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C2C - Unit on Algerbra
Transcript of C2C - Unit on Algerbra
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 = 80
35 + a
+ 80 = 180
35 + a = 180 - 30 - 80
35 + a = 70
35 + a = 2(70)
a = 105
key word solve, we are going to need to formulate an equation..
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
p = 1hour
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
These work booklets are returned
at the end of every lesson
On the very first page write.
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:
meaning take notes
Always put the date
You will see:
That means start writing what is on the screen
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
e) 55d + 4c - 3d - 6d
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
Lets have a go at writing a some
Expressions from sentences
Pronumerals are sometimes called variables
Kirwan State High School
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
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:
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
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..
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
I get $30 for every xbox I sell
let x stand for xbox
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
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
On a given day we do not know what we are going to sell
so thats why "x" remains unknown.
substitute place 0 in where x is.
"Substitution" is simply replacing a pronumeral with a number
to evaluate an expression.
k = 5
6 x 5
Evaluate the following multiplication expressions:
a) 3 x 6 x 10
b) 4 x 4
c) 4 x 5
We can write 3 x t
There is still a Multiplication sign between
the "coefficient" 3 and the "pronumeral" t
Letters are numbers
Examples of simplifying multiplication:
a) 6 x k x t
b) 5y x 7k
= 5 x 7 x y x k
c) 3t x 4t
= 3 x 4 x t x t
Examples of simplifying Division: