3.4 - 3.7 Test Review

C1

100

What is a term?

an expression formed by the product of numbers and/or variables

200

Identify the coefficient and the variable part: -de²f

coefficient: -1

variable part: de²f

300

Explain why the following simplification is incorrect.

(x² - 3x + 1)(-5)

= x² - 3x - 4

Not every term in polynomial is being multiplied by -5. 

They have simply 'dropped' all brackets and evaluated: x² - 3x + 1 - 5

correct: -5x² + 15x -5

400

3x² - 4xy + 5y² - 6 + 3x² + 4xy - 2

6x² + 5y² -8

500

A soccer team earns 4 points for a win, 2 point for a tie, and lose 1 point for each game that they lose.

Write an expression to represent the total number of points for the team.

4w + 2t - s

w= games won

t = tied games

s = lost games

C2

100

What is a polynomial?

an algebraic expression consisting of one or more terms that are added or subtracted together.

200

State the degree of: 0.363ab³y

5

300

State the degree of: 3w - 6w² + 4

2

400

(x² -2x +1) - (x² - 2x - 5)

x² - 2x + 1 - x² +2x +5

= 6

500

An equilateral triangle has an unknown side length, x. Write a simplified expression for its perimeter.

P = x + x + x = 3x

C3

100

What is the degree of a term?

the sum of the exponents on the variables in a term

200

2(5a² - 7a + 2)

10a² - 14a + 4

300

(h + 5) - (3h - 8)

h + 5 - 3h +8

400

Identify like terms: 

2ab,  6ab², 3ba, 2a²b, 0.67b²a

2ab, 3ba

6ab² ,  0.67b²a

500

(2/3)*(3m-2)  - (3/4)*(8m-2)

(2m-4/3) - 24m/4 + 6/4

= 2m - 4/3 - 6m + 3/2

C4

100

What are like terms?

terms that have identical variables

200

What are two ways to classify a polynomial?

1. Number of terms it has

2. Degree

300

6a² - 5a + 3 - 3a² + 5a - 4

3a² - 1

400

Describe the process of subtracting one polynomial from another. Provide an example to support your explanation.

Add the the opposite of the polynomial that is being subtracted

(x-2) - (-x+6) = (x-2) + (x-6) = x-2+x-6 = 2x-8

500

4[-3(r-5)+2r]

4[-3r+15+2r] = 4[15-r] = 60-4r

C5

100

a(x+y) = ax + ay

What is this called?

distributive property

200

State the degree of: 19

0

300

Consider the expression 3(x+5). Why do you need to use the distributive property? Why can you not just add the terms in the brackets first?

Answers may vary: e.g. Need to use distributive property because it allows us to expand algebraic expressions, which is what 3(x+5) is

We cannot add x and 5 because they are not like terms

400

-5h(3h² - 7h - 2)

-15h³ + 35h² +10h

500

A swimming pool manufacturer installs rectangular pools whose length is thrice the width, plus 2. 

Determine expressions for perimeter and area.

Perimeter = 2(3w+2+w) = 8w + 4

Area = w(3w+2) = 3w² +2w