DCA Review

DCA Review

Unit 1 & 2

Overview

01

03

02

04

Squares &
Square Roots

The Real
Number
System

Scientific
Notation

Ordering
Numbers

05

Model & Solve
Equations

06

Writing
Equations &
Inequalities

Squares &

Square Roots

01

Squaring A Number

●Multiplying a number by itself.

●Raising it to a power of 2.

●Area of a square shape = the side length squared.

Square Root of a
Number

●The opposite or inverse of squaring a number.

Area of Square

Non-Perfect Square

●Numbers whose square roots do not result in a whole
number.

Multiple Choice

Which point represents the $$\ \sqrt{47}$$
HINT: Convert number to a decimal

• A

• B

• C

• D

• E

Multiple Choice

Denise is filling a square sandbox for her brother. If the sandbox floor has an area of 14 square feet, about how long is one side of the sandbox?

• Between 3 feet and 3.5 feet

• Between 3.5 feet and 4 feet

• Between 4 feet and 4.5 feet

• Between 4.5 feet and 5 feet

Multiple Choice

HINT: Convert Number to a decimal

• A

• B

• C

• D

Multiple Choice

Lance solved the equation $$x^2$$  =72 to find the length of a diagonal of a square. Which measurement is closest to x, the length of the diagonal of this square?

• 8

• 5184

• 18

• 36

Multiple Choice

Click the image to read the question.

• A

• B

• C

• D

The Real
Number
System

02

Multiple Choice

See image.

• A

• B

• C

• D

Multiple Choice

See image.

• F

• G

• H

• J

Multiple Choice

See Image.

• A

• B

• C

• D

Multiple Choice

See Image.

• A

• B

• C

• D

Scientific
Notation

03

Multiple Choice

The average distance from Earth to the Moon is 384,400 kilometers. What is this distance written in scientific notation?

• 3.844 x 10⁵ km

• 3.844 x 10⁴ km

• 3.844 x 10^-4 km

• 3.844 x 10^-5 km

Multiple Choice

A person weighing 150 pounds will have, on average, 0.000021 pounds of gold in the body. How is this amount of gold expressed in scientific notation?

• 2.1 x 10^-5

• 2.1 x 10^-4

• 2.1 x 10⁴

• 2.1 x 10⁵

Multiple Choice

How is 123,000,000,000 expressed in scientific notation?

• 1.23 x 10^-11

• 12.3 x 10^-11

• 1.23 x 10¹¹

• 12.3 x 10¹¹

Ordering
Numbers

04

Ascending

Least to Greatest


Descending

Greatest to Least


Fastest to Slowest

Least to Greatest


Change all numbers to decimals FIRST

Multiple Choice

See image.

• A

• B

• C

• D

Multiple Choice

See Image

• A

• B

• C

• D

Multiple Choice

See image.

• F

• G

• H

• J

Multiple Choice

A math teacher asked students to write the following numbers in order from greatest to least.

75%, ⅗, 0.84, ⅔

Which list shows the numbers in the correct order?

• 75%, ⅗, 0.84, ⅔

• 0.84, 75%, ⅔, ⅗

• ⅔, ⅗, 0.84, 75%

• ⅗, ⅔, 75%, 0.84

Model & Solve

Equations

05

1.Write the
equation

2.

Move the smallest
variable using
inverse operation.

3.

Move the
coefficient using
inverse operation.

4.

Multiply/Divide by
coefficient.

Calculator Tip:
Menu →3 → 1 → enter
equation,x →enter

Multiple Choice

Write the equation for the model.

• 2x - 2 = -x - 8

• -x - 2x = 2x - 8x

• -x - 2 = 2x - 8

Multiple Choice

An equation is modeled above. What is the equation and the solution to the equation?

• The equation is 4x=x+9. The solution is 3.

• The equation is 5x=9. The solution is 1.8.

• The equation is 4x=x+9. The solution is 4.

• The equation is 4x+9=x. The solution is -3

Multiple Choice

What Value of x makes the equation true?
$$5x-14=8x+4$$

• 6

• -18/3

• -6

• 10/3

Multiple Choice

14p - 8 = 22 + 20p

• -5
• 5
• 30

Writing Equations &

Inequalities from

Situations

06

Keywords:
●

Same

●

Equal

●

Congruent

Equations

Inequalities

Keywords: Per, Each, Every → your x will be attached

Keywords:
<: Less than
≼: Less than or equal to
>:Greater than
≥: Greater than or equal to

Multiple Choice

Select the situation that could be modeled by: 120 + 25x = 45x.

• John bought a car radio for $120 and speakers for $25 each. Joe bought a radio for $45. They each paid the same. How much did they spend?
• George charges a flat fee of $120 to mow a lawn plus $25 an hour. Greg charges $45 a hour to mow a lawn. After how many hours do they make the same amount?
• Lisa pays $120 for each purse she buys plus an additional $25 to have them personalized. Lauren pays $45 for each purse she buys. How many purses must they buy for the amount they spent to be the same?

Multiple Choice

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value? 

• 15x + 2.5 = 10x + 3
• 15 - 2.5x = 10 - 3x
• 15 + 2.5x = 10 + 3x
• 15 - 10 = 2.5x + 3x

Multiple Choice

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal? 

• 150x + 24 = 180 + 20x
• 150 + 24x = 180 + 20x
• 180 - 150 = 24 x + 20x
• 150 - 24x = 180 - 20x

Multiple Choice

You ride an express bus from the center of town to your street. You have two payment options. Option A is to buy a monthly pass and pay $0.80 per ride. Option B is to pay $2.30 per ride. A monthly pass costs $30. After how many rides will the total costs of the two options be the same?

• r=20 rides

• r=10 rides

• r=15 rides

• r=25 rides