1TH/vwo CH11 OVERVIEW

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Overview CH11

We march through all content,

now and then you'll make a task.

In this way all content is revived!

Combining like terms

You can only add or subtract like terms. Terms are called like terms if they have the same variable as a base and the same exponent.

After the ADDING and SUBTRACTING

from the previous slide ...

we now move over to

MULTIPLYING!

Remember that

- we add TERMS and 

- we multiply FACTORS

Multiplying factors

When multiplying factors you multiply the numbers by each other and you multiply the variables by each other.
If you multiply powers with the same variable as a base, you can add the exponents.

Writing formulas shorter

1) First work out all products (multiplication)
2) Then combine the like terms (addition and subtraction)
3) Write terms as 1a or -1a shorter as a or -a
Example:

Powers and negative numbers

x        = ....

A.                             B. 

C.                              D.  

Key in your answer in the next slide.

4a​2​​

3a​2​​

7a​4​​

7a​2​​

12a​2​​

12a​4​​

4 a squared times 3 a squared = .......

1. 7 a to the 4th power
2. 7 a squared
3. 12 a to the fourth power
4. 12 a squared

x        = ....

A.                             B. 

C.                              D.  

4  x  3 =  12         and             x             =   

So the good answer is:  C !

4a​2​​

3a​2​​

7a​4​​

7a​2​​

12a​2​​

12a​4​​

a​2​​

a​2​​

a​4​​

Quadrants

The axes divide the coordinate
system into 4 quadrants.
The axes themselves are NOT
part of the quadrants.

The quadrants are numbered
counterclockwise

first quadrant

second quadrant

third quadrant

fourth quadrant

Quadrants

In which quadrant does

(-4, -5) lie ?

Key in in the next slide.

first quadrant

second quadrant

third quadrant

fourth quadrant

(-4, -5) lies in which quadrant ?

1. 1st
2. 2nd
3. 3rd
4. 4th

Quadrants

In which quadrant does

(-4, -5) lie ?

Just visualise where 

this point lies.

With both coordinates being

negative, it must lie in the 

3rd quadrant!

first quadrant

second quadrant

third quadrant

fourth quadrant

(5, -4) lies in which quadrant?

1. 1st
2. 2nd
3. 3rd
4. 4th

Making linear formulas

How to make a linear formula from a graph.
1) Make a table: horizontal axis = top row, vertical axis = bottom row, fill in easy to read off points on the graph.
2) Find the start value (value on bottom row when top row = 0)
3) Calculate the gradient (= increase in bottom row when the top row increases by 1)              (You don't have the KNOW the word gradient yet!)
4) Make a formula:
vertical variable = start value + gradient x horizontal variable

Make the Formula

for this graph in your

Notebook!

Use the 4 steps!

Key it in in the next

slide.

The formula is:

Making the formula:

1.  see the table above! Only grid points.

2.  start number:  below the 0 for x we see 1 for y. So:    1.

3.  going 1 step to the right means going up 1/2.   So:    1/2.

4.  y = 1/2 x + 1     or      y = 0.5 x + 1

Next a new Example. A Joke first.

-4	-2	0	2	4
-1	0	1	2	3

Start value = 4
Gradient = 0.8

Formula:
height = 4 + 0.8 x distance
h = 4 + 0.8d

Making linear formulas

How to make a linear formula FROM A STORY ?

1) Find the start value
2) Find the gradient
4) Make a formula:
variable you calculate = start value + gradient x variable used for calculation

Nimah is studying her French vocabulary. She has already memorised 100 words. It takes her an half an hour to memorize 20 more words. Make a formula to calculate how many words (w) Nimah knows after studying for a given number of hours (t).

Start value = 100
Gradient = 40 (20 per half hour so 40 per hour)
Formula:            w = 100 + 40t

A parabola is

1. something like ebola
2. a nicely rounded graph
3. a strange animal
4. a messenger

Plotting a parabola

The graph of a quadratic formula is called a parabola.
If you want to plot a parabola, make a table first!

COPY THE FORMULA AND TABLE BELOW IN YOUR NOTEBOOK 

AND FILL  IN the first 4 open spaces !

Plotting a parabola

                                           Use brackets
                                                when filling in
                                              negative numbers!

Plotting a parabola

Parabolas have reflection symmetry.

It means that it is SYMMETRICAL.

So the left and right side are exactly 

the same!

Find out if a point lies on a graph

FOTOVRAAG:         Does (-2, 3) lie on the graph of a = -3b + 12?

1st:    Copy this TASK  in your Notebook 

2nd:  Work it out  and 

3rd:   Send in a picture of your work in the next slide

Forgotten what to do for this task? Here is a recap:

1) Fill in the first coordinate in the formula
2) Calculate the result
3) Compare to given second coordinate and draw a conclusion

One more time...

1) Fill in the first coordinate in the formula
2) Calculate the result
3) Compare to given second coordinate

Does (-2, 3) lie on the graph of a = -3b + 12?
a = -3 x -2 + 12 = 18
No, (-2, 3) does not lie on the graph.

HOMEWORK: