1. www.mathsrevision.com S4 Credit 23-Jun-16 Created by Mr. Lafferty@mathsrevision.com Equations and Inequations Reminder of Solving Equations 1 Inequalities Reminder of Solving Equations 2 Equations with Fractions More Equations with Fractions Solving Inequalities

2. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Starter Questions Q1.Is the following true or false (A)(-3a) x 5a = -15a (B) (-6x) x (-7y) =-42xy Q2.Are the 2 answers the same ? (a)(-3h) 2 =(b)-(3d) 2 = Q3.Spilt £64 pounds into the ratio 7:9 Q4.Explain why 0.0675 is equal to 6.75 x 10 -2

3. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Learning Intention Success Criteria 1.To remind pupils on how to solve various types of equations 1.Understand the process of solving equations using “ the balancing method ” Reminder on Solving Equations

4. www.mathsrevision.com S4 Credit 5(x - 3) = 25 5x Example 1 23-Jun-16Created by Mr. Lafferty@mathsrevision.com - 15 = 25 Multiply out the bracket first and then solve. 5x = 25 + 15 x = 40 ÷ 5 = 40 = 8 Reminder on Solving Equations Substitute value into original equation to check answer

5. www.mathsrevision.com S4 Credit 6(x - 2) = 3(x + 1) 6x Example 2 23-Jun-16Created by Mr. Lafferty@mathsrevision.com - 12 = 3x = 3 + 3 6x – 3x -12 3x -12 = 3 3x = 3 + 12 = 15 x = 15 ÷ (3) = 5 Solve as normal Substitute value into original equation to check answer 18 Reminder on Solving Equations

6. www.mathsrevision.com S4 Credit -3(2 + 2y) = 6 – (y + 2) -6 Example 3 23-Jun-16Created by Mr. Lafferty@mathsrevision.com - 6y = 6 Equations and brackets = 4 - y - y - 2 -6 – 6y -6 - 6y + y = 4 -6 – 5y = 4 – 5y = 10 y = 10 ÷ (-5) = -2 Tidy up RHS Solve as normal Substitute value into original equation to check answer 6 6

7. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Now try Ex 2.1 Ch5 MIA (page 99) Reminder on Solving Equations

8. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Starter Questions Q1. Explain why the following are True or False (a)-3y x 5y =-30y (b)-6q x (-4q) = 24q 2 Q2. Is the following true -2a( b – a) = -2ab +4a Q3.Write down the two numbers that multiply to give 8 and subtract to give 2.

9. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Learning Intention Success Criteria 1.To remind pupils on how to solve equations containing square terms. 1.Understand the process of solving equations with square terms using “ the balancing method ” Reminder on Solving Equations

10. www.mathsrevision.com S4 Credit (x + 2) 2 = x 2 + 8 2 (x + 2)(x + 2) Example 1 23-Jun-16Created by Mr. Lafferty@mathsrevision.com = x 2 + 64 Multiply out the bracket first and then solve. Equations and brackets x 2 + 4x + 4 4x = 60 x = 60 ÷ 4 = 15 FOIL = x 2 + 64 4x + 4 = 64 Substitute value into original equation to check answer 289

11. www.mathsrevision.com S4 Credit m(m + 2) = m 2 + 10 m 2 + 2m Example 2 23-Jun-16Created by Mr. Lafferty@mathsrevision.com = m 2 + 10 Multiply out the bracket first and then solve. Equations and brackets 2m m = 10 ÷ 2 = 5 = 10 Substitute value into original equation to check answer 35

12. www.mathsrevision.com S4 Credit Solve in the usual way A = (x + 7)(x – 2) Example 5 : The two areas are equal. Find the value of x. 23-Jun-16Created by Mr. Lafferty@mathsrevision.com (x + 7) (x – 2) (x + 2) A = (x + 2) 2 (x + 2) 2 = (x + 7) (x - 2) x 2 + 4x + 4 x = 18 Foil Equations and brackets = x 2 + 5x - 14 4x + 4= 5x - 14 4= x - 14 Substitute value into original equation to check answer 400

13. www.mathsrevision.com S4 Credit 25 Equations & Pythagoras Using Pythagoras find the length of all sides of the triangle. x + 3 cm 3cm x + 2 cm (x + 3) 2 = (x + 2) 2 + 3 2 x 2 + 6x + 9 x = 2 = x 2 + 4x + 13 6x + 9= 4x + 13 2x= 4 25 Foil Balancing Method Lengths are 3, 4 and 5 cm 4 5 Check ! Example

14. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Now try Ex 2.2 Ch5 MIA (page 101) Equations and brackets

15. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Starter Questions Q1.Multiply out. (a)3y(x - y) =(b)6q 2 (2 - 4q) = Q2.Explain your working to show that if we split 24 into the ratio 1:5 the answer is 4:20 Q3.Writing out in full 5.2 x 10 -3 to get 0.052 Is the correct?

16. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Equations & Fractions Learning Intention Success Criteria 1. To show how to solve fractional equations using all the rules learned so far. 1. Apply Balancing Method to solve fractional equations. Fractional Equations with Brackets

17. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Process of solving equations with fractions 1.Remove any fraction by multiplying. 2.Remove any fractions. 3.Simply each side of the equation if possible. 4.Carry out balancing method to solve equation. Equations & Fractions

18. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Multiply EVERY term by 5 Equations with Fractions Equations & Fractions

19. www.mathsrevision.com S4 Credit Multiply EVERY term by 3 Equations with Fractions Remove brackets Balancing Method Equations & Fractions

20. www.mathsrevision.com S4 Credit Multiply EVERY term by 4 Equations with Fractions Tidy up Balancing Method Equations & Fractions

21. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Now try Ex 3.1 Ch5 MIA (page 103) Equations & Fractions

22. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Starter Questions Q1.Find the area of the second shape given the first has area 7w - 14 Q2.Split 48 into the ratio 1:3 Q3.In standard form 18294000 is 1.8x10 7 is the correct? (w - 2) 7 (w – 5) 3

23. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Learning Intention Success Criteria 1.To remind pupils on how to solve equations containing fraction terms. 1.Understand the process of solving equations with fraction terms using “ the balancing method ” Equations & Fractions

24. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Multiply EVERY term by LCM 12 Equations with Fractions Tidy up Balancing Method Equations & Fractions

25. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Multiply EVERY term by LCM 6 Equations with Fractions Tidy up Balancing Method Equations & Fractions

26. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Equations with Fractions Balancing Method Equations & Fractions

27. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Now try Ex 4.1 Ch5 MIA (page 106) Equations & Fractions

28. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Starter Questions Q1.Solve for x (a)x + 3 = 8(b)2x – 14 = 50 Q2.Is this statement true (x – 1) – 3(x + 1) = -2x Q3.

29. 23-Jun-16Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To show 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

30. 23-Jun-16Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 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

31. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Now try Ex 5.1 Ch5 MIA (page 108) Removing a Single Bracket

32. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Starter Questions Q1.Does 579300 = 5.793x10 5 Q2.Explain why the answer to 4(w + 2) = 6(w + 1) is w = 1 Q3.

33. 23-Jun-16Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To show 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

34. 23-Jun-16Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 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

35. 23-Jun-16Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Solving inequalities is almost identical to solving equations : Solving Inequalities x is any value less than 4 Even Better News ! Equations & Inequalities Balancing Method Add 1 to both sides Tidy up Divide by 2 both sides

36. 23-Jun-16Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Solving inequalities is almost identical to solving equations : Solving Inequalities x is any value greater than or equal to 5 Equations & Inequalities Multiply out brackets Add 6 to both side Subtract x from each side. Divide both sides by 3

37. www.mathsrevision.com S4 Credit Solving Inequalities Inequalities The only one to watch out for is when you are dividing by a negative Example 1 8 – 3m < 2 -3m < -6 m -6 -3 Subtract 8 from each side Divide across by -3 and change the Sign So m > 2 >

38. www.mathsrevision.com S4 Credit 23-Jun-16 Solving Inequalities Inequalities Example 2 5( x – 1 ) - 8x ≥ - 17 5x – 5 – 8x ≥ - 17 - 3x - 5 ≥ - 17 - 3x ≥ - 12 x -12 -3 ≤ So x ≤ 4

39. www.mathsrevision.com S4 Credit 23-Jun-16Created by Mr. Lafferty@mathsrevision.com Now try 6.1 & 6.2 Ch5 MIA (page 110) Inequalities