2Tvwo Ch7 SUMMARY

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Ch7 SUMMARY p.32-35

First we go through all content of 

§7.1  up and including §7.5 again!

several questions for you to answer and score some points.

Ch7 SUMMARY

Lotta Recap follows!

Recap: Factor

A factor is the number you multiply an original amount by, to get the new amount.

You should be able to calculate the factor for a given increase/decrease in percent and also the other way around.

Drawing a diagram can help!

Recap: Factor

Exercise 1:           to be filled in in next slide!

(so remember your choice)

What factors belong to:

    1. the increase of 21 % and  

    2. the decrease of 32 % ?

A. 121 and 68                  B.  0.79 and 1.32

C.  1.21 and 0.68             D.  79 and 132  

Which factors belong to
1. an increase of 21 % and
2. a decrease of 32 % ?

1. 121 and 68
2. 0.79 and 1.32
3. 1.21 and 0.68
4. 79 and 132

Explanation:

1. an increase of 21 % means:

100 % + 21 % = 121 %   so  factor 1.21

2. a decrease of 32% means:

100 % - 32 % = 68 %  so factor 0.68

Recap: Factor

The key word here 

is 'change'

 (in percentage)!

Exercise 2: the same way as number 1

What change in percentage corresponds to a factor 

of 0.76 ?

A.  a 34 % decrease   B. a 34 % increase

C. a 76 % decrease  D. a 76 % decrease

Change in % if factor is 0.76 ?

1. a 24 % decrease
2. a 24 % increase
3. a 76 % decrease
4. a 34 % decrease

Explanation:

factor  0.76  corresponds to 76 % of the old amount

so  100 % - 76 % = 34 %

Conclusion:

multiplying by factor 0.76 means that 34 % is taken off!

Recap: Factor

The key word here is:

'change' (in percentage) !

Exercise 3: again in the same way.

What change in percentage corresponds to a factor of 3 ?           A. 400 %         B. 300 %

      C. 130 %              D. 200 % 

What change in %
corresponds to a factor of 3 ?

1. 400 %
2. 300 %
3. 130 %
4. 200 %

Explanation:

If you do:                  x 3,

then  you get:

100 %  x  3  =  300 %

But.... at the start we already had 100 %.

So the change is:      300 % - 100 % = 200 % more!

Those nasty percentages ......

These little fellas really made us sweat!

Recap: Exponential formulas

A table or graph shows exponential growth if the bottom row (=vertical variable) is multiplied by the same number everytime the top row/horizontal variable increases by 1. (read this at least two times!)

An exponential formula has the form

b is the initial amount, the value of y when x = 0

g is the growth factor, the number you multiply with.

y=b⋅g​x​​

Recap: Exponential formulas

Recap: Growth factor

If the growth factor is between 0 and 1,

the graph is decreasing.

If the growth factor is 1,

the graph is constant

If the growth factor is more than 1,

the graph is increasing.

The following slides ...

we skip for now, because they are about 

§7.5 Standard notation!

You'll just see them coming by, till the last slide comes up. 

Recap: Standard notation

A number in standard (=scientific) notation is a number between 1 and 10 multiplied by a power of 10.

The power of 10 tells you how many places you should move the decimal point to the right (positive power) or to the left (negative powers).

You should be able to write normal numbers in standard notation and the other way around.

Recap: Standard notation

Write these numbers in standard notation. Round the first number to two decimal places. Try these two on paper!

Next slides provides you with the answers. Then compare.

Recap: Standard notation

Write these numbers in standard notation. Round the first number to two decimal places. These tiny numbers are there to help you counting!

Recap: Standard notation

Write these numbers in normal notation.

Recap: Standard notation

Write these numbers in normal notation.

Homework time

Make, Correct and Hand in :
§7.6, CHOOSE ONLY 3 of THEM!!   That's enough.

Of course I advise you to do 48, which is based on a legend about the invention of the CHESS game!