9-jun-15created by mr. lafferty maths dept. tidying up terms multiplying terms algebra solving...

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Tidying Up Terms

Multiplying Terms

AlgebraAlgebraw

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Solving Simple Equations ( x+1=5 )

Removing Brackets & Simplifying

Harder Equations ( 2x+1=9 )

Solving Equations ( brackets)

Solving Equations (terms either side)

Inequalities

National 4

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.

2. 30% of £300

3. Tidy up the expression

5y + 3d +4d + 10y

4. Explain how do find the area and perimeter of the shape.6cm

National 4EF 1.1c

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Understand the term ‘like Understand the term ‘like terms’.terms’.

1. To explain how to gather ‘algebraic like terms’.

AlgebraAlgebra

2.2. Gather like terms for Gather like terms for simple simple expressions.expressions.

Multiplying TermsNational 4EF 1.1c

18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

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.com First Row : + + =

2c c 4c+ + = 7c

2nd Row : + + =

2d 2d 3d+ + = 7d

Tidying TermsNational 4

EF 1.1c

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.com 3rd Row : + + =

3f f 2f+ + = 6f

In Total we have

7c + 7d + 6f

CANNOTTIDY UP

ANYMORE

WE CAN ONLY TIDY UP “LIKE TERMS”

Tidying TermsNational 4

EF 1.1c

18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

Tidying Termsw

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WE CAN ONLY TIDY UP “LIKE TERMS”

Tidy up the following:

Q1. 2x + 4x + 5y -3y + 18 =

Q2. 4a + 3b + 5a + 6 – b =

6x + 2y + 18

9a + 2b + 6

National 4EF 1.1c

Now try Exercise 1Ch7 (page 85)

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AlgebraAlgebraSimplifying Algebraic Expressions

National 4EF 1.1c

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2. Calculate (a) (-3a) + (-4b) +2a + 3b

1. Find the perimeter.

3. Find all the missing angles.

National 4EF 1.1c

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1.1. Understand the key steps Understand the key steps of multiplying terms.of multiplying terms.

1. To explain how to multiply out algebraic terms.

AlgebraAlgebra

2.2. Apply multiplication Apply multiplication rules rules for simple for simple expressions.expressions.

Multiplying TermsNational 4EF 1.1c

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Reminder !We can only add and subtract “ like terms “

x x x x 4x9 7p p 2p

10 6 1w 3 6a b a b

2 2 2x x x

2 7a b9 6w

National 4EF 1.1c

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Reminder !Multiplying terms

7 a 7a5w 5w

2 4m m b b 2b

( NOT 2b )

( NOT 8m )

National 4EF 1.1c

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National 4EF 1.1c

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1. Find the perimeter and area of the shape.

3. Find all the missing angles.

2. Calculate (a) (-3m) x (-4m) (b) (2b) x (3a)

National 4EF 1.1a

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1.1. Understand the key steps Understand the key steps in removing brackets.in removing brackets.

1. To explain how to multiply out simply algebraic brackets.

AlgebraAlgebra

2.2. Apply multiplication Apply multiplication rules rules for integers numbers for integers numbers when when removing brackets.removing brackets.

Removing bracketsNational 4EF 1.1a

3(b + 5) =3b + 15

Example 1

4(w - 2) =4w - 8

Example 2

Apr 18, 2023Apr 18, 2023 Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com

Removing aRemoving aSingle BracketSingle Bracket

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National 4EF 1.1a

2(y - 1) =2y - 2

Example 3

7(w - 6) =7w- 42

Example 4

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National 4EF 1.1a

8(x + 3) =8x+ 24

Example 5

4(3 -2m) = 12 - 8m

Example 6

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National 4EF 1.1a

7 + 3(4 - y) =7 + 12

Example 7

9 - 3(8 - y) =9 - 24

Example 8

- 3y= 19 - 3y

Tidy Up

= -15 + 3y

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National 4EF 1.1a

4(m - 3) - (m + 2) =4m - 12 - m - 2

Example 9

Example 10

= 3m - 14

Tidy Up

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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National 4EF 1.1a

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AlgebraAlgebra Removing bracketsNational 4

EF 1.1a

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.com 1. 3 - 6 - 3

2. 7( 1) - 3

3. 15% 1500

Simplif y

x x x x

National 4REL 1.1b

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2.2. Solving simple algebraic Solving simple algebraic equations.equations.

1. To solve simple equations using the‘‘Balancing Method’.Balancing Method’.

1.1. Know the process of theKnow the process of the‘‘Balancing Method’.Balancing Method’.

EquationsEquationsSolving EquationsNational 4

REL 1.1b

18 Apr 2018 Apr 202323

Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept

Balancing MethodBalancing Methodw

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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 ?

National 4REL 1.1b

18 Apr 2018 Apr 202323

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Take 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

National 4REL 1.1b

18 Apr 2018 Apr 202323

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Let’s solve it using maths.

Let P be the weight 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

National 4REL 1.1b

18 Apr 2018 Apr 202323

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It would be far too time consuming to draw out

the balancing scales each time.

We will now learn how to use the rules for solving equations.

National 4REL 1.1b

The Balancing Method

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.com The method we use to solve equations is

EquationsEquations

Write down the opposite of the following :

+opposite is

x-÷opposite is

opposite is

opposite is- +÷ x

Solving EquationsNational 4REL 1.1b

x + 3 =20Example 1

x = 20 - 317

Simple EquationsSimple Equationsw

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National 4REL 1.1b

24 – 8 =

24 - x =8Example 2

24 = 8 + xx

Simple EquationsSimple Equations

16 =xx = 16

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National 4REL 1.1b

4x =20Example 3

x = 20 ÷ 45

(÷ 4)

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National 4REL 1.1b

8x =28Example 4

x = 20 ÷ 83.5

(÷ 8)

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National 4REL 1.1b

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Simple EquationsSimple EquationsNational 4REL 1.1b

Apr 18, 2023Apr 18, 2023

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.com Q1. Solve for x

2x + 3 = 15

Q2. 14% of 700

Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com

National 4REL 1.1b

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2.2. Solving harder algebraic Solving harder algebraic equations by using rule equations by using rule repeatedly.repeatedly.

1. To solve harder equations using the rule ‘‘Balancing Method’.Balancing Method’.repeatedly.repeatedly.

1.1. Know the process of Know the process of ‘Balancing Method’.‘Balancing Method’.

EquationsEquationsHarder EquationsNational 4

REL 1.1b

18 Apr 2018 Apr 202323

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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 2Let a be the price of an adult ticket.

We know that a child price = £2

National 4REL 1.1b

18 Apr 2018 Apr 202323

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.com For balance we have

5a + 6 3a + 16=

Subtract 6 from each

5a=3a + 10

Subtract 3a from each

-3a -3a

Divide each side by 2

Adult ticket price is £5

National 4REL 1.1b

18 Apr 2018 Apr 202323

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It would be far too time consuming to draw out

the balancing scales each time.

We will now learn how to use the rules for solving equations.

National 4REL 1.1b

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.com The rule we use to solve equations is

EquationsEquations

Write down the opposite of the following :

+opposite is

x-÷opposite is

opposite is

opposite is- +÷ x

Level E Harder EquationsNational 4REL 1.1b

2x + 4 =22

Example 1

EquationsEquations

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National 4REL 1.1b

9x - 5 =40

Example 2

EquationsEquations

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National 4REL 1.1b

18 Apr 202318 Apr 2023 Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com

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EquationsEquationsNational 4REL 1.1b

Apr 18, 2023Apr 18, 2023

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(a) x + 3 = 8 (b) 2x – 14 = 50

Q2. Is this statement true

(x – 1) – 3(x + 1) = -2x

National 4REL 1.1b

Apr 18, 2023Apr 18, 2023ww

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1. To show how to solve equations that have bracket terms.

1.1. Be able to multiply out Be able to multiply out brackets and solve brackets and solve equations.equations.

Equations and Equations and bracketsbrackets

National 4REL 1.1b

5(x - 3) =25 5x

Example 1

- 15= 25

Multiply out the bracket first and then solve.

5x = 25 + 15 x = 40 ÷ 5

= 40= 8

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National 4REL 1.1b

3(g - 1) =9 3g

Example 2

- 3 = 9

Multiply out the bracket first and then solve.

3g = 9 + 3 g = 12 ÷ 3

= 12= 4

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National 4REL 1.1b

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National 4REL 1.1b

Apr 18, 2023Apr 18, 2023

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(a) x + 7 = 29 (b) 2x – 5 = 21

Q2. Is this statement true

(x + 1) – 2(x + 1) = -x

National 4REL 1.1b

Apr 18, 2023Apr 18, 2023ww

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1. To show how to solve equations with terms on both sides.

1.1. Be able to solve equations Be able to solve equations with terms on both sides.with terms on both sides.

National 4REL 1.1b

6x - 3 = x + 7 5x

Example 1

- 3 = 7

5x = 7 + 3 x = 10 ÷ 5

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National 4REL 1.1b

8y + 1 = 5y + 7 3y

Example 2

+ 1= 7

3y = 6 y = 2

(- 5y)

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National 4REL 1.1b

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National 4REL 1.1b

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.com 7 4 9 11 3

2. Find two numbers that add to give 10

and multiply to give 24

1. Simplify

3. Find LCM of 4 qand 7

a a b b ab

National 4REL 1.1b

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2.2. Solving simple Solving simple inequalities equations.inequalities equations.

1. To explain the various symbols for inequalities.

1.1. Know rule the 4 symbols Know rule the 4 symbols forforinequalities.inequalities.

InequalitiesInequalitiesNational 4REL 1.1b

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The equations you were solving were called equations because they contained an “=“ sign.

InequalitiesInequalities

greater than

less than

greater than or equal to

less than or equal to

There are 4 other Mathematical symbolsThey are called inequalities :

National 4REL 1.1b

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Examples : Write in words what each mean.

-7 < -6

y ≤ -5

x ≥ 2

means 5 is greater than 3

means -7 is less than -6

means x can take the value2 or greatermeans y can take the value-5 or less

Arrow ALWAYS points to the

smallest number

National 4REL 1.1b

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.com Examples : Write out an inequality for the numbers

(a) 14 and 6

(b) -2 and 1

(c) -3 and -7

(d) 34 and -35

14 > 6

-2 < 1

-3 > -7

34 > -35

National 4REL 1.1b

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.com Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3

(a) y < 0

(b) y > 2

(c) y ≤ -2

(d) y > 3

-3, -2, -1

-3, -2

No solution

National 4REL 1.1b

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The Good News

Same rule as solving equations

National 4REL 1.1b

2x + 4 ≥30

Example 1

≥ 26

x ≥ 13

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4x - 5 ≤19

Example 2

≤ 24

x ≤ 6

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Now try Extension Booklet

8E (page 27)

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9-jun-15created by mr. lafferty maths dept. tidying up terms multiplying terms algebra solving...

c slide

terms algebra

algebraic terms

d tidying terms national

brackets national

equations terms

algebraic expressions

o national

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