Algebra 1 Easter Revision Session

Algebra 1

Manipulating algebra, collecting like terms, expanding brackets, factorising, and substitution

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Draw

How do you feel about algebra generally?

Poll

Which of these do you struggle with the most?

• Collecting like terms/ simplifying

• Expanding brackets

• Factorising into brackets

• Substituting into formulae/ expressions

Let's Speak Algebrese

Yes, really.

Getting confident in algebra all stems from being able to look at something with letters in and understand what it's trying to tell us.

Let's Speak Algebrese

We use letters in Algebra to represent either a missing number we want to find, or as a stand in if we might want to change that number a few times. It's also called a VARIABLE

Let's Speak Algebrese

I think of a mystery number and call it n.
Now, I can do stuff to it, and line up the list of things I'm going to do to it so I can work out the final answer WHEN I know the number.

Let's Speak Algebrese

I think of a mystery number and call it n.
I want to add 3 to that number...
So I can call that n + 3
Now, if I say that n is really 10, we know we just do 10 + 3 to get 13. Lovely!

Let's Speak Algebrese

I send you to the shop to buy 10 Easter eggs and 8 Lindt eggs.
I don't know the cost but I could write an expression for how much I'll spend using
10E + 8L then put in the prices later.

Multiple Choice

I think of a number and call it n.

I then add 5 to it.

What is the expression?

• 5n

• n - 5
• n + 5
• n / 5

Multiple Choice

I think of a number and call it n.

I then want to take off 4.

What is the expression?

• n + 4
• 4n

• n / 4
• n - 4

Multiple Choice

I think of a number and call it n.

I then decide to double it.

What is the expression?

• 3n
• n²

• n + 2

• 2n

Multiple Choice

I think of a number and call it n.

I then want to multiply it by 3.

What is the expression?

• n³

• 3n

• n3

• n + 3

Multiple Choice

I think of a number and call it n.

I divide it by 7.

What is the BEST expression below?

• n ÷ 7

• n - 7
• 7n

• n / 7

Multiple Choice

I think of a number and call it n.

I divide it by 5.

What is the BEST expression below?

• n ÷ 5

• n / 5

• 5 / n

• n - 5

Multiple Choice

I think of a number and call it n.

I multiply it by itself.

What is the BEST expression below?

• n + n

• 2n
• n²

• n x n

Multiple Choice

I think of a number and call it n.

I multiply it by 3 and add 7.

What is the expression below?

• 3n + 7
• 7n + 3

• 3n - 7
• n + 7 x 3

Multiple Choice

I think of a number and call it n.

I multiply it by 4 and subtract 9.

What is the BEST expression below?

• 4n - 9
• 4n + 9
• 9 - 4n
• 9n - 4

Multiple Choice

I think of a number and call it n.

I divide it by 8 and add 1.

What is the BEST expression below?

• n/8 - 1

• n/8 + 1

• n/8 + 8

• 8n + 1

Multiple Choice

I think of a number and call it n.

I add 4 THEN multiply by 9.

What is the BEST expression below?

• (n + 4) / 9
• (n - 4) * 9
• (n * 4) + 9
• 9(n + 4)

Multiple Choice

I think of a number and call it n.

I subtract 2 and then multiply by 11.

What is the BEST expression below?

• (n + 2) x 11

• (n - 2) / 11
• (n x 2) - 11

• 11(n - 2)

Draw

I think of a number and call it n.

I add 5 and then multiply by 9.

Draw the expression:

Draw

I think of a number and call it n.

I add 6 and then divide by 9.

Draw the expression:

Draw

I think of a number and call it n.

I take away 3, then multiply by 4, then divide by 5 and add 6.

Draw the expression:

Sorry.

n x n = n²
n x n x n = n³
2n x 4n = 8n²
n x p = np

Multiplying and Dividing

n + n + n = 3n
4n - 2n = 2n
3x + 3y + x + 2y = 4x + 5y
4x² + 2x + x + x² = 5x² + 3x

Adding and Subtracting

Some Key Rules & Examples

Simplifying Algebraic Expressions - Quiz

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Expanding Brackets 1

Expanding = multiplying out

Expanding this bracket looks like this:
3(a + 6)
3 x a = 3a
3 x 6 = 18
3a + 18

Expanding Brackets 1

Expanding = multiplying out

Expanding this bracket looks like this:
3(a - 6)
3 x a = 3a
3 x -6 = -18
3a - 18

Expanding Brackets 1

Expanding = multiplying out

Expanding this bracket looks like this:
4(2a - 7)
4 x 2a = 8a
4 x -7 = -28
8a - 28

Expanding Brackets 1

Expanding = multiplying out

Expanding this bracket looks like this:
a(2a + 7)
a x 2a = 2a²
a x 7 = 7a
2a² + 7a

Expanding Brackets 1

Expanding = multiplying out

Expanding this bracket looks like this:
a(2a + 7b)
a x 2a = 2a²
a x 7b = 7ab
2a² + 7ab

Expand AND simplify:
2(x + w) + 3(2w + x)

3(a – b) + 7(2b – a)

4(t – s) – 3(s – 2t)

a(4a – 2b) – 3(a – b)

• 3(2x + 4)

• 4(x - 1)

• 2a(a + b)

• 3x(x + 4y)

• -4(2x + 3)

• -x(xy - y + x - 7)

​ Have a go.... Challenge!

(x - 5)(2x - 3)

(x + 3)(x + 6)

Expanding double brackets

Sorry.

Factorising

Factorising = putting back into brackets

Now that we've spent time taking things out of brackets, we need to be able to put them back in again, and how we do that is in the name - we need to find the highest common factor of the terms, and divide the whole thing by that...

Q: Factorise 3x + 9
A:
Find the highest common factor of 3 & 9
Find any letters in common
Stick it/them on the outside of a bracket 3(? + ?)
Then find out what needs to be on the inside so that we still get back to the start when we expand
3(x + 3)

Q: Factorise 12x - 4
A:
Find the highest common factor of 12 & 4
Find any letters in common
Stick it/them on the outside of a bracket 4(? - ?)
Then find out what needs to be on the inside so that we still get back to the start when we expand
4(3x - 1)

Q: Factorise 2x² - 3x
A:
Find the highest common factor of 2 & 3
Find any letters in common
Stick it/them on the outside of a bracket x(? - ?)
Then find out what needs to be on the inside so that we still get back to the start when we expand
x(2x - 3)

Multiple Choice

What is the highest common factor of 4 and 8?

• 8

• 4
• 2
• 6

Multiple Choice

What is the highest common factor of 3 and 12?

• 9
• 12

• 3
• 4

Multiple Choice

What is the highest common factor of 3x and 11x?

• 3x
• 33x
• x
• 6x

Draw

Factorise 12x - 9

Draw

Factorise 9p² + 27p

Draw

Factorise this gorgeous expression:

60x²+ 12x - 48xy

Substitution

Substitution = swapping the letters for numbers

Now we've spent ages playing with the letters, let's get rid of them by swapping them out for numbers, also known as substituting.
This means we can find out final answers or evaluate expressions

Substitution

Q:
If a = 4 and b = 5, evaluate
ab

A:
ab means a x b, so we replace each letter with their respective numbers
4 x 5 = 20
so ab = 20 too

Substitution

Q:
If a = 4 and b = 5, evaluate
4a - b

A:
4a - b means 4 x a then take away b, so replace with numbers
4 x 4 - 5 (and using BIDMAS) = 16 - 5 = 11
so 4a - b = 11 too

Substitution

Q:
If a = -3 and b = -2, evaluate
9a - 2b

A:
9a - 2b means 9 x a then take away 2 x b, so replace with numbers
(9 x -3) - (2 x -2) = -27 - -4 = -27 + 4 = -23
So 9a - 2b = -23 too

Multiple Choice

3a + 2b = ?

when a = 4 and b = 2

• 14
• 18
• 20
• 16

Multiple Choice

4a - b = ?

when a = 3 and b = 5

• 3
• 7
• 1
• 38

Multiple Choice

a - 6b = ?

when a = 10 and b = 2

• 4
• -2
• 2

• -8

Multiple Choice

$$\frac{3a+b}{2}=?$$

when a = 5 and b = -3

• 4
• 7
• 6
• 10

Multiple Choice

a² + 5b = ?

when a = 5 and b = 6

• 30
• 40

• 12
• 55

Multiple Choice

$$\frac{2(a-b)}{a}=?$$

when a = 20 and b = -10

• 1

• 3
• 10
• 5

Multiple Choice

2a² = ?

when a = 4

(BIDMAS!!!!)

• 64
• 8
• 16
• 32

Multiple Choice

¾a + ½b = ?

when a = 20 and b = 8

• 17
• 23
• 21
• 19

Graphing

Now you can plot the graph of

y = 2x + 3

Graphing

Now you can plot the graph of

y = 3x + 1

Graphing

Now you can plot the graph of

y = x² - x - 2