Algebra

Properties of Real Numbers

Laws of Exponents Review

Properties of Logs

Fractions

Simplifying Radicals

Algebra 2 Live Lesson

Complex Numbers

GEOMETRIC SEQUENCE

Arithmetic Sequences

Commutative Property

 GEOMETRIC SEQUENCE

Multiple Choice

Is this an arithmetic sequence?

1, 5, 9, 13, ...

• yes

• no

Multiple Choice

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Open Ended

What is the common difference of this arithmetic sequence:

1, 5, 9, 13, ...

GEOMETRIC SEQUENCE

Multiple Choice

Is this an arithmetic sequence?

1, 3, 6, 10, ...

• yes

• no

How to simplify a radical

Multiple Choice

Is this an arithmetic sequence?

6, 2, -2, -6, ...

• yes

• no

Multiple Choice

Determine whether the given sequence is geometric sequence.

3, 6, 9, 12, 15, ...

• It is a geometric sequence.

• It is not a geometric sequence.

Open Ended

What is the common difference of this arithmetic sequence:

6, 2, -2, -6, ...

Multiple Choice

Simplify √-28

• -√28
• -2i√7
• 2i√7
• 28i

Multiple Choice

Is this an arithmetic sequence?

-2, 4, -8, 16

• yes

• no

Multiple Choice

Determine whether the given sequence is geometric sequence.

$$-1,\ -5,\ -25,\ -125$$  

• It is a geometric sequence.

• It is not a geometric sequence.

Open Ended

What are the next 2 terms of this arithmetic sequence:

12, 9, 6, 3, ...

Open Ended

What are the next 2 terms of this arithmetic sequence:

-2, 2, 6, 10, ...

Multiple Choice

Determine whether the given sequence is geometric sequence.

$$2,\ 8,\ 32,128$$  

• It is a geometric sequence.

• It is not a geometric sequence.

Finding the next terms is pretty easy, but what if I asked you to find the 54th term?

Or the 372nd term?

Never fear, I have a way for you to find ANY term :)

Multiple Choice

Simplify -√-48

• 4i√3
• -4i√3
• i√48
• -48i

Multiple Choice

Determine whether the given sequence is geometric sequence.

$$-6,\ -4,\ -2,\ 0$$  

• It is a geometric sequence.

• It is not a geometric sequence.

Multiple Choice

 The formula for finding the $$n^{th}$$  term of the arithmetic sequence:

15, 13, 11, 9 ...

* what is the first term?
* what is the common difference?

• $$15+\left(n-1\right)\left(2\right)$$  

• $$9+\left(n-1\right)\left(2\right)$$  

• $$15+\left(n-1\right)\left(-2\right)$$  

Multiple Choice

What is the largest perfect square that you use to simplify

$$\sqrt{24}$$  

• 1

• 4

• 9

• 16

Fill in the Blank

Find 141st term of the arithmetic sequence: 15, 13, 11, 9...

1) Use the formula  $$a_n=a_1+\left(n-1\right)\left(d\right)$$

2. Replace $$n$$  with the term you are looking for ( $$141$$   )

3. Replace $$a_1$$  with the first tern in the arithmetic sequence ( $$15$$  ) 

4. Say to yourself, this is why I was told to have a calculator ;)

5. The 141st term of the arithmetic sequence is _______

Multiple Choice

Determine whether the given sequence is geometric sequence.

3, 15, 75, 375

• It is a geometric sequence.

• It is not a geometric sequence.

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Multiple Choice

Simplify √-23

• -√23
• 23i
• 23
• i√23

GEOMETRIC SEQUENCE

Review

GEOMETRIC SEQUENCE

Multiple Choice

√-36

• 6
• -6
• -6i
• 6i

GEOMETRIC SEQUENCE

Multiple Choice

Simplify

$$\sqrt{24}$$  

• $$4\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$6\sqrt{2}$$  

• $$6\sqrt{4}$$  

Fill in the Blank

Determine the common ratio of the given geometric sequence

$$-3,\ -6,\ -12,\ -24$$  

Multiple Choice

-3√80a⁷

• 4a³√5a
• -12a³√5a
• -3a³√5a
• -48a³√5a

Fill in the Blank

Determine the common ratio of the given geometric sequence

$$3,\ -6,\ 12,\ -24$$  

Fill in the Blank

Determine the common ratio of the given geometric sequence

$$64,\ 32,\ 16,\ 8$$  

Operations with complex numbers

Adding and Subtracting

Fill in the Blank

Determine the common ratio of the given geometric sequence

$$10,\ 20,\ 40,\ 80$$  

Multiple Choice

Simplify:

$$\sqrt{98}$$  

• $$7\sqrt{2}$$  

• $$2\sqrt{7}$$  

• $$49\sqrt{2}$$  

• $$2\sqrt{49}$$  

Multiple Choice

Determine whether the sequence is an Arithmetic Sequence or a Geometric Sequence.

2, 4, 8, 16

• GEOMETRIC SEQUENCE

• ARITHMETIC SEQUENCE

Multiple Choice

Simplify: 
(10+ 15i) - (48 - 30i)

• 58 - 45i
• 58 - 15i
• -38 - 15i
• -38 + 45i

Multiple Choice

Determine whether the sequence is an Arithmetic Sequence or a Geometric Sequence.

4, 10, 16, 22

• GEOMETRIC SEQUENCE

• ARITHMETIC SEQUENCE

What is an exponent?

A simplified notation for repeated multiplication of the same number, term, or variable.

Multiple Choice

Determine whether the sequence is an Arithmetic Sequence or a Geometric Sequence.

15,24,33,42,...

• GEOMETRIC SEQUENCE

• ARITHMETIC SEQUENCE

Multiple Choice

Find the sum.
(5-2i) + (-7+8i)

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

Determine whether the sequence is an Arithmetic Sequence or a Geometric Sequence.

$$3,\ -6,\ 12,\ -24,\ ...$$  

• GEOMETRIC SEQUENCE

• ARITHMETIC SEQUENCE

What if you have a number on the outside?

Multiple Choice

Determine whether the sequence is an Arithmetic Sequence or a Geometric Sequence.

$$2,\ 1,\ \frac{1}{2},\frac{1}{4}$$  

• GEOMETRIC SEQUENCE

• ARITHMETIC SEQUENCE

Multiple Choice

Simplify: 
(10+ 15i) - (48 - 30i)

• 58 - 45i
• 58 - 15i
• -38 - 15i
• -38 + 45i

Multiple Choice

Determine whether the sequence is an Arithmetic Sequence or a Geometric Sequence.

$$2,\ 10,\ 50,\ 250,\ ...$$  

• GEOMETRIC SEQUENCE

• ARITHMETIC SEQUENCE

THANK YOU!!!

Multiple Choice

Simplify:

$$10\sqrt{96}$$  

• $$40\sqrt{6}$$  

• $$160\sqrt{6}$$  

• $$96\sqrt{10}$$  

• $$60\sqrt{16}$$  

Multiple Choice

Simplify:
-3i(4 + 2i)

• 6 - 12i
• 6 + 12i
• -12i - 6i²
• -12i + 6i²

Review on properties of exponents

Multiple Choice

Simplify:
(2 - 3i)(5 + 4i)

• 22 - 7i
• 22 + 7i
• 22 - 7i²
• 22 + 7i²

Multiple Choice

Simplify:

$$3\sqrt{125}$$  

• $$75\sqrt{3}$$  

• $$8\sqrt{5}$$  

• $$15\sqrt{5}$$  

• $$15\sqrt{25}$$  

Multiple Choice

Simplify
(-6 - 2i)²

• 32
• 36-4i
• 36+24i
• 32+24i

Multiple Choice

(4-5i)(4+5i)

• 41
• -9
• 41+40i
• -9+40i

What if you have variables?

1. Make sure the variable is an even power
2. If it's not even, subtract one from the exponent and rewrite as a product
3. Take the variable with the even power and divide by 2 - put that on the outside of the radical

Multiple Choice

Use the commutative property to re-write the expression

$$123+x+9$$  

• $$x+9+123$$  

• $$\left(123+x\right)+9$$  

Multiple Choice

Simplify:

$$\sqrt{x^{15}}$$  

• $$x^{7.5}$$  

• $$x^{14}\sqrt{x}$$  

• $$x^7\sqrt{x}$$  

Multiple Choice

Simplify:

$$\sqrt{x^2y^7}$$  

• $$xy^3$$  

• $$xy^3\sqrt{y}$$  

• $$xy^3\sqrt{xy}$$  

Multiple Choice

Simplify:

$$\sqrt{80x^2y^4}$$  

• $$2xy^2\sqrt{20}$$  

• $$4xy^2\sqrt{5}$$  

Add/Subtract Radicals

Multiple Choice

How do you use exponents to represent numbers?

• repeated multiplication

• repeated addition

• repeated subtraction

• repeated division

Multiple Choice

Simplify:

$$2\sqrt{24}+5\sqrt{54}$$  

• $$7\sqrt{78}$$  

• $$19\sqrt{6}$$  

• $$7\sqrt{6}$$  

How to Multiply Radicals

Multiple Choice

Condense

   $$\log_39+\log_33$$  

• $$\log_312$$  

• $$\log_327$$  

• $$\log_39$$  

Multiple Choice

Multiply:

$$3\sqrt{8}\times4\sqrt{10}$$  

• $$12\sqrt{80}$$  

• $$7\sqrt{80}$$  

• $$24\sqrt{20}$$  

• $$48\sqrt{5}$$  

Associative Property

Multiple Choice

Expand

  $$\log_216$$  

• $$\log_28+\log_22$$  
  

• $$\log_22+\log_24$$  
  

Multiple Choice

Which is equivalent to 7 x 7 x 7 x 7 x 7 x 7

?

• 7⁵

• 7⁶

• 6⁷

• 7⁷

Poll

In the following equation, are we applying the product rule correctly?

$$\log_5x+\log_5y+\log_5z=\log_5xyz$$  

• Yes

• No

Multiple Choice

Which correctly applies the associative property to the expression

$$\left(x+5\right)+7$$  

• $$\left(5+x\right)+7$$  

• $$x+\left(5+7\right)$$  

• $$7+\left(5+x\right)$$  

When multiplying, ADD the exponents and keep the same base.

Multiple Choice

$$\ \ \ \ \ \ \ \ \ \ 2\frac{\text{2}}{\text{3}}\ \ \$$  

• Zero Fraction

• Proper Fraction

• Whole Fraction

• Improper Fraction

Multiple Choice

Condense 

$$\log_5y-\log_525$$  

• $$\log_5\left(y-25\right)$$  

• $$\log_5\left(25y\right)$$  

• $$\log_5\left(\frac{y}{25}\right)$$  

• $$\log_5\left(\frac{25}{y}\right)$$  

Multiple Choice

$$\ \ \ \ \ \ \ \ \ \ \ \frac{0}{3}$$  

• Zero Fraction

• Whole Fraction

• Proper Fraction

• Improper Fraction

Identity Property

Multiple Choice

$$\ \ \ \ \ \ \ \ \ \ \frac{11}{\ 11}$$  

• Improper Fraction

• Proper Fraction

• Zero Fraction

• Whole Fraction

Multiple Choice

Expand
$$\log_6\left(\frac{y}{36}\right)$$  

• $$\log_6y+\log_636$$  

• $$\log_6y-\log_636$$  

• $$\log_636+\log_6y$$  

• $$\log_636-\log_6y$$  

Multiple Choice

$$\frac{x}{y}\ where\ x\ =\ 20\ and\ y\ =\ 40$$  

• Improper Fraction

• Zero Fraction

• Whole Fraction

• Proper Fraction

Multiple Choice

According to exponent rules, when we multiply the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

$$\ \ \ \ \ \ \ \ \ \ \ \ \ 1\frac{\text{2}}{\text{1}}$$  

• Zero Fraction

• Whole Fraction

• Proper Fraction

• Improper Fraction

Multiple Choice

Solve 

$$\log_264-\log_2y=\log_216$$  

• y=2

• y=3

• y=4

• 4=8

Multiple Choice

Which correctly represents the identity property?

• $$x-x=0$$

• $$x+3=3$$

• $$x\cdot1=x$$

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form.

4³⋅4⁵

• 4⁸

• 16⁸

• 4¹⁵

• 16¹⁵

Multiple Choice

Condense 

$$2\log_39$$  

• $$\log_39^2$$  

• $$\log_32^9$$  

Inverse Property

Multiple Choice

Expand 

$$\log_24^2$$  

• $$4\log_22$$  

• $$2\log_42$$  

• $$2\log_24$$  

• None of these

Multiple Choice

Simplify:

b² ⋅ b⁴

• b⁸

• b⁶

• b²

• 2b⁶

Poll

How would you gauge your understanding of this lesson?

• I have a good understanding.

• I understand in so well I could teach it to a peer.

• I'm still need more practice.

• I don't understand at all.

Multiple Choice

Which correctly shows the inverse property?

• $$x+-x=0$$

• $$x\cdot1=x$$

• $$a+x=x+a$$

When dividing, SUBTRACT the exponent in the denominator (bottom) and keep the base.

Property of Zero

Multiple Choice

According to exponent rules, when we divide the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

Is this the property of zero?

• $$3-0=3$$

• $$6+0=6$$

• $$1-1=0$$

• $$9\cdot0=0$$

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵

• 9⁹

• 1⁵

• 9^-5

Distributive Property 

Multiple Choice

Simplify the expression.

• 7⁶
• 7^-5
• 1/7⁵
• 7⁵

Multiple Choice

Is this a correct use of the distributive property?

$$5\left(x-8\right)=5x-8$$  

• Yes

• No

When you have an exponent raise to an exponent, MULTIPLY the exponents.

Multiple Choice

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

Simplify:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Multiple Choice

(r⁴)⁶

• 10r
• r¹⁰
• 24r
• r²⁴

Anything with a power/exponent of zero equals 1!

Multiple Choice

Simplify (-1/2)⁰

• 1

• 0

• -1

• -2