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Formulae

S4 Credit. Formulae. Using Formulae. Making Formulae. Change the Subject of Formula. www.mathsrevision.com. Harder Subject of Formula. Understanding Formulae. S4 Credit. Starter Questions. 1. Does 3 + 2 x 4 = 11 or 20 . Formulae. S4 Credit. Learning Intention. Success Criteria.

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Formulae

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  1. S4 Credit Formulae Using Formulae Making Formulae Change the Subject of Formula www.mathsrevision.com Harder Subject of Formula Understanding Formulae www.mathsrevision.com

  2. S4 Credit Starter Questions 1. Does 3 + 2 x 4 = 11 or 20 www.mathsrevision.com

  3. Formulae S4 Credit Learning Intention Success Criteria • To explain how to evaluate formulae • Understand the term • formulae. • 2. Be able to substitute values into formulae and evaluate properly using BODMAS. www.mathsrevision.com www.mathsrevision.com

  4. S4 Credit A formula is the process calculating a quantity based on a known relationship e.g. Length, Area, Volume etc........ Formulae It is VERY important that we remember a keypoint when working with formulae. B Brackets O Other  squares and square root etc.... D Divide M Multiplication A Addition S Subtraction

  5. Formula for Parallelogram S4 Credit Example 1 : Find the area of parallelogram. 3cm 9cm

  6. Formulae for the Volume of a Sphere S4 Credit D = diameter r D www.mathsrevision.com Q. If the above sphere has radius 10cm. Calculate it’s volume.

  7. Formulae for Volume of a Cone S4 Credit h r www.mathsrevision.com • If the above cone has radius 15cm and height • of 10 cm. Calculate it’s volume.

  8. Formulae S4 Credit Now try MIA Ex 2.1 & 2.2 Ch4 (page 80)

  9. r D S4 Credit Starter D = 6 cm www.mathsrevision.com

  10. Making Formulae S4 Credit Learning Intention Success Criteria • To explain how to construct a formula. • Understand the process of constructing a formula. • 2. Apply knowledge to construct formulae. www.mathsrevision.com www.mathsrevision.com

  11. Making Formulae S4 Credit Try and make a formula for the money I have left, £M , after h hour. I started my shopping trip with £250. On average, each hour I spent £40. M = 250 - 40h Calculate M for h = 3 M=250 – 40 x 3 = 250 -120 = £130

  12. Making Formulae S4 Credit Try and make a formula for the cost C of tiling a kitchen floor. A tile fitter charges £20 per hour h. The tiles cost £15 per m2 A. C = 20h + 15A Calculate C for h = 5 and A = 10 C=20 x 5 + 15 x 10 = £250

  13. 3 Tables 1 Table 2 Tables Task : Find a formula connecting the number of surfers and the number of tables. Making Formulae S4 Credit A internet café decides to change it’s table design to.

  14. 3 Tables 1 Table 2 Tables 2 4 5 1 3 6 4 8 2 2 2 2 Making Formulae S4 Credit Fill empty boxes Number of Tables Step 1 : Number of Surfers 10 12 Step 2 : Find difference What is the formula Same difference linear pattern

  15. Number of Tables Number of Surfers 10 12 1 3 4 6 2 4 8 5 2 2 2 2 S = 2 x T Can you write down formula connecting the number of surfers and the number of tables. Part of the Formula Making Formulae S4 Credit Find a number so formula works Step 3 : Step 4 : S = 2T + 2 Correction factor “add on 2”

  16. Making Formulae S4 Credit Now try MIA Ex 3.1 Ch4 (page 84)

  17. h r S4 Credit Starter Questions D = 6 cm h = 10 cm www.mathsrevision.com

  18. Harder Formulae S4 Credit 1 cm • Find a formula for the : • Perimeter • Area • for the shaded shape below. 2x + 2cm C = πDbig- πDsmall 2x cm C = π(Db –Ds) C = π(2x + 2 – 2x) C = 2π

  19. Harder Formulae S4 Credit 1 cm • Find a formula for the : • Perimeter • Area • for the shaded shape below. 2x + 2cm A = πr2big - π r2small 2x cm A = π(r2b –r2s) A = π((x + 1)2 – x2) A = π(x2 +2x + 1 – x2) = π(2x + 1)

  20. Harder Formulae S4 Credit 1 cm • Find a formula for the : • Perimeter • Area • for the shaded shape below. 2x + 2cm A = πr2big - π r2small 2x cm A = π(r2b –r2s) A = π((x + 1)2 – x2) A = π(x2 +2x + 1 – x2) = π(2x + 1)

  21. Harder Formulae S4 Credit • Show that for the square with and equilateral triangle cut out has : • Perimeter = 10x • Area = (4 - √3)x2 • for the shaded shape below. 2x √3x P = 2x + 2x + 2x +2x + 2x =10x P =

  22. Harder Formulae S4 Credit • Show that for the square with an equilateral triangle cut out has : • Area = (4 - √3)x2 • for the shaded shape below. 2x h √3x Area = Square - Triangle As = 2xx 2x = 4x2 AT = 0.5 x 2xx √3x = √3x2 AT = 4x2- √3x2 = (4 - √3)x2

  23. Harder Formulae S4 Credit Now try MIA Ex 3.2 Ch4 (page 87)

  24. S4 Credit Starter 5 cm 3 cm 3 cm 2.5 cm 4 cm www.mathsrevision.com

  25. Formulae The Subject of a Formula S4 Credit Learning Intention Success Criteria • To explain how to change the subject of a formula using • “The balancing Method” • Know “The balancing Method” for solving equations. • 2. Apply knowledge to change subject of a formula. www.mathsrevision.com www.mathsrevision.com

  26. Changing the Subject of a Formula S4 Credit 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. www.mathsrevision.com

  27. Changing the Subject of a Formula S4 Credit We can make D the subject of the formula by simple using “ The Balancing Method “ www.mathsrevision.com

  28. What Goes In The Box ? Rearrange into y = S4 Credit Make y the subject of the formulae using “the balancing method” x + y = 8 -x + 2y = 2 y = 8 - x y2 = x x = 4( y + 1 ) y = √x 2x =√y x = 3( y - k ) y = 4x2

  29. Changing the Subject of a Formula S4 Credit Now try MIA Ex 4.1 Ch4 (page 88)

  30. S4 Credit Starter Questions Make g the subject of each formula : Nothing new ! simply use the “balancing method” www.mathsrevision.com

  31. Changing the Subject of a Formula S4 Credit Learning Intention Success Criteria • To explain how to change the subject of a formula containing square and square root terms. • Know “ The balancing Method” for solving equations. • 2. Apply knowledge to change subject of harder formulae including square and square root terms. www.mathsrevision.com www.mathsrevision.com

  32. Changing the Subject of a Formula S4 Credit Example : The force of the air against a train is given by the formula below. Make the speed (S) the subject of the formula. www.mathsrevision.com

  33. Changing the Subject of a Formula S4 Credit 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. www.mathsrevision.com

  34. Changing the Subject of a Formula S4 Credit Example : The formula below is used to change degrees Celsius to Fahrenheit. Change the subject to C. www.mathsrevision.com

  35. Changing the Subject of a Formula S4 Credit Now try MIA Ex 4.2 Ch4 (page 91)

  36. S4 Credit Starter Questions Make w the subject of each formula : Nothing new ! simply use the “balancing method” www.mathsrevision.com

  37. Understanding Formulae S4 Credit Learning Intention Success Criteria • To explain the effect on the subject by changing one or more of the values in the formula. • 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. www.mathsrevision.com www.mathsrevision.com

  38. Understanding Formulae S4 Credit In real-life we often want to see what effect changing the value of one of the variables has on the subject. The Circumference of circle is given by the formula : C = πD The Circumference doubles What happens to the Circumference if we double the diameter C = π(2D) = 2πD New D = 2D www.mathsrevision.com

  39. Understanding Formulae S4 Credit In real-life we often want to see what effect changing the value of one of the variables has on the subject. The Area of circle is given by the formula : A = πr2 The Area increasing by a factor of 4. What happens to the Area if we double the radius r C = π(2r)2 = 4πr2 New r = 2r www.mathsrevision.com

  40. Understanding Formulae S4 Credit In real-life we often want to see what effect changing the value of one of the variables has on the subject. The Area of circle is given by the formula : A = πr2 The Area increasing by a factor of 4. What happens to the Area if we double the radius r C = π(2r)2 = 4πr2 New r = 2r www.mathsrevision.com

  41. Understanding Formulae S4 Credit 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. The thickness of the rope T increasing by a factor of 10. New W = 100W www.mathsrevision.com

  42. Understanding Formulae S4 Credit Now try MIA Ex 5.1 Ch4 (page 94)

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