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MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities www.mathsrevision.com.

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Presentation on theme: "MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities www.mathsrevision.com."— Presentation transcript:

1 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Algebra Harder Equations Equations & Inequalities Equations with Brackets Equations with Fractions Solving Inequalities Harder Fractions

2 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

3 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 2.Solving simple algebraic equations. 1.To revise Level 2 using the rule Balancing Method Revision of Level 2 1.Understand the process of the Balancing Method Equations & Inequalities

4 MTH 3-15a MTH 4-15a 13-Jun-14 Created by Mr Lafferty Maths Dept Balancing Method 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 ?

5 MTH 3-15a MTH 4-15a 13-Jun-14 Created by Mr Lafferty Maths Dept Balancing Method 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 =8 kg

6 MTH 3-15a MTH 4-15a 13-Jun-14 Created by Mr Lafferty Maths Dept Balancing Method PP 4 P 44 4 Lets solve it using maths. Let P be the weigh of a big bag. We know that a small bag = 4 2P + 4P + 12 What symbol should we use for the scales ? = Subtract 4 from each side -4 2P=P + 8 Subtract P from each side -P P=8

7 MTH 3-15a MTH 4-15a 13-Jun-14 Created by Mr Lafferty Maths Dept Balancing Method 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 childs ticket costs £2. If a childs ticket costs £2. How much for an adult ticket ? aa2 a 2 a a 2 Let a be the price of an adult ticket. We know that a child price = £2 2 aa 2a

8 MTH 3-15a MTH 4-15a 13-Jun-14 Created by Mr Lafferty Maths Dept Balancing Method For balance we have 5a + 63a + 16 = Subtract 6 from each side -6 5a=3a + 10 Subtract 3a from each side -3a 2a=10 aa a a a aa a Divide each side by 2 a=5 Adult ticket price is £5 1

9 MTH 3-15a MTH 4-15a 13-Jun-14 Created by Mr Lafferty Maths Dept Balancing Method 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.

10 13-Jun-14Created by Mr. Lafferty Maths Dept. The Balancing Method Revision of Level 2 Reminder ! Examples Equations & Inequalities MTH 3-15a MTH 4-15a x – 5 = x = 16 x + 8 = x = 29

11 13-Jun-14Created by Mr. Lafferty Maths Dept. The Balancing Method Revision of Level 2 Reminder ! Examples Equations & Inequalities MTH 3-15a MTH 4-15a 6x = 72 x = 12 (÷ 6) 2x = 11 x = 5.5 (÷ 2)

12 13-Jun-14Created by Mr. Lafferty Maths Dept. Revision of Level 2 Examples Equations & Inequalities MTH 3-15a MTH 4-15a 4x – 2 = x = 36 x = 9 (÷ 4) 2x + 9 = x = 22 x = 11 (÷ 2)

13 13-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch43 (page 171) Revision of Level 2 Equations & Inequalities MTH 3-15a MTH 4-15a

14 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6x 2x 100 o 60 o

15 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Apply balancing method to solve equations with more than one x term. 1. We are learning how to apply balancing method to solve harder equations. Harder Equations Equations & Inequalities

16 Examples 13-Jun-14Created by Mr. Lafferty Maths Dept. Harder Equations Equations & Inequalities MTH 3-15a MTH 4-15a 3x + 2 = x x = x + 8 2x = 8 (÷ 2) - x x = 4 4x - 5 = 2x x = 2x – 20 2x = -20 (÷ 2) - 2x x = -10 Each group has 2 minutes come up with a method for solving this type of equation

17 13-Jun-14Created by Mr. Lafferty Maths Dept. Harder Equations Equations & Inequalities MTH 3-15a MTH 4-15a x + 4 = 3x x = 3x x = x + 14 (÷ 2) + 14 x = 7 Swap Round ! 3x - 14 = x - x 2x = 14 4x - 1 = 7x x = 7x x = 4x - 12 (÷ 3) - 12 x = -4 Swap Round ! 7x + 12 = 4x - 4x 3x = -12 Examples

18 13-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch43 (page 173) Harder Equations Equations & Inequalities MTH 3-15a MTH 4-15a

19 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

20 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. We are learning how to solve equations with brackets. 1. Remember rule for Multiply out brackets. 2. Apply Balancing Method to solve equations. Equations with Brackets Equations & Inequalities

21 13-Jun-14Created by Mr. Lafferty Maths Dept. Multiply out the brackets first and then Balancing Method Equations with Brackets Equations & Inequalities MTH 3-15a MTH 4-15a 3(x – 2) = 33 3x - 6 = 33 3x = x = 13 (÷ 3) Example Each group has 2 minutes come up with a method for solving this type of equation

22 13-Jun-14 Created by Mr. Lafferty Maths Dept. Example Equations with Brackets Equations & Inequalities MTH 3-15a MTH 4-15a 5(3x + 2) – 2(4x - 3) = 2x x + 16 = 2x x = 2x x 5x = 20 (÷ 5) x = 4 15x + 10 – 8x + 6 = 2x + 36 Tidy up terms !

23 13-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch43 (page 174) Equations with Brackets Equations & Inequalities MTH 3-15a MTH 4-15a

24 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 5cm 11cm

25 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. We are learning how to solve equations that contain fractional terms. 1. Remember to multiply every term to get rid of fractional term. Equations with Fractions 2. Apply Balancing Method Equations & Inequalities

26 13-Jun-14Created by Mr. Lafferty Maths Dept. Multiply EVERY term to get rid of fractional term. and then apply Balancing Method Equations with Fractions Equations & Inequalities MTH 3-15a MTH 4-15a x + 3 = (x 2) x + 6 = 14 x = Each group has 2 minutes come up with a method for solving this type of equation Example

27 13-Jun-14Created by Mr. Lafferty Maths Dept. Equations with Fractions Equations & Inequalities MTH 3-15a MTH 4-15a x - = (x 4) 3x - 2 = 16 3x = (÷ 3) x = 6 Multiply EVERY term to get rid of fractional term. and then apply Balancing Method Example

28 13-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch43 (page 175) Equations with Fractions Equations & Inequalities MTH 3-15a MTH 4-15a

29 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 7cm 13cm 15cm

30 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 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 Equations & Inequalities

31 13-Jun-14Created by Mr. Lafferty Maths Dept. Harder Fractional Equations with Brackets Equations & Inequalities MTH 3-15a MTH 4-15a + 5 = 8 x (x 4) x = 32 x + 22 = x = 10 Multiply EVERY term to get rid of fractional term. and then apply Balancing Method Example Tidy Up !

32 13-Jun-14Created by Mr. Lafferty Maths Dept. Harder Fractional Equations with Brackets Equations & Inequalities MTH 3-15a MTH 4-15a (x 6) 18x 22x - 36 = 96 (÷ 22) x = 6 (2x – 4) + x = (2x – 4) + x = x = x = 96 Example Tidy Up ! + 36

33 13-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch43 (page 176) Harder Fractional Equations with Brackets Equations & Inequalities MTH 3-15a MTH 4-15a

34 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

35 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 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. Solving Inequalities Equations & Inequalities

36 13-Jun-14Created by Mr. Lafferty Maths Dept. Inequalities are similar to equations except we replace the = with one of the following symbols : Solving Inequalities Less than or equal to Greater than or equal to Greater than Less than The Good News Equations & Inequalities MTH 3-15a MTH 4-15a

37 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Solving inequalities is almost identical to solving equations : Solving Inequalities x is any value less than 4 Even Better News ! Equations & Inequalities Example 2x – 1 < x < 8 x < 4 (÷ 2) NEVER put in an equal sign

38 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Solving Inequalities Equations & Inequalities Example 2(2x – 3) x x 5 NEVER put in an equal sign 4x x + 9– 6 4x x x x is any value greater than or equal to 5 (÷ 3) 3x 15

39 13-Jun-14 Solving Inequalities Equations & Inequalities The only one to watch out for is when you are dividing by a negative Example MTH 3-15a MTH 4-15a 8 – 3m < m < -6 m > 2 (÷ -3) FLIP sign

40 MTH 3-15a MTH 4-15a 13-Jun-14Created by Mr. Lafferty Maths Dept. Solving Inequalities Equations & Inequalities Example 5(x – 1) - 8x x 4 5x - 8x -17– 5 -3x x is any value less than or equal to 4 (÷ -3) -3x -12 Tidy Up ! FLIP sign

41 13-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 6 Ch43 (page 177) Solving Inequalities Equations & Inequalities MTH 3-15a MTH 4-15a


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