Grab a mini whiteboard on the way in - PowerPoint Presentation

Slide1

Grab a mini whiteboard on the way inSlide2

Notices and the WebsiteSlide3

AssignmentsSlide4

What is the symbol for ‘implies’?

Define proof by deduction.

What is a conjecture?Slide5

⇒

Proof by deduction consists of a logical argument as to why the conjecture must be true. This will often require you to use algebra.

A

n idea, or theory, supported by evidence from the cases you testedSlide6

Chapter

2.1

Using and Manipulating Surds

“It’s not that I’m so smart, it’s just that I stay with problems longer.”

- Albert EinsteinSlide7

Lets see that prep workSlide8

Grab a mini whiteboard and let’s see what you can do!Slide9

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Simplify the following, giving your answers in the simplest surd form.

 Slide10

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Simplify the following, giving your answers in the simplest surd form.

 Slide11

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Simplify the following, giving your answers in the simplest surd form.

 Slide12

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

The largest square number

which is a factor of 32 is 16.

Multiply out the brackets.

Collect like terms.

It’s a good idea to write the positive term

first since

it is easy to lose a minus sign at

the start

of an expression.

 Slide13

Using and Manipulating Surds

Chapter

2.1

Multiply out and simplify:

Surd

Simplest Form

Rationalise

DenominatorSlide14

Using and Manipulating Surds

Chapter

2.1

Multiply out and simplify:

Surd

Simplest Form

Rationalise

DenominatorSlide15

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Notice that the first

and last

terms are

rational numbers

.

 Slide16

Using and Manipulating Surds

Chapter

2.1

Simplify the following, giving your answers in the simplest surd form.

Surd

Simplest Form

Rationalise

DenominatorSlide17

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Multiplying top and

bottom by

 Slide18

Using and Manipulating Surds

Chapter

2.1

Simplify the following, giving your answers in the simplest surd form.

Surd

Simplest Form

Rationalise

DenominatorSlide19

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Multiplying top and

bottom by

This can also be

written

as

 Slide20

Using and Manipulating Surds

Chapter

2.1

Simplify the following, giving your answers in the simplest surd form.

Surd

Simplest Form

Rationalise

DenominatorSlide21

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Rationalising the

denominator

 Slide22

Using and Manipulating Surds

Chapter

2.1

Simplify the following, giving your answers in the simplest surd form.

Surd

Simplest Form

Rationalise

DenominatorSlide23

Using and Manipulating Surds

Chapter

2.1

Simplify the following, giving your answers in the simplest surd form.

Surd

Simplest Form

Rationalise

DenominatorSlide24

Using and Manipulating Surds

Chapter

2.1

Surd

Simplest Form

Rationalise

Denominator

Multiplying top and

bottom by

Rationalising the

denominator

In algebra it is usual to write

letters in alphabetical order

 Slide25

So what are the important rules you need to know from this topic?Slide26

Simplifying a surd by splitting it up

Adding two surds

Multiplying surds

Rationalising

the denominatorSlide27

Do we need to practice any of those skills?Slide28

Let’s get stuck into some activitiesSlide29

Which is the odd one out?

Try this in pairs and don’t forget to fill in the final boxSlide30

Surds

Arithmagons

!!

This one is on your own on your mini whiteboardsSlide31

Can you make your own

Arithmagon

for the person next to you?Slide32
Slide33

You may want to work in pairs or use the big whiteboards of these next couple of questions

–

time to think!Slide34

Angry Surd

What is the value of

a

in the diagram shown? Slide35