3Tvwo §8.6 or §10.6 Mixed exercises

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Good morning!  By the way:

After this LessonUp:

+ ask me a question by mail if you are stuck! I will explain a bit

   easier or a bit differently than the book.

+ I am going to look into your Homework, giving some advice and sometime a mark.

+ 

§8.6 or §10.6 Mixed exercises.

For both Math types (A and B)

 I have one exercise,

 that we will look into a bit deeper!

First Math A : exercise 34, p.30

Math B pupils:

You may start already, doing §10.6 Mixed exercises.

Please keep an eye on this LessonUp, so that you can follow your Math B part!

Answer it in the next slide:

a. 132 %                     b. 1.32 %

c. 32 %            d. 3.2 % 

How many percent?

1. 132 %
2. 1.32 %
3. 32 %
4. 3.2 %

Solution 34a:

This is an easy one, just look:

34b is more difficult however.

Because there is no index number 100 now and we have o calculate more!

A possible 'plan' to tackle 34b:

• 1.      read off the index numbers for Finland's salaries in 

                             a. class 30-34  and also

                             b. class 55-59

• 2.         result:  class 30-34 = 2800 euros = indexnumber 112   (= 112 %)
• 3.          class 55-59 =  indexnumber 128    (=128 %)
• 4.           calculate indexnumber 1  (or 1 %)   and finally :
• 5.           calculate indexnumber 128 !       THE NEXT SLIDE PUTS THIS ALL INTO PRACTICE!!

Try 34c by yourself now!

•        Homework: §8.6 Mixed exercises. 
•        You may leave out one exercise!
•        As usual, Mixed exercises sometimes is a bit more difficult than the                      preceding paragraphs.
•          Don't hesitate to have a peep in the Solutionsbook, to have an idea                       of what you are supposed to do!

Math B, finally!

Your attention for a very difficult exercise: 

the last question of 38, for which we need the results of a up to h!

So we will concentrate on:   38 i, p.110.

(Remember I wrote lately that if you managed to do this one by yourself, you are at the good level for Mah B in 4th Form?)

Try to follow every little step

of the coming slides.

I cut up the whole content of 34 i, making use of earlier results,

in 34 a,b,c,d,e !

38

This alone does say much ....

So here comes the whole exercise!

Just open your Textbook p.110,

and maybe your Notebook to, to compare.

Below you the results of 38a,b,c and f (that we just use now):

Also keep in mind the result of 38e, 

that we don't work out now, but just use, later!

Just a reminder:

Before doing 38i, we already explained this:

And that gives us the idea to describe the whole area of ABCD in the areas of 4 triangles.  See next slide for this!

Which 4 triangles? Choose in next slide from:

a. BMX, AMX, AYM, DYM   b. BCM, ADM, ABC, ACD

c. ACD, BCD, ABC, ACD  d. ABM, BCM, CMD, DMA

The right triangles are:

1. BMX, AMX, AYM, DYM
2. BCM, ADM, ABC, ACD
3. ACD, BCD, ABC, ACD
4. ABM, BCM, CMD, DMA

calculating AREAS ? HOW? 

 The calculations of the 4 areas all contain the same part.

That part is a multiplication of 2 factors.

Which 2 factors?

Key in in next slide!

The part that stays the same is
.... x ....

the answer:

That part is:                1/2 x r .........

Because we make use of the ground rule for areas of a right-angled triangle:

area triangle = 1/2 x base x height (!)

Here 'r' is the height.

The next step is then working out these areas into:

Now first AB and CD, then also BC and AD 

are taken together, so that we can use:

So there we go:

repeating the last result:

,we can finally finish the task:

Do you still remember what we were supposed to 'explain'?

I can image very well, if not. But it was this last step!

That the area is r x (AB + CD).

Compliment yourself,

if you managed to follow (and understand) every little step!

+ If it went too quick, just read it all back in the Solutionsbook!

+ Did you notice how many steps were needed, in order to

arrive at the conclusion?

+ That makes it typical for MATH B!

Hopefully it's not that bad with you, now! 

Anyway, a little exercise would be good for all of us.

And not just for the brains!

Homework time.

§10.6 Mixed exercises.

Just choose 3 of them.

We already spend a lotta time and energy on 43...