Jeopardy

Order of Operations

100

What does PEMDAS or GEMS stand for? 

PEMDAS- Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
GEMS- Grouping, Exponents, Multiplication/Division, and Subtraction/Addition

200

Solve the following problems using PEMDAS or GEMS 

(4+3) x 10 / 2 + (5 x 6)

(4+3) x 10 / 2 + (5 x 6)
(7) x 10 / 2 + (30)

70 / 2 + 30 

35 + 30

65

300

Solve the following problems using PEMDAS or GEMS

(10-7) + (2 X 14 / 4)

(10-7) + (2 X 14 / 4)

3 + (28/4)

3 + 7

10

400

Solve the following problems using PEMDAS or GEMS

64 - 8 + 12 x 2 + 9

64 - 8 + 12 x 2 + 9

64 - 8 + 24 + 9

64 - 8 + 24 + 9

56  + 24 + 9

80 + 9

89

500

Solve the following problems using PEMDAS or GEMS

4^{3 -} 3³

4^{3 -} 3³

(4x4x4) - (3x3x3)

64 - 27

37

Rules of Exponents

100

What is the Rule of Exponents when it comes to the product of powers? In other words when we multiple with the same base
Provide an Example

When we multiple exponents with the same base, we keep the base and add our exponents.
a^m x aⁿ = a^m+n

2³ x 2⁴ = 2³⁺⁴= 2⁷

200

What is the Rule of Exponents when it comes to the Quotient of Powers? In other words when we divide with the same base
Provide an Example

Division Rule 

When dividing by same bases with exponents, we keep the base the same but subtract our exponents 

a^x/a^y= a^x-y

2⁶ / 2⁴= 2^6-4 = 2²

300

What is the Rule of Exponents when it comes to the Power of a Power? When an exponent is raised to a power
Provide an Example

Power to a Power Rule

When an exponent is raised to a power we multiply the two exponents and keep the same base

(a^x)^y= a^x*y

(3²)⁴= 3^2x4 = 3⁸

400

What is the Rule of Exponent when we have a Zero Exponent

Provide an example

Zero Exponent 

Anything raised to the power of zero is 1 

a⁰=1 

143⁰=1

500

What is the Rule of Exponents when it comes to Negative Exponent
Provide an Example

Negative Exponent Rule

When we have a negative exponent, it becomes a fraction with the positive base and exponent in the denominator 

a^-x = 1/a^x 

7^-6= 1/7⁶

Polynomials

100

Solve this Polynomial
(3x + 2) + (5x + 3)

Solve this Polynomial
(3x + 2) + (5x + 3)
3x + 2 + 5x + 3

8x + 5

200

Solve this Polynomial
4x - 3 - 2x + 6

Solve this Polynomial
4x - 3 - 2x + 6

4x - 2x     -3 +6 

2x + 3

300

Solve the following Polynomial

(2x - 3y + 5) - (-8 + y - 4x) 

(2x - 3y + 5) - (-8 + y - 4x) 

            - (-8 + y - 4x) = +8 - y + 4x

2x - 3y + 5 + 8 - y + 4x

2x + 4x -3y -y +5 +8

6x -4y + 13

400

Solve the following Polynomial

3x (2x²  + 5x - 4)

3x (2x²  + 5x - 4)

3x (2x²) + 3x (+5x) + 3x (- 4)

6x³ + 15x² - 12x

500

2 (5x - 4) - 3 (2x + 6)

2 (5x) + 2(-4)   -3 (2x) - 3 (+6)

10x - 8 - 6x - 18 

10x - 6x   -8 - 18

4x - 26

Integers

100

Adding Integers 

-6 + -12

-5 + 14

23 + -8

34 + -74

Adding Integers 

-6 + -12 = -18

-5 + 14 = 9

23 + -8 = 15

34 + -74 = -40

200

Subtracting Integers

-35 - -49

-20 - 18

-15 - -15

48 - -52

Subtracting Integers

-35 - -49 = -35 + 49 = 14 

-20 - 18 = -38 

-15 - -15 = -15 + 15 = 0 

48 - -52 = 48 + 52 = 100

300

Multiply the following

-8 x -20

-5 x 13

9 x 14

12 x -2

86 x 0

-8 x -20 = 160 * multiplying two negatives gives us a positive answer  

-5 x 13 = -65

9 x 14 = 126

12 x -2 = -24

-86 x 0 = 0 * zero times anything will always be zero 

400

Dividing Integers 

144 / - 12

-180 / 3

-81 / -9

100 / 5

144 / - 12 = -12

-180 / 3 = -60

-81 / -9 = 9

100 / 5 = 20

500

Identify if the following answers are incorrect, answer the following in your own words:

Why? What should be the correct answer?

-25 / 5 = 5

-13 + -24 = 11

-13 - -14= -17

-15 x -15 = 0

- 13 + - 12 = 1

All of the following were incorrect, in your own words answer: 

Why? What should be the correct answer?  

-25 / 5 = 5  

-13 + -24 = 11  

-13 - -4= -17   

-15 x -15 = 0   

- 13 + - 12 = 1 

Identifying Terms

100

Take a look at the term below

How many parts does this have

Identify what are they called?

3x²

3x²

One term 

Our coefficient is 3 

Our variable is x²

200

What does "like terms mean"?
Provide an example to your explanation 

Explanation and example will vary 

300

Identify if any are like terms 

7y 

4x

3 

-2x

8xy 

3y²

z

7

8z

These are like terms 

4x and -2x 

3 and 7

z and 8z

These do not have like terms 

8xy 

3y²

 7y 

400

How many terms are in the following 

x² + 10x + 16 

Identify each of them, are there any like terms? 

Three terms x² and 10x and 16

There are no like terms, it was in simplest form 

500

Identify like terms and simplify 

10xy + 5y - 6xy - 14y 

Identify like terms and simplify 

10xy + 5y - 6xy - 14y

10xy and -6xy are like terms 

5y and -14y are like terms

10xy - 6xy +5y -14y

     4xy  -  9y