Post on 19-Dec-2015
transcript
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
18 Apr 202318 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.
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
2cm
2cm
3cm
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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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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2c c 4c+ + = 7c
2nd Row : + + =
2d 2d 3d+ + = 7d
Tidying TermsNational 4
EF 1.1c
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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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
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 1Ch7 (page 85)
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AlgebraAlgebraSimplifying Algebraic Expressions
National 4EF 1.1c
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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2. Calculate (a) (-3a) + (-4b) +2a + 3b
1. Find the perimeter.
3. Find all the missing angles.
4d
5d
120o
40o
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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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
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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AlgebraAlgebraSimplifying Algebraic Expressions
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
23x
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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AlgebraAlgebraSimplifying Algebraic Expressions
Reminder !Multiplying terms
7 a 7a5w 5w
2 4m m b b 2b
28m
( NOT 2b )
( NOT 8m )
National 4EF 1.1c
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 2Ch7 (page 86)
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AlgebraAlgebraSimplifying Algebraic Expressions
National 4EF 1.1c
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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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)
6h
2a
100o
60o
National 4EF 1.1a
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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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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Removing aRemoving aSingle BracketSingle Bracket
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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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Removing aRemoving aSingle BracketSingle Bracket
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National 4EF 1.1a
7 + 3(4 - y) =7 + 12
Example 7
9 - 3(8 - y) =9 - 24
Example 8
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Removing aRemoving aSingle BracketSingle Bracket
- 3y= 19 - 3y
Tidy Up
+ 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
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= 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
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch7 (page 86)
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AlgebraAlgebra Removing bracketsNational 4
EF 1.1a
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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2. 7( 1) - 3
3. 15% 1500
Simplif y
Simplif y
Find
x x x x
p
of
National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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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
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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 ?
National 4REL 1.1b
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Balancing MethodBalancing Methodw
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4 44
4
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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Balancing MethodBalancing Methodw
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P P4
P44
4
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
P=8
National 4REL 1.1b
18 Apr 2018 Apr 202323
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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 learn how to use the rules for solving equations.
National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The Balancing Method
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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
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x = 20 - 317
(- 3)
x =
Simple EquationsSimple Equationsw
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National 4REL 1.1b
24 – 8 =
24 - x =8Example 2
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24 = 8 + xx
(+ x)
Simple EquationsSimple Equations
(- 8)
16 =xx = 16
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National 4REL 1.1b
4x =20Example 3
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x = 20 ÷ 45
(÷ 4)
x =
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National 4REL 1.1b
8x =28Example 4
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x = 20 ÷ 83.5
(÷ 8)
x =
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National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Now try Exercise 4Ch7 (page 87)
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Simple EquationsSimple EquationsNational 4REL 1.1b
Apr 18, 2023Apr 18, 2023
Starter QuestionsStarter Questionsw
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2x + 3 = 15
Q2. 14% of 700
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National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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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
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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
National 4REL 1.1b
18 Apr 2018 Apr 202323
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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
National 4REL 1.1b
18 Apr 2018 Apr 202323
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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 learn how to use the rules for solving equations.
National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The Balancing Method
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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
2x
Example 1
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= 18
EquationsEquations
x = 9
(- 4)
(÷2)
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National 4REL 1.1b
9x - 5 =40
9x
Example 2
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= 45
EquationsEquations
x = 5
(+ 5)
(÷9)
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National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com
Now try Exercise 5Ch7 (page 88)
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EquationsEquationsNational 4REL 1.1b
Apr 18, 2023Apr 18, 2023
Starter QuestionsStarter Questionsw
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(a) x + 3 = 8 (b) 2x – 14 = 50
Q2. Is this statement true
(x – 1) – 3(x + 1) = -2x
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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.
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Equations and Equations and bracketsbrackets
National 4REL 1.1b
5(x - 3) =25 5x
Example 1
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- 15= 25
Multiply out the bracket first and then solve.
Equations and Equations and bracketsbrackets
5x = 25 + 15 x = 40 ÷ 5
= 40= 8
(+15)
(÷5)
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National 4REL 1.1b
3(g - 1) =9 3g
Example 2
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- 3 = 9
Multiply out the bracket first and then solve.
Equations and Equations and bracketsbrackets
3g = 9 + 3 g = 12 ÷ 3
= 12= 4
(+3)
(÷3)
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National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com
Now try Exercise 6Ch7 (page 89)
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Equations and Equations and bracketsbrackets
National 4REL 1.1b
Apr 18, 2023Apr 18, 2023
Starter QuestionsStarter Questionsw
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(a) x + 7 = 29 (b) 2x – 5 = 21
Q2. Is this statement true
(x + 1) – 2(x + 1) = -x
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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.
Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com
Equations and Equations and bracketsbrackets
National 4REL 1.1b
6x - 3 = x + 7 5x
Example 1
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- 3 = 7
Equations and Equations and bracketsbrackets
5x = 7 + 3 x = 10 ÷ 5
= 10
2
(- x)
(+3)
(÷5)
x =
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National 4REL 1.1b
8y + 1 = 5y + 7 3y
Example 2
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+ 1= 7
Equations and Equations and bracketsbrackets
3y = 6 y = 2
(- 5y)
(-1)
(÷2)
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National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr. Created by Mr. Lafferty@mathsrevision.comLafferty@mathsrevision.com
Now try Exercise 7Ch7 (page 89)
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Equations and Equations and bracketsbrackets
National 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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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
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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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
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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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
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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InequalitiesInequalities
Examples : Write in words what each mean.
5 > 3
-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
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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InequalitiesInequalities
(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
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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InequalitiesInequalities
(a) y < 0
(b) y > 2
(c) y ≤ -2
(d) y > 3
-3, -2, -1
3
-3, -2
No solution
National 4REL 1.1b
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InequalitiesInequalities
The Good News
Same rule as solving equations
The Balancing Method
National 4REL 1.1b
2x + 4 ≥30
2x
Example 1
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≥ 26
x ≥ 13
(- 4)
(÷2)
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InequalitiesInequalitiesNational 4REL 1.1b
4x - 5 ≤19
4x
Example 2
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≤ 24
x ≤ 6
(+ 5)
(÷6)
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InequalitiesInequalitiesNational 4REL 1.1b
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Now try Extension Booklet
8E (page 27)
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InequalitiesInequalitiesNational 4REL 1.1b