Algebra

Polynomial Terms

100

True or False: 

a monomial is not a polynomial 

false

200

State the variable(s) in this expression:

8y (24 - 3x) + 2n - 8

The variables in this expression are y, x, and n

300

Give the meaning of "coefficient"

A Coefficient is a number used to multiply a variable

(ex: 4x - 15 = 7)

400

What are like terms?

Like terms are expressions with the same variable and exponent. 

500

What's the difference between an algebraic expression and an algebraic equation?

An expression has combinations of numbers with variables and operation symbols, it can be simplified or expanded.

An equation is meant to solve and has combinations of numbers with a number after the equal.

SimplifyingPolynomials

100

Simplify: 3x + 5 - 5x + 2

-2x + 7

200

What are the like terms in this equation?

4x + 3 + 2x - 6

4x and 2x, 3 and -6

300

What are the like terms in this equation? 

3x² + x - 2 - 5x - 4x²

3x² and -4x², x and 5x, and -2

400

-15x(3x² - 6x)

-45x³ + 90x²

500

Simplify: (3x² - 6x + 8) - (3 - x² - 2x)

= 3x² - 6x + 8 - 3 + x² + 2x

=4x² - 4x + 5

Solving Equations

100

5k = -35

k = -7

200

Solve: 2x - 3 = 8x + 9

x = -2

300

After solving for x, what is the answer to the equation?

5x + 2 = 3x - 8

x = -5

5 x -5 + 2 = -23

3 x -5 - 8 = -23

400

Solve: 7(x - 2) = 4x + 1

x = 5

500

-18 - 6k = 6(1 + 3k)

k = -1

Solving EquationsFractions

100

6 = 1/3(8 + x)

x = 10

200

(k+2)/3 = (k - 4)/5

k = -11

300

(x + 1)/5 = x/6

x = -6

400

(x/3) - (3/2)x = (1/6) - x

x = -1

500

(x -2)/3 + (x+1)/2 = 4

x = 5

Application

100

A number, n, is tripled and then decreased by 40. The resulting value is 146. determine the value of n.

n = 62

200

The length of a field is 3x + 4 and the width is 2x. Find the simplified perimeter. 

p = 2l + 2w

= 10x + 8

300

Amara works at a pet store where she sells pet treats. She is paid 10/h plus a 50-cent commission for every treat she sells. 

Determine Amara's earnings if he sells 41 snacks during a 4-hour shift.

e = 10(4) + 0.50 (42)

e= 40 + 221 = 61

400

A rectangle has a length of 4x + 3 and a width of 5x

- Determine a simplified expression for the area of the rectangle 

a = l x w

= 5x (4x + 3)

= 20x² + 15x

500

Samuel wants to build a fence for his rectangular backyard. He bought 160 m of the material. 

Determine the perimeter of his yard if the length is x + 20 and the width is x - 10.

p = 2l + 2w

x = 35: LS = 55 - RS = 25

55 + 55 + 25 + 25 = 160m