3Tvwo §8.6 or §10.6 Mixed exercises

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.
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Slide 1: Slide
WiskundeMiddelbare schoolvwoLeerjaar 3

This lesson contains 31 slides, with interactive quizzes and text slides.

time-iconLesson duration is: 50 min

Items in this lesson

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.

Slide 1 - Slide

§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!

Slide 2 - Slide

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!

Slide 3 - Slide

Slide 4 - Slide




Answer it in the next slide:
a. 132 %                     b. 1.32 %
c. 32 %            d. 3.2 % 

Slide 5 - Slide

How many percent?
A
132 %
B
1.32 %
C
32 %
D
3.2 %

Slide 6 - Quiz

Solution 34a:
This is an easy one, just look:

Slide 7 - Slide

34b is more difficult however.
Because there is no index number 100 now and we have o calculate more!

Slide 8 - Slide

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!!

Slide 9 - Slide

Slide 10 - Slide

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!

Slide 11 - Slide

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?)

Slide 12 - Slide

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 !

Slide 13 - Slide

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.

Slide 14 - Slide

Slide 15 - Slide

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

Slide 16 - Slide

Also keep in mind the result of 38e, 
that we don't work out now, but just use, later!

Slide 17 - Slide

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!

Slide 18 - Slide

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

Slide 19 - Slide

The right triangles are:
A
BMX, AMX, AYM, DYM
B
BCM, ADM, ABC, ACD
C
ACD, BCD, ABC, ACD
D
ABM, BCM, CMD, DMA

Slide 20 - Quiz

Slide 21 - Slide

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!

Slide 22 - Slide

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

Slide 23 - Mind map

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.

Slide 24 - Slide



The next step is then working out these areas into:

Slide 25 - Slide

Now first AB and CD, then also BC and AD 
are taken together, so that we can use:


So there we go:

Slide 26 - Slide

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).

Slide 27 - Slide

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!

Slide 28 - Slide

Slide 29 - Slide

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!

Slide 30 - Slide

Homework time.
§10.6 Mixed exercises.
Just choose 3 of them.
We already spend a lotta time and energy on 43...

Slide 31 - Slide