2Tvwo Ch9 SUMMARY p.110-113 (long version)

• Wiskunde
• Middelbare school
• havo
• Leerjaar 2

SUMMARY p.110-113

This LessonUp is meant to:

+ pimp your knowledge and to

+ increase your skill in applying it

 You'll get some information several times, followed by a task.

Now some practice!

+ open your Notebook

+ Copy and make the following task and

+ key in your answer in the slide after the next one

+ maybe using the 'Skill' on p.1112 (the same content as just shown)

 Solve linear equations

Work out on paper in your Notebook:

TASK 1:

Solve          y + 137 = 3(6y-113) - 3y

TASK 1
y + 137 = 3(6y-113) - 3y
The solution is:

1. y = -34
2. y = 36
3. y = 34
4. y = -36

Solve linear equations

SOLUTION TASK 1:

Solve          y + 137 = 3(6y-113) - 3y

                     y + 137 = 18y -339 - 3y       work out brackets

                      y + 137 = 15y - 339              adding like terms

                             137 = 14y - 339              variables on one side

                            476 = 14y                          adding 339 on both sides

                               34 = y                              divide by 14

                                  y = 34

'New old stuff' now: 

+ reading off the p.o.i. of two graphs

+ how to calculate the p.o.i. of the graphs of two lines

+ see next slides!

In this example the graphs were given.

If this isn't the case, we have to

calculate the p.o.i.

How? See next slides!

Calculate point of intersection

TASK 2:

Calculate the coordinates of the point of intersection between

y = 8x + 5 and y = 11 - 2x                

Again:

+ copy and work it out in your Notebook, maybe using Method p.97 

    (the same as just shown)

+ fill in your answer in the next slide

+ the answer -the coordinates- are not whole numbers!

TASK 2:
The p.o.i. is:

1. (9.8 , 0.6)
2. (9.6 , 0.9)
3. (6.9 , 0.8)
4. (0.6 , 9.8)

Calculate point of intersection

SOLUTION TASK 2:

Calculate the coordinates of the point of intersection between

y = 8x + 5 and y = 11 - 2x

8x + 5 = 11 - 2x                  

10x + 5 = 11

10x = 6

x = 0.6                     Point of intersection is (0.6, 9.8)

y=8⋅0.6+5=9.8

y=11−2⋅0.6=9.8

You are doing great, 

+ going through the whole Chapter in one LessonUp!

+ refreshing your memory and 

+ practising are more important than

+ learning new things now!

High time for everybody's favorite (?):

solving inequalities !

TASK 3:

 For which values of x is are the

results for formula A greater than the results for

formula B?

Key in your answer in the next slide!

TASK 3:
For which values of x are the results for graph A greater than the results for graph B?

SOLUTION:
For x is greater than 30 the results for graph 

A are greater than the results for graph B.

Because then the graph for A lies higher

than the graph for B!

SOLVING INEQUALITIES goes on: 

On the right you see the steps to take.

Next slide shows an example

 (which explains much more!).

Solve inequalities

TASK 4:

Solve 5x - 6 > 10 - 3x          

Time for action from your side!

+ copy the inequality and

+ solve it, using the 4 steps you find in the SKILL on p.112

+ key in your answer in the next slide

TASK 4:

1. x is smaller than 4
2. x is smaller than 2
3. x is greater than 2
4. x is greater than 4

SOLUTION TASK 4:

Solve inequalities

Solve 5x - 6 > 10 - 3x

5x - 6 = 10 - 3x

8x - 6 = 10

8x = 16

x = 2

                 Solution: x > 2

Next slide is about:

rearranging (herschrijven) a formula, so that

+ you can express one variable p in  variable q so that

+  you can calculate p, when you know  q 

+ confused? you won't be, after the following explanation!

Rearrange formulas

TASK 5:

Express h in terms of t and write as short as possible:

2(h - 5) = t + 5  

+ copy this task in your Notebook and 

+ work it out, maybe using the first SKILL on p.113 (the same as just shown!)

+ key in your answer in the next slide

TASK 5:
Rearranging 2(h-5) = t + 5
gives: h = ...................

​2​​1​​

​2​​1​​

​2​​1​​

1. h = 7.5 + 0.5t
2. h = t + 7 1/2
3. h = -0.5t + 7.5
4. h = 0.5t + 7.5

SOLUTION TASK 5:

Rearrange formulas

Express h in terms of t and write as short as possible:

2(h - 5) = t + 5

2h - 10 = t + 5

2h = t + 15

h = 0.5t + 7.5

Finally ....

Substitution!

In football this is something similar:

someone is taken out and 

somebody else takes his place.

Substitute formulas

TASK 6:

Substitute and simplify:

A: a  = 7 - 5t            B: t = -2h + 3. 

Once more:

+ copy this exercise and

+ work it out in your Notebook; then

+ key in your answer n the next slide

TASK 6:

1. a = 10h - 8
2. a = 8 - 10h
3. a = -8 -10h
4. a = -8 + 10h

Substitute formulas

SOLUTION TASK  6:

Substitute and simplify:

A: a  = 7 - 5t            B: t = -2h + 3

a = 7 - 5(-2h + 3)

a = 7 + 10h - 15

a = 10h - 8      or a = -8 + 10h

Homework time

p.110-113 SUMMARY

Make (at least) four of the 8 Tasks.

Of course it makes sense trying those Tasks you find difficult!

First Study the Skill prior to (=voorafgaand aan) the Task you make.