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

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.
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Slide 1: Slide
WiskundeMiddelbare schoolhavoLeerjaar 2

This lesson contains 36 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

## Items in this lesson

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.

#### Slide 3 -Slide

Now some practice!
+ 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)

#### Slide 4 -Slide

Solve linear equations
Work out on paper in your Notebook:

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

timer
2:00

#### Slide 5 -Slide

y + 137 = 3(6y-113) - 3y
The solution is:
A
y = -34
B
y = 36
C
y = 34
D
y = -36

#### Slide 6 -Quiz

Solve linear equations
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

#### Slide 7 -Slide

'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!

#### Slide 8 -Slide

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!

#### Slide 10 -Slide

Calculate point of intersection
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)
+ the answer -the coordinates- are not whole numbers!
timer
2:30

The p.o.i. is:
A
(9.8 , 0.6)
B
(9.6 , 0.9)
C
(6.9 , 0.8)
D
(0.6 , 9.8)

#### Slide 12 -Quiz

Calculate point of intersection
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=80.6+5=9.8
y=1120.6=9.8

#### Slide 14 -Slide

You are doing great,
+ going through the whole Chapter in one LessonUp!
+ practising are more important than
+ learning new things now!

#### Slide 15 -Slide

High time for everybody's favorite (?):
solving inequalities !

#### Slide 16 -Slide

For which values of x is are the
results for formula A greater than the results for
formula B?

#### Slide 17 -Slide

timer
0:20
For which values of x are the results for graph A greater than the results for graph B?

#### Slide 18 -Mind map

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!

#### Slide 19 -Slide

SOLVING INEQUALITIES goes on:

On the right you see the steps to take.
Next slide shows an example
(which explains much more!).

#### Slide 21 -Slide

Solve inequalities
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

timer
3:00

#### Slide 22 -Slide

A
x is smaller than 4
B
x is smaller than 2
C
x is greater than 2
D
x is greater than 4

#### Slide 23 -Quiz

Solve inequalities
Solve 5x - 6 > 10 - 3x

5x - 6 = 10 - 3x
8x - 6 = 10
8x = 16
x = 2
Solution: x > 2

#### Slide 24 -Slide

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!

#### Slide 26 -Slide

Rearrange formulas
Express h in terms of t and write as short as possible:
2(h - 5) = t + 5

+ work it out, maybe using the first SKILL on p.113 (the same as just shown!)
timer
2:00

#### Slide 27 -Slide

Rearranging 2(h-5) = t + 5
gives: h = ...................
21
21
21
A
h = 7.5 + 0.5t
B
h = t + 7 1/2
C
h = -0.5t + 7.5
D
h = 0.5t + 7.5

#### Slide 28 -Quiz

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

#### Slide 30 -Slide

Finally ....
Substitution!
In football this is something similar:
someone is taken out and
somebody else takes his place.

#### Slide 32 -Slide

Substitute formulas
Substitute and simplify:
A: a  = 7 - 5t            B: t = -2h + 3.

Once more:
+ copy this exercise and
+ work it out in your Notebook; then

timer
2:00

A
a = 10h - 8
B
a = 8 - 10h
C
a = -8 -10h
D
a = -8 + 10h

#### Slide 34 -Quiz

Substitute formulas
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

#### Slide 35 -Slide

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.