Unit 1 Review

Unit 1 Review

by Jasmine Gray

Perfect Squares and Cubes​

EE2: I can solve equations using square/cube roots ​

​Perfect Squares/Cubes

​What do we think about when we see a problem involving a square root?

​- we think " what number times itself gives me the number in question"

​

​What do we think about when we see a problem involving a cube root?

​- we think " what number times itself 3 times gives me the number in question

​Things to Remember

​Cubed roots have 1 answer only

​Square roots have 2 answers

Multiple Choice

$$\sqrt{16}=?$$  

• 8

• 2

• 4

• 32

Multiple Choice

$$\sqrt{-144}$$  

• 12

• -12

• 72

• none of the above (imaginary number)

Multiple Choice

$$3_{\sqrt{8}}$$    (cube root of 8) 

• 2

• $$\pm2$$  

• -2

• None of the above 

Multiple Choice

The area of a square painting is 81 $$cm^2$$  . What is the length of one side?

• 9

• -9

• 40.5

• -40.5

Multiple Choice

A cube with side length s has a volume of 64 cubic units. What is the length of one side?

• 4

• 8

• 16

• 32

Exponent Rules​

EE1: I can evaluate expressions using all exponent rules ​

​Exponent Rules

​This section of the test covers all exponent rules. Please ignore the fractional exponent (we did not cover that). Remember that these rules are something that needs to be put in long term memory

Multiple Choice

$$x^{-5}$$  =

• $$\frac{1}{x^{-5}}$$  

• $$\frac{1}{x^5}$$  

• $$\frac{x^5}{1}$$  

• $$\frac{x^{-5}}{1}$$  

Multiple Choice

$$365^0=$$  

• 0

• 1

• 365

• $$\frac{1}{365}$$  

Multiple Choice

The product rule says that when you are multiplying two exponents with the same base, you keep the base and ________ the exponents

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

$$x^3\cdot x^4\ =$$  

• $$x^{12\ }$$  

• $$x^{-1}$$  

• $$x^7$$  

• $$x^{34}$$  

Multiple Choice

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

• Add

• Subract

• Multiply

• Divide

Multiple Choice

$$\frac{x^9}{x^4}$$  =

• $$x^{13}$$  

• $$x^{36}$$  

• $$x^5$$  

• $$x^{-5}$$  

Multiple Choice

$$\frac{x^{17}}{x^8}$$  

• $$x^9$$  

• $$x^{25}$$  

• $$x^{-9}$$  

• $$x^{-25}$$  

Multiple Choice

$$\frac{a^5b^{10}}{a^3b^6}=$$  

• $$a^8b^{16}$$  

• $$a^2b^4$$  

• $$a^{15}b^{60}$$  

• $$a^2b^{16}$$  

Multiple Choice

$$\left(x^5\right)^4$$  

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

• add

• subtract

• multiply

• divide

Multiple Choice

$$\left(x^7\right)^2$$  =

• $$x^{14}$$  

• $$x^9$$  

• $$x^5$$  

• $$2x^7$$  

Multiple Choice

$$\left(a^3b^5\right)^7$$  =

• $$a^3b^{35}$$  

• $$a^{10}b^{12}$$  

• $$a^8b^8$$  

• $$a^{21}b^{35}$$  

Multiple Select

Select ALL that are correct.

Simplify the following: $$\left(2x^4y^{-3}\right)^{-1}$$  

• $$2^{-1}x^{-4}y^3$$  

• $$-\frac{2}{x^4y^3}$$  

• $$\frac{1}{2x^4y^3}$$  

• $$\frac{y^3}{2x^4}$$  

Scientific Notation and Comparing​

EE3: I can write numbers in scientific notation

I can compare numbers in scientific notation​

​Writing Numbers in Scientific Notation

​A number in scientific notation is made up of 2 factors and a multiplication sign. The first factor (also called the coefficient) is a number between 1 and 10 (can not be less than 1 or greater than 10) and the second factor is a power of 10. To find power of 10 count how many jumps to make coefficient between 1 and 10

​Ordering Numbers in Scientific Notation

​First look at the exponents, greater exponents are greater.

​If exponents are the same then look at the coefficient

Multiple Choice

How would you write 564,000,000 in scientific notation?

• 5.64 x 10^-7

• 5.64 x 10⁶

• 5.64 x 10⁸

• 56.4 x 10⁷

Multiple Choice

Express the following in scientific notation: .000457

• 457 x 10⁶

• 457 x 10^-6

• 4.57 x10⁴

• 4.57 x 10^-4

Multiple Choice

When your exponent is negative, you move your decimal....

• to the right

• to the left

• to both sides

• nowhere.... the decimal goes nowhere

Multiple Choice

Which of the following is correct scientific notation?

• 20.35 x 10⁴

• .2035 x 10⁴

• 2035 ⁴

• 2.035 x10⁴

Multiple Choice

How would you write 5.6 x 10^-3 in standard form?

• 56,000

• 5,600

• 0.00056

• 0.0056

Multiple Choice

Place the following numbers in order from least to greatest:
7.8 x 10⁶,    5.1 x 10⁴,  
1.25 x 10⁵,    4.09 x 10⁴

• 4.09 x 10⁴,   
  1.25 x 10⁵,    
  5.1 x 10⁴,   
  7.8 x 10⁶,
• 4.09 x 10⁴,    
  5.1 x 10⁴,    
  1.25 x 10⁵,  
  7.8 x 10⁶, 
• 1.25 x 10⁵,  
  4.09 x 10⁴,    
  5.1 x 10⁴,     
  7.8 x 10⁶,  

Multiple Choice

The diameter of the planet Mercury is 4.87 x 10³ km.  The diameter of the planet Venus is 1.21 x 10⁴ km. The diameter of the planet Mars is  1.28 x 10³ km.    Which planet has the smallest diameter?

• Mercury

• Mars

• Venus

Multiple Choice

Order the following from greatest to least:  5 x 10³   3.2 x 10⁸  1.2 x 10⁸  7 x 10⁵ 

•  7 x 10⁵ ,  5 x 10³ ,  3.2 x 10⁸,  1.2 x 10⁸

•  3.2 x 10⁸, 1.2 x 10⁸,  7 x 10⁵, 5 x 10³ 

•  1.2 x 10⁸, 3.2 x 10⁸,  5 x 10³ , 7 x 10⁵ 

Operations in Scientific Notation​

EE4: I can perform all operations with scientific notation​

​Multiplying/Dividing

​The greatest thing to remember is that you don't need the same exponent to multiply and divide in scientific notation.

​

​** Remember after you perform the operation if the number is not in scientific notation then you need to put in it scientific notation**

​Remember LARS "left, add, right, subtract"

Multiple Choice

What is the simplified version of

• 3.9 x 10⁶

• 4 x 10²⁰

• 4 x 10⁶

• 3.9 x 10²⁰

Multiple Choice

Multiply: (9.4 x 10⁶)(3.2 x 10⁵)

• 30.08 x 10¹¹

• 3.8 x 10¹

• 3.008 x 10¹²

• 2.9375 x 10¹

Multiple Choice

(2 x 10⁹)(4 x 10^-4)

• 8 x 10¹³

• 8 x 10³⁶

• 8 x 10⁵

• 8 x 10^-36

Multiple Choice

If you subtract from your exponent of 10, you move your decimal to the ....

• Right

• Left

• North

• South

Multiple Choice

If you add to your exponent of 10, you move your decimal...

• Left

• Right

• Up

• Down

Multiple Choice

Solve: (6 x 10⁶) / (2 x 10³)

• 12 x 10³

• 3 x 10⁹

• 1.2 x 10⁴

• 3 x 10³

​Adding/Subtracting

​#1 rule when adding and subtracting is to remember that the exponents must be the same to perform this operation. if you struggle with moving the decimal you can write the numbers in standard form and then perform the operation and convert back to scientific notation.

Multiple Choice

Give the sum of (2.6 x 10⁶) + (4.2 x 10⁶)

• 6.8 x 10⁶

• 6.8 x 10¹²

• 8.4 x 10⁶

• 3.2 x 10¹²

Multiple Choice

Give the sum of (4.8 x 10⁸) + (5.4 x 10⁸) in scientific notation

• 1.02 x 10⁸

• 1.02 x 10⁹

• 9.2 x 10⁸

• 2.1 x 10⁹

Multiple Choice

Give the difference of (9.87 x 10⁷) - (7.42 x 10⁷) in scientific notation

• 2.45 x 10⁰

• 3.5 x 10⁷

• 2.45 x 10⁷

• 17.29 x 10⁷

Multiple Choice

Give the difference of (7.2 x 10⁷) - (4.5 x 10⁷)

• 2.7 x 10⁷

• 2.7 x 10⁰

• 1.17 x 10⁷

• 3.3 x 10⁷

Multiple Choice

Give the difference of (8.7 x 10⁹) - (2.5 x 10⁷)

• 6.2 x 10²

• 6.2 x 10⁹

• 7.23 x 10⁷

• 8.675 x 10⁹

Multiple Choice

Give the sum of (8.7 x 10⁵) + (7.32 x 10⁷) in scientific notation

• 16.02 x 10⁷

• 7.407 x 10⁵

• 7.407 x 10⁷

• 1.602 x 10⁷