QR Semester 1 MidTerm Review

Let's Review for the Midterm

​Exponent Rules

Product Rule
Quotient Rule
Power Rule
Negative Exponent Rule
Zero Power Rule

Multiple Choice

Simplify the following expression: $$x^2\cdot x^5=$$

• $$x^7$$

• $$x^3$$

• $$x^{10}$$

• $$x^{25}$$

• $$2x^7$$

Multiple Choice

Simplify the following expression: $$3x^{-2}\cdot4x^4=$$

• $$12x^2$$

• $$7x^{-8}$$

• $$\frac{256}{9}x^{-8}$$

• $$-96x^2$$

​Product rule

Multiple Choice

Simplify the expression: $$\frac{x^5}{x^3}$$

• $$x^2$$

• $$x^{1.3}$$

• $$x^{15}$$

• $$x^8$$

Multiple Choice

Simplify the expression: $$\frac{5x^8}{25x^3}$$

• $$\frac{x^5}{5}$$

• $$-20x^{11}$$

• $$5x^5$$

• $$125x^{24}$$

​Quotient rule

Multiple Choice

Simplify the expression: $$\left(x^3\right)^5$$

• $$x^{15}$$

• $$5x^8$$

• $$x^8$$

• $$5x^2$$

Multiple Choice

Simplify the expression: $$\left(2x^4y\right)^3$$

• $$8x^{12}y^3$$

• $$6x^7y^4$$

• $$8x^4y$$

• $$5x^7y^3$$

​Power rule

Multiple Choice

Simplify the expression: $$\frac{x^{-3}}{y^{-4}}$$

• $$\frac{y^4}{x^3}$$

• $$xy$$

• $$xy^7$$

• $$x^{12}y^{12}$$

Multiple Choice

Simplify the expression: $$\frac{x^4y^{-2}}{x^{-2}y^6}$$

• $$\frac{x^6}{y^8}$$

• $$\frac{x^2}{y^4}$$

• $$x^{-8}y^{-12}$$

• $$x^2y^4$$

Negative Exponent rule

Multiple Choice

Convert to scientific notation: 451000

• $$4.51\cdot10^5$$

• $$4.51\cdot10^1$$

• $$4.51\cdot10^3$$

• $$451\cdot10^3$$

Multiple Choice

Convert to scientific notation: 0.0000024

• $$2.4\cdot10^{-6}$$

• $$2.4\cdot10^{-1}$$

• $$4.2\cdot10^{-1}$$

• $$2.4\cdot10^{-7}$$

​Converting to Scientific Notation

Multiple Choice

Convert from scientific notation to standard notation: $$4.02\cdot10^1$$

• 40.2

• 402

• 4.02

• 4020

Multiple Choice

Convert from scientific notation to standard notation: $$3.802\cdot10^{-5}$$

• $$0.00003802$$

• $$0.4$$

• 0.0000038

• 380200

​Converting to Standard Notation

Multiple Choice

Simplify using operations with Powers of 10

$$10^3\cdot10^{-5}=$$

• $$10^{-2}$$

• $$20^{-15}$$

• $$10^{-15}$$

• $$10^2$$

Multiple Choice

Simplify using operations with Powers of 10

$$10^4+10^2=$$

• $$10100$$

• $$20^6$$

• $$10^8$$

• $$20^8$$

​Operations with Powers of 10

Multiple Choice

Simplify the expression: $$\left(2.5\cdot10^4\right)\cdot\left(3.0\cdot10^3\right)$$

• $$7.5\cdot10^7$$

• $$5.5\cdot10^7$$

• $$75\cdot10^{12}$$

• $$417625$$

Multiple Choice

Simplify the expression: $$\frac{6.0\cdot10^{-2}}{1.5\cdot10^8}=$$

• $$4.0\cdot10^{-10}$$

• $$4.5\cdot10^{-10}$$

• $$5.5\cdot10^6$$

• $$4.0\cdot10^6$$

Multiple Choice

Simplify the expression: $$\left(5.0\cdot10^5\right)\cdot\left(8.0\cdot10^2\right)=$$

• $$4.0\cdot10^8$$

• $$40.0\cdot10^7$$

• $$1.3\cdot10^{11}$$

• $$13.0\cdot10^7$$

Operations with Scientific Notation

Multiple Choice

Determine the unit rate. A person purchased 120 stickers for $30.

• $$\frac{0.25}{1\ stic\ker}$$

• $$\frac{1\ stic\ker}{4\ dollars}$$

• $$90$$ stickers

Multiple Choice

Determine the unit rate. A person ran 3.5 miles in 24.5 minutes. How long would it take the person to run 5 miles?

• 35 minutes

• 17.5 minutes

• 40 minutes

• 1 minute

​Determining Unit Rate

Multiple Choice

Determine which is the better buy. 24 cans of tomato sauce for $11.52 or 5 cans of tomato sauce for $2.55

• 24 cans at $0.48 each can

• 5 cans at $0.51 each can

• 24 cans at $2.08 each can

• 5 cans at $1.96 each can

Multiple Choice

Determine which is the better buy. 10 piece chicken nuggets for $8.22 or 12 piece chicken nuggets for $9.49

• 10 piece at $0.82 each nugget

• 12 piece at $1.26 each nugget

• 10 piece at $1.22 each nugget

• 12 piece at $0.79 each nugget

Best Buy

Multiple Choice

Convert 5.6 kilometers to centimeters.

1 kilometer = 1000 meters

1 meter = 100 centimeters

• 560000 cm

• 56 cm

• 5600 cm

• 0.000056 cm

​Convert 5.6 kilometers to centimeters

​Set up the equation so that units cancel and we are left with the appropriate unit
Use the given conversion factors to change to each type of unit.
Multiply all the terms on top together.
Multiply all the terms on the bottom together.
Divide the top by the bottom to get your answer.

Multiple Choice

Convert 120 meters per second to miles per hour.

1 mile = 1.61 kilometers

1 kilometer = 1000 meters

• 268.32 miles per hour

• 53.7 miles per hour

• 5.4 miles per hour

• 695520000 miles per hour

​Convert 120 meter per second to miles per hour

Multiple Choice

Given the equation for the perimeter of a rectangle, solve for length (L)

$$P=2W+2L$$

• $$L=\frac{P-2W}{2}$$

• $$L=P-2W-2$$

• $$L=P-W$$

• $$L=2P+W$$

Multiple Choice

If the equation for density is $$Density=\frac{mass}{volume}$$ , what is the volume of silver that has a mass of 2500 g and a density of 10.5 grams per cubic centimeter?

• 238.1 cubic centimeters

• 0.0042 cubic centimeters

• 25500 cubic centimeters

Multiple Choice

The formula to convert temperature from Celsius to Fahrenheit is $$F=\frac{9}{5}C+32$$ . If the temperature in Gilbert was $$113\degree F$$ , what is that temperature in Celsius?

• $$45\degree C$$

• $$235.4\degree C$$

• $$30.8\degree C$$

• $$130.8\degree C$$

​Literal Equations

Multiple Choice

Convert $$\frac{2}{5}$$ to a decimal

• 0.4

• .25

• .52

• 2.5

Multiple Choice

Convert $$\frac{9}{2}$$ to a decimal

• 4.5

• 9.2

• .7

• -.07

Multiple Choice

Convert $$\frac{6}{8}$$ to a decimal

• 0.75

• .25

• .625

• 0.68

​Converting from fractions to decimals

Multiple Choice

Convert 0.25 to a percentage

• 25%

• 
  $$\frac{0.25}{100}\%$$

• 52%

• 4%

Multiple Choice

Convert 0.05 to a percentage

• 5%

• 0.5%

• 50%

• 0.0005%

Multiple Choice

Convert 1.68 to a percentage

• 168%

• 16.8%

• 0.0168%

• $$\frac{42}{25}\%$$

​Convert from decimal to percentage

Multiple Choice

Convert 14% to a decimal

• 0.14

• 1.4

• $$\frac{14}{100}=\frac{7}{50}$$

• 1400

Multiple Choice

Convert 300% to a decimal

• 3.0

• 30

• .3

• 30000

Multiple Choice

Convert 0.05% to a decimal

• 0.0005

• 5

• .5

• 50

​Convert from percentage to a decimal

​convert 46% to a decimal  

Multiple Choice

Convert $$\frac{1}{4}$$ to a percent

• 25%

• 0.25%

• $$\frac{1}{4}\cdot100=\frac{100}{4}=25$$

• $$\frac{1}{4}\cdot\frac{1}{100}=\frac{1}{400}$$

Multiple Choice

Convert $$\frac{5}{10}$$ to a percent

• 50%

• $$\frac{1}{2}\%$$

• 15%

• 2%

Multiple Select

Convert $$\frac{6}{9}$$ to a percent

• $$66.\overline{6}\%$$

• 96%

• 3%

• $$66\ \frac{2}{3}\%$$

​Converting fractions to percentage

Multiple Choice

Express the following statement as a fraction. There are 110 teachers at Higley High School. 12 of them are math teachers.

• $$\frac{6}{55}$$

• $$\frac{3}{25}$$

• $$\frac{55}{61}$$

• $$\frac{49}{50}$$

Multiple Choice

Express the following statement as a percentage. There are 60 students in Quantitative Reasoning. 3 of the students received a 100 on the last quiz. What percentage received a 100 on the last quiz?

• 5%

• 3%

• $$\frac{3}{5}\%$$

• 50%

Multiple Choice

Express the following statement as a decimal. There are 180 days in the school year. 9 of these days are half days. What amount of school days are not half days?

• 0.95

• 0.05

• 0.09

• 5%

• 9%

​Writing statements as... There are 365 days of the year. 52 are Saturdays.