below. What is the measure of the angle formed at the southeast corner of Main Street and Patrick Street? (Note: Each street is straight and has the same uniform width.)

Choice H

73e

2016 April(73E) Math Question 25

Probability Practice

- More than One Event

25. Of the 900 students enrolled at Sierra Elementary School, 45% live south of Highway R. Of the students who live south of Highway R, 20% do NOT ride the bus to school. How many students who live south of Highway R ride the bus to school?
Back to top↑

Choice C

$$Number \ of \ students …

Choice G

Let the line be: $$y …

Choice C

Definition: Function, domain, range

A …

Choice H

73e

$$Distance \ from \ Wilderness …

Choice A

$$\frac{x}{\frac{1}{x}}=\frac{4}{25} \\$$$$ \Rightarrow x^2=\frac{4}{25} \\ …

Choice F

73e

$$\sin x=\frac{10}{26} \\ \Rightarrow x=\sin^{-1}(\frac{10}{26})$$

2016 April(73E) Math Question 31

Perimeter, Area, Volume Practice

- Mixed Shapes

31. In the figure shown below, trapezoid ABCD is formed by AABC and AACD. The lengths are given in inches. What is the area of ABC, in square inches?

Choice E

73e

$$Area \ of \ \triangle …

Choice K

By definition, $$\cos \angle B …

Choice C

73e

$$x=\sqrt{13^2-12^2}=5$$

2016 April(73E) Math Question 34

Word Problems Practice

- 1 Variable Equations

34. A family will rent a picnic shelter for $200 for a reunion. The cost of the shelter will be distributed equally among the people who plan to attend. The current cost per person will decrease by $1 if 10 more people plan to attend the reunion. How many people are currently planning to attend the reunion?

Choice H

$$(\frac{200}{x}-1)\cdot(x+10)=200 \\ $$$$\Rightarrow x= 40$$

Choice C

$$Length \ of \ each …

Choice F

$$6a+3b=12 \ (I.) \\$$ $$ …

Choice E

$$\angle C=\frac{180°-42°}{2}=69°$$

2016 April(73E) Math Question 38

Trigonometry Practice

- Graphing Trig Functions

38. The function f(x) = 0.25 sin(4x) is graghed below for 0 <= x

Choice F

73e

As seen from the graph, …

Choice B

73e

$$AB=\sqrt{4^2+7^2}=\sqrt{65}$$

Choice K

$$g=\frac{3t+s}{3+n} \\ $$$$\Rightarrow g(3+n)=3t+s \\ …

Choice B

$$\frac{x^2+5x+6}{x+2}+x+5 = \frac{(x+2)(x+3)}{x+2}+x+5 =x+3+x+5=2x+8$$

Choice J

$$Area \ of \ shaded …

Choice A

$$(1+2i)^2=1+4i+(2i)^2=1+4i+4i^2=1+4i+4(-1)=-3+4i$$

2016 April(73E) Math Question 44

Probability Practice

- One Event

44. A box contains a combination of solid-colored tickets: 1/10 of the tickets are green, 1/2 are red, 1/4 are blue, and the remaining 30 tickets are white. How many blue tickets are in the box?

Choice H

$$Number \ of \ blue …

Choice A

$$80x^3y+48x^2y^2=\underline{16x^2y}(5x+3y)$$

Choice K

The coordinates of the center …

Choice D

73e

$$\tan \angle DCE=\frac{5-2}{13-11}=\frac{3}{2}$$

Choice J

73e

$$AAD=\sqrt{11^2+3^2}=11.4 \ light \ years …

Choice A

The denominator of any fraction …

Choice G

The statement illustrates the commutative …

2016 April(73E) Math Question 51

Perimeter, Area, Volume Practice

- Other Shapes

51. The volume of a right circular cone with radius r and height h is 1/3 pi r^2h, where r and h have the same unit of measure. Cones A and B are both right circular cones. The radius of Cone B is 2 times the radius of Cone A. Cone B's height is 1/2 Cone A's height. Compared to the volume of Cone A, the volume of Cone B is:

Choice D

$$V_{Cone \ B}=\frac{1}{3} \pi r_{Cone …

2016 April(73E) Math Question 52

Angles Practice

- Circles

52. From point A outside a circle and in the same plane as the circle, 2 rays are drawn tangent to the circle with the points of tangency labeled B and C, respectively. Segment BC is then drawn to form LABC. If A measures 70°, what is the measure of ABC ?

Choice B

73e

Since the two lines are …

2016 April(73E) Math Question 53

Conics Practice

- Ellipse

53. Graphed in the standard (x,y) coordinate plane below is an ellipse. The center of the ellipse is (0,0), and points (-5,0), (Q,3), (5,0), (0,-3), A(3,a), and B(3 ,b) lie on the ellipse. What is the distance, in coordinate units, from A to B ?

Choice D

73e

What is the standard equation …

Choice K

To be the side lengths …

2016 April(73E) Math Question 55

Word Problems Practice

- Distance, Speed, Time

55. Carrie and Manuel are side by side when they begin to run at the same time in the same direction around a track. Carrie runs at a constant rate of 30 seconds per lap, while Manuel runs at a constant rate of 50 seconds per lap. How many seconds after beginning to run will Carrie have run exactly 1 more lap than Manuel?

Choice C

Let the number of seconds …

Choice G

ab is a positive even …

Choice B

The sum of the fractions: …

Choice K

$$x^{6a}=(x^{2a})^3=(3)^3=27$$

Choice D

$$The \ slope \ of …

2016 April(73E) Math Question 60

Angles Practice

- Vertex Angles & Bisectors

60. As shown in the figure below, AC and BD intersect at O. Given that 180° < x° < 360° and that x = 4y, what is the value of y ?

Choice J

73e

$$x+y=360° \\$$ $$ \Rightarrow 4y …