mth 3-15a mth 4-15a 13-jun-14created by mr. lafferty maths dept. revision of level 2 algebra harder...

MTH 3-15aMTH 4-15a

11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Revision of Level 2 Algebra

Harder Equations

Equations & Equations & InequalitiesInequalities

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Equations with Brackets

Equations with Fractions

Solving Inequalities

Harder Fractions

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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 3-15aMTH 4-15a

11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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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’


MTH 3-15aMTH 4-15a

11 Apr 2011 Apr 202323

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.


The Balancing Method

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Revision of Level 2

Reminder !

Examples


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x – 5 = 11+ 5 + 5

x = 16

x + 8 = 37- 8 - 8

x = 29


The Balancing Method

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Revision of Level 2

Reminder !

Examples


MTH 3-15aMTH 4-15a

6x = 72

x = 12

(÷ 6)

2x = 11

x = 5.5

(÷ 2)


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Revision of Level 2

Examples


MTH 3-15aMTH 4-15a

4x – 2 = 34+ 2 + 2

4x = 36

x = 9

(÷ 4)

2x + 9 = 31+ 9 + 9

2x = 22

x = 11

(÷ 2)


Now try Exercise 1Ch43 (page 171)

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Revision of Level 2


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4 ( )2. Expand out the brackets y x y

1. Find the perimeter and area of the shape.

3. Find all the missing angles.

6x

2x

100o

60o

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1.1. Apply balancing method Apply balancing method to solve equations with to solve equations with more than one x term.more than one x term.

1. We are learning how to apply balancing method to solve harder equations.

Harder Equations


Examples


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Harder Equations


MTH 3-15aMTH 4-15a

3x + 2 = x + 10- 2 - 2

3x = x + 8

2x = 8

(÷ 2)

- x - x

x = 4

4x - 5 = 2x - 25+ 5 + 5

4x = 2x – 20

2x = -20

(÷ 2)

- 2x - 2x

x = -10

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

equation


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Harder Equations


MTH 3-15aMTH 4-15a

x + 4 = 3x - 10- 4 - 4x = 3x - 14

3x = x + 14

(÷ 2)

+ 14 + 14

x = 7

Swap Round

!3x - 14 = x

- x - x2x = 14

4x - 1 = 7x + 11+ 1 + 1

4x = 7x + 12

7x = 4x - 12

(÷ 3)

- 12 - 12

x = -4

Swap Round

!7x + 12 = 4x

- 4x - 4x3x = -12

Examples



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Harder Equations


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What is my shape?

3 12. Calculate of

4 8

3. Remove brackets 4(5k - 8)

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

1. Remember rule for Multiply out brackets.

2. Apply ‘Balancing Method’ to solve equations.




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Multiply out the brackets first and then

Balancing Method



MTH 3-15aMTH 4-15a

3(x – 2) = 33

3x - 6 = 33

3x = 39

+ 6 + 6

x = 13(÷ 3)

Example


equation

11 Apr 202311 Apr 2023

Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

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Example



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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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7 (3 9 )

51. of 63

7

1 12. Calculate 2 1

2 4

3. Expand the brackets

4. Calculate the area of the shape.

f e f

5cm

11cm

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1. We are learning how to solve equations that contain fractional terms.

1. Remember to multiply every term to get rid of fractional term.


2. Apply ‘Balancing Method’



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Multiply EVERY term to get rid of fractional term.

and then apply ‘Balancing Method’



MTH 3-15aMTH 4-15a

x + 3 = 712

(x 2)x + 6 = 14

x = 8

- 6 - 6


equation Example


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x - = 434

(x 4)3x - 2 = 16

3x = 18

+ 2 + 2

12

(÷ 3)

x = 6



Example



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7 14

1. 75% of 160

1 12. Calculate 2 - 1

2 6

3. Factorise

4. Calculate the area of the shape.

f e 7cm

13cm15cm

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1. We are learning how to solve HARDER fractional equations using all the rules learned so far.

1. Apply Balancing Method to solve harder equations.

Harder Fractional Equations with Brackets



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MTH 3-15aMTH 4-15a

+ 5 = 8x + 24

(x 4)

x + 2 + 20 = 32

x + 22 = 32- 22 - 22

x = 10



Example

Tidy Up !


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(x 6)

18x

22x - 36 = 96

(÷ 22)x = 6

(2x – 4) + x = 1632

23

(2x – 4) + x = 969 4

22x = 132

- 36 + 4x = 96

Example

Tidy Up !

+ 36 + 36



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2 2

1. 5.67 + 2.3 - 0.07

2. Find the highest common f actor f or

(a) 8 and 12 (b) 20x and 48x

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

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1. We are learning how we can solve inequalities using the same rules we use for equations.

1. Understand the term inequality.

2. Solve inequalities using the same method as equations.




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Inequalities are similar to equations except we replace the “=“ with one of the following symbols :


" <"," >"," "or " "

Less than or

equal to

Greater than or

equal toGreater than

Less than

The Good News


MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a


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Solving inequalities is almost identical to solving equations :


x is any value less than 4

Even Better News !


Example 2x – 1 < 7+ 1 + 1

2x < 8

x < 4(÷ 2)

NEVER put in an equal sign

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Example2(2x – 3) ≥ x + 9

+ 6 + 6

x ≥ 5

NEVER put in an equal sign

4x ≥ x + 9– 6

4x ≥ x + 15- x - x

x is any value greater than or equal to 5

(÷ 3)

3x ≥ 15

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The only one to watch out for is when you are dividing by a negative

Example

MTH 3-15aMTH 4-15a

8 – 3m < 2- 8 - 8

-3m < -6

m > 2(÷ -3) FLIP sign

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Example5(x – 1) - 8x ≥ -17

+ 5 + 5

x ≤ 4

5x - 8x ≥ -17– 5

-3x - 5 ≥ -17

x is any value less than or equal to 4

(÷ -3)

-3x ≥ -12

Tidy Up !

FLIP sign



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MTH 3-15aMTH 4-15a

mth 3-15a mth 4-15a 13-jun-14created by mr. lafferty maths dept. revision of level 2 algebra harder...

Documents

x term

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o slide

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inequalities harder

big bag