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Understanding and Using Formulae: A Comprehensive Guide

This guide introduces key concepts in working with formulae, including evaluation, substitution, and construction. Learn how to calculate values such as area and volume using established formulae. Master the BODMAS rule for order of operations while substituting values. Gain skills in making your own formulae based on real-life scenarios, such as budgeting and calculating costs. Additionally, understand how to change the subject of a formula using the balancing method. This resource is essential for improving your mathematics proficiency at the S4 Credit level.

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Understanding and Using Formulae: A Comprehensive Guide

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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 1. Calculate 3 + 2 x 4 Starter Questions 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 : 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 : 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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