1TH/vwo CH12 OVERVIEW

Overview CH12
We march through all content,
now and then you'll make a task.
In this way all content is revived!


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Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 1

In deze les zitten 32 slides, met interactieve quizzen en tekstslides.

time-iconLesduur is: 50 min

Onderdelen in deze les

Overview CH12
We march through all content,
now and then you'll make a task.
In this way all content is revived!


Slide 1 - Tekstslide

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.

Slide 2 - Tekstslide

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.

Slide 3 - Tekstslide

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:

Slide 4 - Tekstslide

Powers and negative numbers

Slide 5 - Tekstslide

x        = ....
A.                             B. 
C.                              D.  
Key in your answer in the next slide.
4a2
3a2
7a4
7a2
12a2
12a4
timer
0:30

Slide 6 - Tekstslide

4 a squared times 3 a squared = .......
A
7 a to the 4th power
B
7 a squared
C
12 a to the fourth power
D
12 a squared

Slide 7 - Quizvraag

x        = ....
A.                             B. 
C.                              D.  
4  x  3 =  12         and             x             =   
So the good answer is:  C !
4a2
3a2
7a4
7a2
12a2
12a4
a2
a2
a4

Slide 8 - Tekstslide

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

Slide 9 - Tekstslide

Quadrants
In which quadrant does
(-4, -5) lie ?
Key in in the next slide.
first quadrant
second quadrant
third quadrant
fourth quadrant

Slide 10 - Tekstslide

(-4, -5) lies in which quadrant ?
timer
0:15
A
1st
B
2nd
C
3rd
D
4th

Slide 11 - Quizvraag

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

Slide 12 - Tekstslide

(5, -4) lies in which quadrant?
timer
0:15
A
1st
B
2nd
C
3rd
D
4th

Slide 13 - Quizvraag

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

Slide 14 - Tekstslide

Make the Formula
for this graph in your
Notebook!
Use the 4 steps!
Key it in in the next
slide.
timer
1:30

Slide 15 - Tekstslide

The formula is:

Slide 16 - Woordweb

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

Slide 17 - Tekstslide

Slide 18 - Tekstslide

Slide 19 - Tekstslide

Slide 20 - Tekstslide

Start value = 4
Gradient = 0.8

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

Slide 21 - Tekstslide

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

Slide 22 - Tekstslide

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

Slide 23 - Tekstslide

A parabola is
A
something like ebola
B
a nicely rounded graph
C
a strange animal
D
a messenger

Slide 24 - Quizvraag

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 !

Slide 25 - Tekstslide

Plotting a parabola



                                           Use brackets
                                                when filling in
                                              negative numbers!

Slide 26 - Tekstslide

Plotting a parabola



Parabolas have reflection symmetry.
It means that it is SYMMETRICAL.
So the left and right side are exactly 
the same!

Slide 27 - Tekstslide

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


Slide 28 - Tekstslide


Slide 29 - Open vraag

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.

Slide 30 - Tekstslide

HOMEWORK:
p.194:
52, 53 and 54

Slide 31 - Tekstslide

Slide 32 - Tekstslide