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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
AlgebraAlgebra
Collecting Like Terms
Removing Brackets
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Removing Brackets & Simplifying
Evaluating Expressions & Formulae
Solving Simple Equations
Solving Equations with Brackets
Constructing Formulae
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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1. A TV has been reduced in the sale
by 20%. I t was £250. How much is it now.
3. 30% of £300
4. Tidy up the expression
5y + 3d +4d + 10y
5. Find the area and
2. Simplif y the ratio 16:64
perimeter of the shape.6cm
2cm
2cm
3cm
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
1.1. Understand the key steps Understand the key steps in removing brackets.in removing brackets.
1. We are learning how to multiply out simply algebraic brackets.
AlgebraAlgebra
2.2. Apply multiplication Apply multiplication rules rules for positive and for positive and negative negative numbers numbers when removing when removing brackets.brackets.
Removing brackets
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
3(b + 5) =3b + 15
Example
4(w - 2) =4w - 8
Example
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Removing aRemoving aSingle BracketSingle Bracket
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
8(x + 3) =8x+ 24
Example
4(3 -2m) = 12 - 8m
Example
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Removing aRemoving aSingle BracketSingle Bracket
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
Example : Write down an expressionfor the amount indicate belowin two difference ways.
5(y - 2) = 5y - 10
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Removing aRemoving aSingle BracketSingle Bracket
y-2
y-2 y-2
y-2y-2
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
a(b + 5) =ab + 5a
Example
p(w - 2) =pw - 2p
Example
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Removing aRemoving aSingle BracketSingle Bracket
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
y(y - 1) = y2 - y
Example
7w(w - 3) =7w2 - 21w
Example
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Removing aRemoving aSingle BracketSingle Bracket
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
a(a2 + 3b) =a3 + 3ab
Example
y2(3y -2c) =3y3 - 2cy2
Example
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Removing aRemoving aSingle BracketSingle Bracket
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
-(x + y) = -x - y
Example
-5(a - 7) =-5a + 35
Example
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Removing aRemoving aSingle BracketSingle Bracket
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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AlgebraAlgebra
y + 5
4
Question : Find the area of the rectangle (i) With brackets(ii) Without brackets.
Removing brackets
= 4(y + 5)
(i) A = L x B
(ii) = 4(y + 5)= 4y + 20
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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1. Remove brackets and simplif y 5f - (f - 4)
2. Calculate the perimeter of the rectangle.
3cm
(x-6)cm
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3a
Ex 2Ch7 (page 56)
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AlgebraAlgebraRemoving Brackets
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
1.1. Understand the key steps Understand the key steps in removing brackets and in removing brackets and simplifying.simplifying.
1. We are learning how to multiply out simply algebraic brackets and collecting like terms.
AlgebraAlgebra
2.2. Apply multiplication Apply multiplication rules rules for positive and for positive and negative negative numbers numbers when removing when removing brackets.brackets.
Removing brackets
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
7 + 3(4 - y) =7 + 12
Example
9 - 3(8 - y) =9 - 24
Example
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Removing aRemoving aSingle BracketSingle Bracket
- 3y= 19 - 3y
+ 3y
Tidy Up
= -15 + 3y
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Tidy Up
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
A = 10(x – 2)
Example
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Removing aRemoving aSingle BracketSingle Bracket
Find my Area (x - 2)
10
Find my Areax
12
A = 12x
A = L x B A = L x B
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MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
4(m - 3) - (m + 2) =4m - 12 - m - 2
Example
Example
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= 3m - 14
7(y - 1) - 2(y + 4) =7y - 7 - 2y - 8 = 5y - 15
Tidy Up
Removing Two Single Removing Two Single BracketsBrackets
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Tidy Up
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
Example : Find area of the orange border
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Removing aRemoving aSingle BracketSingle Bracket
(x - 2)10
x
12 Area =Big Rec – Small Rec
= 12x – 10(x - 2)
= 12x
= 2x + 20
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-10x+ 20
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
Calculate difference if
y = 14
Diff = 3 x 14 – 8= 34
A = 4(y – 5)
Example : Find an expression for the difference inthe areas.
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(y - 5)
47 A = 7(y - 4)
(y - 4)Difference = 7(y - 4) - 4(y – 5)
= 7y - 28= 3y - 8
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- 4y + 20
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
Calculate difference if
x = 4
Diff = 2 x 4 + 20
=28
A = 7(x + 1)
Example : Find an expression for the difference inthe areas.
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(x + 1)
79 A = 9(x + 3)
x + 3Difference = 9(x + 3) - 7(x + 1) = 9x + 27
= 2x + 20
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– 7x - 7
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
As= 4(x - 3)
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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AlgebraAlgebra
x
6
Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section.
4x-3
Removing Brackets & Simplifying
Ab= 6x
= 4x
As= 6x - 4(x - 3)= 6x = 2x + 12
- 12
- 4x+ 12
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3a
Ex 3Ch7 (page 57)
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AlgebraAlgebraRemoving Brackets
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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20 4
2. The ratio of apples to pears is 3:1.
I f there are 24 pieces of f ruit in total.
How many apples are there.
x x x x
x
1. Mulitply out and simplify
3. Factorise
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
1.1. Understand the process of Understand the process of thethe
‘‘Balancing Method’Balancing Method’
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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4
44
4
Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags.
If a small bags weighs 4 kgs. How much does a large bag weigh?
What instrument measures balance
How can we go about solving this using balance ?
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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4 44
4Take a small bag away
from each side.
Take a big bag away from each side.
We can see that a big bag is equal to
4 + 4 =8 kg
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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P P4 P
44
4Lets solve it using maths.
Let P be the weigh of a big bag.
We know that a small bag = 4
2P + 4 P + 12
What symbol should we use for
the scales ?
= Subtract 4 from each
side-4 -4
2P=P + 8Subtract P from each
side-P -P
P=8
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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Group of 5 adults and 3 children go to the local swimming.Another group of 3 adults and 8 children also go swimming.The total cost for each group is the same. A child’s ticket costs £2.
If a child’s ticket costs £2. How much for an adult ticket ?
a a 2
a 2
a a 2Let a be the price of an adult ticket.
We know that a child price = £2
2 aa
2 a
2 22
2 22
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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5a + 6 3a + 16=
Subtract 6 from each
side
-6 -6
5a=3a + 10
Subtract 3a from each
side
-3a -3a
2a=10
a a
a
a a
2
2
2
aa
a
2
2
2
2
22
22
Divide each side by 2
a=5
Adult ticket price is £5
1
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
Balancing MethodBalancing Methodw
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It would be far too time consuming to draw out
the balancing scales each time.
We will now review how to use the rules for solving equations.
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level 2
Examples
EquationsEquations
x – 5 = 11+ 5 + 5
x = 16
x + 8 = 37- 8 - 8
x = 29
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level 2
Examples
EquationsEquations
6x = 72
x = 12
(÷ 6)
2x = 11
x = 5.5
(÷ 2)
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level 2
Examples
EquationsEquations
½x = 5
x = 10
(x 2)¾x = 9
3x = 36
(x 4)
x = 12(÷ 3)
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Revision of Level 2
Examples
EquationsEquations
4x – 2 = 34+ 2 + 2
4x = 36
x = 9
(÷ 4)
2x + 9 = 31- 9 - 9
2x = 22
x = 11
(÷ 2)
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3a
Ex 4Ch7 (page 58)
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AlgebraAlgebraRemoving Brackets
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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1. I have an infi nite amount of line symmetry.
What is my shape?
2. Remove brackets 4(5k - 8)
MTH 3-14aMTH 3-15aMTH 3-15bMTH 4-14aMTH 4-15a
20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.