Algebra 3 - Unit 1 Review

Algebra 3 - Unit 1 Review

We have covered all of the review lessons for our first unit.  Let's do some practice questions together to prepare you for your first assessment. 

INTEGERS

• Add and subtract with the number line in mind

• Multiply and divide with sign rules in mind

• Be able to calculate with two integers without a calculator...just in your mind

• Be able to explain using the number line or sign rules

Fill in the Blanks

3 + 18 =

Fill in the Blanks

3 - 18 =

Fill in the Blanks

3 + (-18) =

Fill in the Blanks

3 - (-18) =

Fill in the Blanks

(-8) + (-11) =

Fill in the Blanks

(-8) - (-11) =

Fill in the Blanks

7 x 4 =

Fill in the Blanks

(-7) x 4 =

Fill in the Blanks

 $-30\ \div-5\ =\ _{ }$  

Multiple Choice

Explain why 3 + (-18) = -15 using the number line.

• Start at -15, then adding positive 3 is like moving to the right 3 and ending up at (-18)

• Start at 3, then adding (-18) is like moving to the left 18 spaces and ending up at -15

• Adding a positive with a negative will always give you a negative answer

Multiple Choice

Explain why 8 x (-10) = -80 using sign rules

• Multiplying integers with matching signs will lead to a positive answer.

• Multiplying integers with different signs will lead to a positive answer.

• Multiplying integers with different signs will lead to a negative answer.

FRACTIONS

• Draw pictures to represent fractions & write fractions to match pictures

• Explain and fill-in-the-blanks of equivalent fractions

• Convert between mixed numbers and improper fractions

• Write fractions to represent rates and ratios (word problems)

Multiple Choice

Which picture best represents the fraction 4/6?

Multiple Choice

Which fraction best represents the picture?

•  $\frac{1}{3}$  

•  $\frac{10}{5}$  

•  $\frac{5}{10}$  

Poll

Critique the following statement about equivalent fractions: 3/4 and 6/8 are not equivalent because 6/8 is more than 3/4.

• I agree because 6 and 8 are greater than 3 and 4.

• I disagree because 3/4 times 2 equals 6/8, so they are equivalent.

• I disagree because 3/4 and 6/8 are equivalent.

Fill in the Blanks

Fill in the blank to make these equivalent fractions:  $\frac{3}{5}=\frac{?}{20}$  

Fill in the Blanks

Fill in the blank to make these equivalent fractions:  $\frac{1}{?\ }=\frac{5}{50}$  

Fill in the Blanks

Convert the mixed number into an improper fraction:  $3\ \frac{4}{7}=\frac{?}{?}$  

Fill in the Blanks

Convert the improper fraction into a mixed number:  $\frac{13}{5}=\ ?\ \frac{?}{?}$  

EXPONENTS

• Write exponents as multiplication and simplify (positive and negative exponents)

• Solve for x when x is squared by using a square root.

• Convert between scientific and standard notation

Multiple Choice

Write

 $6^4$  as repeated multiplication 

• 6 x 4

• 6 x 6 x 6 x 6

• 4 x 4 x 4 x 4 x 4 x 4

Multiple Choice

Write

 $\left(-3\right)^5$  as repeated multiplication 

• -3 x -3 x -3 x -3 x -3

• -3 x 5

•  $\frac{1}{5\times5\times5}$  
  

Multiple Choice

Write

 $7^{-2}$  as repeated multiplication 

•  $7\times7$  
  

•  $7\times-2$  
  

•  $\frac{1}{7\times7}$  
  

Multiple Choice

Write

 $710^1$  as repeated multiplication 

•  $1$  
  

•  $710$  
  

•  $0$  
  

Fill in the Blanks

Solve

 $x^{2\ }=\ 36$  
*keep in mind that the inverse of squaring is square rooting

Multiple Choice

Convert 8,203,000 into scientific notation

• 8,203,000

• 10 x 820,300

• $8.203\ \times10^6$

Multiple Choice

Convert .000954 into scientific notation

•  $9.54\ \times10^4$  

•  $9.54\ \times10^{-4}$  

•  $10\ \times-954$ 

ORDER OF OPERATIONS

• Parentheses and Exponents first

• Multiplication and Division next

• Addition and Subtraction last

Multiple Select

What is the first step in simplifying this complex math problem:

 $32\ \div2^3\times\left(5\ +3\right)-\left(21+6\right)$  

•  $\left(5+3\right)$  

•  $\left(21+6\right)$  

•  $32\div2$  

•  $2^3$