MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept....

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



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


20 Apr 202320 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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1.1. Understand the Understand the techniques for simplifying techniques for simplifying terms.terms.

1. We are learning to simplify terms.

AlgebraAlgebraSimplifying Algebraic Expressions

2.2. Be able too simplify Be able too simplify algebraic expressions.algebraic expressions.



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Collecting LIKE terms

- m + a

1 + 4g (NOT 5g )

7 k2 (NOT 7k6)



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Multiplying Terms

6 d

4 h

(NOT 2e )

8 (NOT 8a)

e2

a2



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Dividing Terms

4

3 e


Below is a floor plan of the down stairs of a house.

Apr 20, 2023Apr 20, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com

y 5

y

3y2+ 8y + 15

Living Room

KitchenBathroom

Bedroomy2 5y

3y 15

Tidy up !

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What is the total area of the

downstairs house?



Now try TJ3a

Ex 1Ch7 (page 54)

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AlgebraAlgebraRemoving Brackets




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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



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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


3(b + 5) =3b + 15

Example

4(w - 2) =4w - 8

Example


Removing aRemoving aSingle BracketSingle Bracket

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8(x + 3) =8x+ 24

Example

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

Example



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Example : Write down an expressionfor the amount indicate belowin two difference ways.

5(y - 2) = 5y - 10



y-2

y-2 y-2

y-2y-2

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a(b + 5) =ab + 5a

Example

p(w - 2) =pw - 2p

Example



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y(y - 1) = y2 - y

Example

7w(w - 3) =7w2 - 21w

Example



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a(a2 + 3b) =a3 + 3ab

Example

y2(3y -2c) =3y3 - 2cy2

Example



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-(x + y) = -x - y

Example

-5(a - 7) =-5a + 35

Example



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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




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1. Remove brackets and simplif y 5f - (f - 4)

2. Calculate the perimeter of the rectangle.

3cm

(x-6)cm



Now try TJ3a

Ex 2Ch7 (page 56)

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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


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

Example

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

Example



- 3y= 19 - 3y

+ 3y

Tidy Up

= -15 + 3y

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Tidy Up


A = 10(x – 2)

Example



Find my Area (x - 2)

10

Find my Areax

12

A = 12x

A = L x B A = L x B

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

Example

Example


= 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


Example : Find area of the orange border



(x - 2)10

x

12 Area =Big Rec – Small Rec

= 12x – 10(x - 2)

= 12x

= 2x + 20

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-10x+ 20


Calculate difference if

y = 14

Diff = 3 x 14 – 8= 34

A = 4(y – 5)

Example : Find an expression for the difference inthe areas.


(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


Calculate difference if

x = 4

Diff = 2 x 4 + 20

=28

A = 7(x + 1)

Example : Find an expression for the difference inthe areas.


(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


As= 4(x - 3)


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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



Now try TJ3a

Ex 3Ch7 (page 57)

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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



EquationsEquationsw

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

1. To revise Level 2 using the rule

‘‘Balancing Method’Balancing Method’

Revision of Level 2

1.1. Understand the process of Understand the process of thethe

‘‘Balancing Method’Balancing Method’


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 ?




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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




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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




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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




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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




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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.



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Revision of Level 2

Examples

EquationsEquations

x – 5 = 11+ 5 + 5

x = 16

x + 8 = 37- 8 - 8

x = 29



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Revision of Level 2

Examples

EquationsEquations

6x = 72

x = 12

(÷ 6)

2x = 11

x = 5.5

(÷ 2)



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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)



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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)



Now try TJ3a

Ex 4Ch7 (page 58)

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1. I have an infi nite amount of line symmetry.

What is my shape?

2. Remove brackets 4(5k - 8)



EquationsEquationsw

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1. We are learning how to solve equations with brackets and fractions .

1. Remember rule for Multiply out brackets.

2. Apply ‘Balancing Method’ to solve fractional equations.

Equations with Brackets



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Multiply out the brackets first and then

Balancing Method


EquationsEquations

3(x – 2) = 33

3x - 6 = 33

3x = 39

+ 6 + 6

x = 13(÷ 3)

Example

Each group has 2 minutes come up with a method for solving this type of

equation



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Example


EquationsEquations

5(3x + 2) – 2(4x - 3) = 2x + 36

7x + 16 = 2x + 36- 16 - 167x = 2x + 20- 2x - 2x

5x = 20(÷ 5)

x = 4

15x + 10 – 8x + 6 = 2x + 36Tidy up terms !



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Multiply EVERY term to get rid of fractional term.

and then apply ‘Balancing Method’

Equations with Fractions

EquationsEquations

x + 3 = 712

(x 2)x + 6 = 14

x = 8

- 6 - 6

Each group has 2 minutes come up with a method for solving this type of

equation Example



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Equations with Fractions

EquationsEquations

x - = 434

(x 4)3x - 2 = 16

3x = 18

+ 2 + 2

12

(÷ 3)

x = 6

Multiply EVERY term to get rid of fractional term.

and then apply ‘Balancing Method’

Example



Now try TJ3a

Ex 5Ch7 (page 59)

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1. My shape has 2 pairs of parallel lines

equal lengths and opposite angles are equal.

What is my shape?

1 12. Calculate of

3 4

3. Remove brackets and simplif y 4e- (8e -12)

4. Calculate the perimeter of the rectangle.

7cm

(x+2)cm



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1. We are learning how to evaluate an expression.

1. Be able to substitute numbers for letters in an expression.

AlgebraAlgebra

2. Use previous knowledge of Number to evaluate a expression.

Evaluating Expressions – number for letter



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AlgebraAlgebraEvaluating Expressions – number for letter

Given the following information find the values of :-

a = 3 ; b = 4 and c = -1BODMAS

2a + c

= 2x3 + (-1)

= 2x3 - 1= 6 - 1

= 5

b2 – a2

= 42 – 32

= 16 – 9

= 7

2b2

= 2x(4)2

= 2x16

= 32



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a = 3 ; b = 4 and c = -1

2a2 + 3b + 30c

= 2x(3)2 + 3x4 + 30x(-1)

= 18 + 12 - 30

= 0



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d = 3 ; e = 4 and f = -1BODMAS

2(d - f)

= 2(3 -(-1))

= 2 x 4= 8

¾(d + f2)= ¾(3 + (-12))

= ¾(4)

= 3

√(16e)

= √(16x4)

= √64

= 8



Now try TJ3a

Ex 6Ch7 (page 60)

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angles and adjcent lengths are equal.

What is my shape?

2. Find the highest common f actor f or

(a) 12 and 24 (b) 2x and 10x

3. Calculate 6a+ 5ab when a=(-1) b=(-2)


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1. To explain how to work with formulae expressed in words.

1.1. Understand formulae Understand formulae expressed in words.expressed in words.

Formulae

2.2. Solve problems given Solve problems given formulae in words.formulae in words.


Sometimes formulae are expressed in words.

Formulae

A tile fitter charges £20 per hour.

How much will he charge for 8 hours of work.

C = 20xh

For h = 8

C = 20 x 8 =

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Formulae

The cost for hiring a carpet cleaner is

£30 plus £3 a day

How much will it cost to hire for a week.

C = 30 + 3d

For d = 7

C = 30 + 3 x 7 =

£51w

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Formulae

Profit :

Subtract how much you paid for goods in the first place from the amount you actually sold them for.

How much profit did Daniel make if he bought a CD for £9.99 and sold it for £12

Profit = 12 – 9.99 =

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p = s - b



Now try TJ3a

Ex 7Ch7 (page 62)

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MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept....

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