1. www.mathsrevision.com Formulae www.mathsrevision.com Change the Subject of Formula Harder Subject of Formula Understanding Formulae Nat 5 Exam Type Questions

2. www.mathsrevision.com Starter Questions Find the area of the major arc. Nat 5 10m 60 o

3. www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to change the subject of a formula using “The balancing Method” 1.Know “The balancing Method” for solving equations. Formulae 2.Apply knowledge to change subject of a formula. The Subject of a Formula Nat 5

4. www.mathsrevision.com Changing the Subject of a Formula The formula below is used to work out the circumference of a circle Since the formula works out C, then C is called the subject of the formula. Nat 5

5. MTH 3-14a MTH 3-15a MTH 3-15b 15-Aug-15Created by Mr.Lafferty Maths Dept The Balancing Method www.mathsrevision.com The method we use to solve equations is Write down the opposite of the following : + opposite is x - ÷ - + ÷ x Changing the Subject of a Formula

6. www.mathsrevision.com Changing the Subject of a Formula We can make D the subject of the formula by simple using “ The Balancing Method “ Nat 5

7. www.mathsrevision.com Changing the Subject of a Formula Nat 5 Examples y + x = z (y) - x y = z - x p = q + r (r) Swap q + r = p - q q + r = p

8. www.mathsrevision.com Changing the Subject of a Formula Nat 5 Examples d = st (T) Swap ÷ s both sides h = b (b) a Always get rid of fraction Swap x a both sides b = h a t = d s st = d b = ah

9. www.mathsrevision.com Changing the Subject of a Formula Nat 5 Examples 3g + f = y (g) ÷ 3 both sides g = y - f 3 3g = y - f - f - f k = 4d - 2w (w) ÷ 2 both sides w = 4d - k 2 2w + k = 4d + 2w+2w -k -k 2w = 4d - k

10. www.mathsrevision.com What Goes In The Box ? Make y the subject of the formulae using “the balancing method” x + y = 8 y 2 = x -x + 2y = 2 x = 4( y + 1 ) y = 8 - x y = √x Rearrange into y = 2x =√yx = 3( y - k ) y = 4x 2 Nat 5

11. www.mathsrevision.com Now try N5 TJ Ex 10.1 Ch10 (page 99) Nat 5 Changing the Subject of a Formula

12. www.mathsrevision.com Starter Questions Make g the subject of each formula : Nat 5 Nothing new ! simply use the “balancing method”

13. www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to change the subject of a formula containing square and square root terms. 1.Know “ The balancing Method” for solving equations. 2.Apply knowledge to change subject of harder formulae including square and square root terms. Changing the Subject of a Formula Nat 5

14. MTH 3-14a MTH 3-15a MTH 3-15b 15-Aug-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com We should already know that : + opposite is x - ÷ - + ÷ x √ opposite is opposite is  ² √  ² Changing the Subject of a Formula

15. www.mathsrevision.com Changing the Subject of a Formula Example : The force of the air against a train is given by the formula below. Make the speed (S) the subject of the formula. Nat 5 F = kS 2 kS 2 = F Swap ÷ k S 2 = F k √

16. www.mathsrevision.com Changing the Subject of a Formula Example : The thickness of a rope T cm to lift a weight W tonnes can be worked out by the formula below. Make W the subject of the formula. Nat 5 x 9 ÷ 4  ² Swap

17. www.mathsrevision.com Changing the Subject of a Formula Example : The formula below is used to change degrees Celsius to Fahrenheit. Change the subject to C. Nat 5 x 5 - 160 HCF Swap ÷9

18. www.mathsrevision.com Now try N5 TJ Ex 10.2 Q1... Q8 Ch10 (page 101) Nat 5 Changing the Subject of a Formula

19. www.mathsrevision.com Starter Questions Make w the subject of each formula : Nat 5 Nothing new ! simply use the “balancing method”

20. www.mathsrevision.com Learning Intention Success Criteria 1.We are learning the affect on the subject by changing one or more of the values in the formula. 1.Understand the meaning of doubling and halving. 2.Apply knowledge so far to work out the effect on the subject by varying one or more values in the formula. Understanding Formulae Nat 5

21. www.mathsrevision.com Nat 5 Understanding Formulae The Circumference of circle is given by the formula : C = πD What happens to the Circumference if we double the diameter C = π(2D) New D = 2D The Circumference doubles In real-life we often want to see what effect changing the value of one of the variables has on the subject. = 2(πD) Original Value

22. www.mathsrevision.com In real-life we often want to see what effect changing the value of one of the variables has on the subject. Nat 5 Understanding Formulae The Area of a circle is given by the formula : A = πr 2 What happens to the Area if we double the radius r C = π(2r) 2 New r = 2r The Area increases by a factor of 4. = 4(πr 2 ) Original Value

23. www.mathsrevision.com The thickness of a rope T cm to lift a weight W tonnes can be worked out by the formula below. If we increase W by a factor of 100. What effect does this have on the thickness of the rope T. Nat 5 Understanding Formulae New W = 100W The thickness of the rope T increasing by a factor of 10. Original Value

24. www.mathsrevision.com Now try N5 TJ Ex 10.2 Q9 onwards Ch10 (page 102) Nat 5 Understanding Formulae