2122 vwo allround CH10 Lesson 10.1+10.2

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CH10 Formulas and equations

recap 10.1 and 10.2

Recap:
- Shortening formulas

Formulas

Sometimes formulas are written in a different order.  They all give the same result, because they follow the order of operations.

4 + 0.8 x distance = height
4 + distance x 0.8 = height
0.8 x distance + 4 = height
height = distance x 0.8 + 4
etc.

Wat mag je NIET doen om een formule korter te schrijven?

1. De volgorde van vermenigvuldigen omdraaien
2. Een keerteken weglaten
3. Een plus/min-teken weglaten
4. Woorden afkorten met letters

Writing formulas shorter

The formula 24 - 3 x time = height can be shortened.

When you write a formula shorter you do two things:
- replace the variable with a letter that represents that variable
- leave out the multiplication sign.

Writing formulas shorter

24 - 3 x time = height
- replace the variable with a letter that represents that variable.
24 - 3 x t = h
- leave out the multiplication sign.
24 - 3t = h

Mistakes to watch out for!

- replace the variable with a letter that represents that variable
12 + 3 x time = temperature
12 + 3 x t = t  is WRONG, because you use the letter t for two different variables. Possible ways to shorten the formula are:
12 + 3 x t = T
12 + 3 x t = c                (c for temperature in degrees Celcius)
12 + 3 x h = c               (h for time in hours)
etc.

Mistakes to watch out for!

- replace the variable with a letter that represents that variable
50 - 4 x time = water level
50 - 4 x t = w l  is WRONG, because you use two letters for one variable (water level).
Only use one letter per variable:
50 - 4 x t = w

Shorten the formula
12 + 3 x time = height

Mistakes to watch out for!

- leave out the multiplication sign.
12 - a x 3 = t
12 - a3 = t is WRONG! When leaving out the multiplication sign in a x 3, you always write the number before the letter. a x 3 = 3 x a = 3a.

You shorten the formula like this:
12 - 3a = t

Shorten the formula
price = 50 + time x 10

Shorten the formula
b = a x 15 -2

Shorten the formula
number of yellow beads = number of blue beads x 5

10.2: shortening formulas

You can write formulas shorter by combining the like terms.
Terms are the parts of a formula that you add up.
Terms are called like terms if they have the same variable.

In the formula p = 3a + 5b + 4c + 8 - 2b + a - 13,
3a and a are like terms, 5b and -2b are like terms and 8 and -13 are like terms.
You can shorten this formula to p = 4a + 3b + 4c -5

Hoeveel termen en variabelen zie je hier:
3x + x + 4 + 2

1. 4 termen, 2 variabele
2. 4 termen, 1 variabele
3. 3 termen, 2 variabelen
4. 2 termen, 1 variabele

Geef een voorbeeld van 2 termen die je WEL mag samennemen en 2 termen die je NIET mag samennemen

§ 10.3 Working with formulas

We've done so much with formulas, in § 10.1 and § 10.2:

+ shortening                + simplifying            + you name it!

However you might wonder:

What on earth can we DO with those formulas ?!

This burning question will be answered now!                            

Important: When you replace variables(letters) with numbers, the multiplication sign returns.

And here is an example:

To show you that there can be more solutions to a question:

+ let's first read this information

+ how to make a formula for this situation?

+ you don't have to know how to do this yet, but let's look at a try, in the next        slide!

There are a few more complicated exercise in this paragraph.

That's why we now look at one of them!

Making it easier to deal with them on your own,

later.

Yes indeed, you will experience the return of the multiplication sign very soon...

Just watch the next slide!

Below are two examples:

What's wrong here is this:    the number of days should be done times 40, but it isn't! 

TIP for improvement:     BRACKETS are missing. 

But where to put them? Think about it and be amazed in the next slide!

Below you see how the formula can be corrected.

Watch how important the brackets are!

So the brackets make sure that all the days, spent in the hotel -plus the 1.5 days for cleaning!-  are multiplied by 40 euros.

For an alternative solution, watch the next slide.

In this paragraph we will practise how to calculate the result of a formula

Wat is het verschil tussen een uitkomst berekenen en een vergelijking oplossen?
Geef zelf een voorbeeld van het één en het ander.
Gebruik hiervoor de formule y = 4x + 6