**Any Questions?**

**Roots of polynomials**

x + y = z Is an equation

x + y Is a expression

Anything separated by a "plus" and a "minus" sign are known as "terms"

a = b Is an equation

**If we have the following expression**

**b + b + b + b + b + 5b**

**Wouldnt it be simplier to write....**

**We can add the like temrs**

The value out the front of a variable is known as the "Coefficient".

**2x - 12y = z**

What are the coefficients for x,y and z for the following equation?

2x - 12y = z

The coefficient of x is 2

The coefficient of y is - 12

The coefficient of z is 1

Solve for the value of a within the following triangle

we know that supplementary angles add to 180

we know that interior angles with a triangle add to 180

lable unknown angle b

100 + b = 180

b = 180 - 100

b

b = 80

30 +

35 + a

+ 80 = 180

2

35 + a = 180 - 30 - 80

2

35 + a = 70

2

35 + a = 2(70)

a = 105

key word solve, we are going to need to formulate an equation..

**Word problems**

Ebony reads a novel at a page a minute. Approximately (to the nearest hour) how long will it take her (not counting breaks) to read all 890 pages of James Patterson novel Along came a spider?

let P denote number of pages

she reads one page a minute the answer is required in hours.

write down usefull information from question

give yourself space

write down information from question

let p denote page

p = 1min

p/min = 1

she reads one page per minute

she reads 890 pages total

ans wanted in nearest hours

1hour = 60 min

1hour = min

60

p = 1hour

60

sub in for min

890p = 890hours / 60

890p = 14.83 hours

It will take Ebony 15 hours to read her James Patterson Book.

then a sentance

working out space

New work booklets

Algebra

These work booklets are returned

at the end of every lesson

On the very first page write.

Class Rules

on the next two pages.... Create a Title Page

A l g e b r a

everyday we put the date:

During this unit you will see:

Copy Down

meaning take notes

Always put the date

You will see:

That means start writing what is on the screen

Copy Down

**Equations and Expressions**

**How many terms in each of the following? State the**

Pronumerals, are they an Equation or an Expression?

a) a + b + 6c

b) p + q + w - 3 - 7

c) r + 2r + 3r + 9r

d) - 4k - 2m = 6m

Pronumerals, are they an Equation or an Expression?

a) a + b + 6c

b) p + q + w - 3 - 7

c) r + 2r + 3r + 9r

d) - 4k - 2m = 6m

**Copy Down**

**e) 55d + 4c - 3d - 6d**

f) 55nk + 10kn

g) 4r - 6p - k

h) -k + k - k + k

f) 55nk + 10kn

g) 4r - 6p - k

h) -k + k - k + k

In algebra, letters (Pronumerals) are like numbers.

A Coefficient is the number out the front a Pronumeral

Copy Down

Date:

Lets have a go at writing a some

Expressions from sentences

Pronumerals are sometimes called variables

Kirwan State High School

**http://prezi.com/5ksvhwiwul6f/view/**

Writing Expressions

The convention for writing expressions is:

6w + 7m - 2

number then pronumeral

Ready with white boards...

We are going to write expressions from sentences

The sum of g and 20

Decrease w by 29

multiply 5 by d

reduce b by 870 then add 15 to the result

Steven is t years old how old will be be in 10 years time?

Andrew receives x amount of money per week, how much does he have in 4 weeks.

Tim receives y amount of money per week as well as $50 per week, how much does he have in 6 weeks.

three lots of k and five lots of n

Josh k number of items and finds another 6

What is the Coefficient of k in the following expression?

3m + 5k - 6j + 12n

What is the Coefficient of b in the following expression?

6n + 13m - 12b + 5

Paul is k years old, how old was he five and a half years ago?

Like Terms and Simplifying

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An expression

3k + 2K + 5m - 2m + 3b

can be "simplified" to

5k + 3m + 3b

Instead of writing

k + k + k + k + k + k + k + 3k + 10k

It is a lot "simpler" to write:

20k

Simplifying involves collecting like terms (terms with the

same pronumrals (letters)). Then adding or subtracting

to give final amount of.

We cannot add different letters.

3 Apples (3A) and 4 Pears (4P)

cannot be simplified past:

3A + 4P

Simplify the following expressions, then write the

coefficients.

a) 3w + 4w + 7k + 8w + 3w

b) n + n + 4n + 5k - 2k

c) 4t + 19t + 4k + 5t - 5m - 2k + 6t

d) 5p - 5p + 2k - 3m - 2k + 3m

Where you are at.....

Think number line.....

-4 + 8

where do you end up...

-3k + 4b + 6k -4b

Where do you end up..

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Simplify the following expressions

a) -3w + 2w + 5n + 6n

b) -5m + 2m

c) -4k + 5b + 5k

d) -6n + 10m - 2n - 5m

e) -2j + 3k - 4j + 3j

f) 6n - 5k - 9k

g) 5p - 5k - 6t

h) -5h + t

Copy down

I get $30 for every xbox I sell

let x stand for xbox

30x

on particular day I might not sell any.

I might want $50 for coming into work that day

so if I sell no xbox's I get $50

x = 0

30 (0) + 50

30x + 50

Recap:

The following expression:

2w + 6k + 3 + 2k

Has 4 terms

2 pronumerals (w and k) and can be simplified down to:

2w + 8k + 3

Apples n Oranges

+

+

+

+

+

+

+

+

Group Terms

On a given day we do not know what we are going to sell

so thats why "x" remains unknown.

3

2

+

substitute place 0 in where x is.

6

3

10

3

4

+

+

+

+

Group

10

"Substitution" is simply replacing a pronumeral with a number

to evaluate an expression.

Copy Down

for example

6k

k = 5

6 x 5

30

**Multiplication**

Evaluate the following multiplication expressions:

a) 3 x 6 x 10

b) 4 x 4

c) 4 x 5

and

**Division**

We can write 3 x t

as 3t

There is still a Multiplication sign between

the "coefficient" 3 and the "pronumeral" t

Copy down

Letters are numbers

Examples of simplifying multiplication:

a) 6 x k x t

= 6kt

b) 5y x 7k

= 5 x 7 x y x k

= 35yk

c) 3t x 4t

= 3 x 4 x t x t

= 12t

2

Examples of simplifying Division:

16k

12

14t

7t

a)

b)

**_**

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