2TH §7.6 Mixed exercises.

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• Middelbare school
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• Leerjaar 2

§7.6 Mixed exercises

Lot of Recap follows! And some questions too.

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 table can help!

Recap: Factor

Exercise 1:           ANS

What factors belong to:

    1. the increase of 21 % and  

    2. the decrease of 32 % ?

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 24 % decrease   B. a 24 % increase

C. a 76 % decrease    D. a 34 % 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 % = 24 %

Conclusion:

multiplying by factor 0.76 means that 24 % 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!

§7.3 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, because   

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

y=b⋅g​x​​

g​0​​=1

Recap: MAKING Exponential formulas

First we CHECK from the TABLE IF there is exponential growth.

Only the FORMULA is made.  Just have a good look and be amazed:

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.

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. 

MAKE THIS TASK IN YOUR NOTEBOOK, now!

COPY the two tasks and then write down the answers.

Next slides will provides you with the answers, later on.

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.

MAKE THIS TASK IN YOUR NOTEBOOK, AGAIN.

COPY the two exercises and then write down the answers.

Recap: Standard notation

Write these numbers in normal notation.

Homework time

Do §7.6 Mixed exercises: Exercises 45 + 49

Upload your corrected work in Classroom!

Next lesson is Tuesday. We will start with Chapter 8.