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Direct Proportion

Direct Proportion. Direct Proportion. Direct Proportion Graphs. Direct Proportion formula and calculations. www.mathsrevision.com. Other Direct Proportion formula. Inverse Direct Proportion. Starter Questions. 9. 8. 6. www.mathsrevision.com. Direct Proportion. Direct Proportion.

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Direct Proportion

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  1. Direct Proportion Direct Proportion Direct Proportion Graphs Direct Proportion formula and calculations www.mathsrevision.com Other Direct Proportion formula Inverse Direct Proportion Created by Mr. Lafferty Maths Dept.

  2. Starter Questions 9 8 6 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  3. Direct Proportion Direct Proportion Learning Intention Success Criteria 1. Understand the idea of Direct Proportion. • To explain the term Direct • Proportion. 2. Solve simple Direct Proportional problems. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  4. Direct Proportion Direct Proportion Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT Proportion, if : “ .. When you double the number of cakes you double the cost.” Example : The cost of 6 cakes is £4.20. find the cost of 5 cakes. www.mathsrevision.com Cakes Cost Write down two quantities that are in direct proportion. 6  4.20 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50 Created by Mr. Lafferty Maths Dept.

  5. Direct Proportion Direct Proportion Example : On holiday I exchanged £30 for $45. How many $ will I get for £50. What name do we give to this value Exchange rate £ $ 30  45 www.mathsrevision.com 1  45 ÷ 30 = 1.5 50  1.5 x 50 = $75 Created by Mr. Lafferty Maths Dept.

  6. Direct Proportion Direct Proportion Example : To make scrambled eggs for 2 people we need 2eggs, 4g butter and 40 ml of milk. How much of each for (a) 4 people (b) Just himself (a) Simply multiple by 2 : 4 eggs, 8g butter, 80 ml of milk. www.mathsrevision.com (b) Simply half original amounts: 1 eggs, 2g butter, 20 ml of milk. Created by Mr. Lafferty Maths Dept.

  7. Direct Proportion Direct Proportion Now try Exercise 1 Ch8 (page 101) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  8. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  9. Direct Proportion Direct Proportion Graphs Learning Intention Success Criteria 1. Understand that Direct Proportion Graph is a straight line. • 1. To explain how Direct Direct Proportion Graph is always a straight line. 2. Construct Direct Proportion Graphs. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  10. Direct Proportion Direct Proportion Graphs The table below shows the cost of packets of “Biscuits”. www.mathsrevision.com We can construct a graph to represent this data. What type of graph do we expect ? Created by Mr. Lafferty Maths Dept.

  11. Notice that the points lie on a straight line passing through the origin Direct Proportion Graphs This is true for any two quantities which are in Direct Proportion. Created by Mr. Lafferty Maths Dept.

  12. Direct Proportion Direct Proportion Graphs KeyPoint Two quantities which are in Direct Proportion always lie on a straight line passing through the origin. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  13. Direct Proportion Direct Proportion Graphs Example : Plot the points in the table below. Are they in Direct Proportion? www.mathsrevision.com We plot the points (1,3) , (2,6) , (3,9) , (4,12) Created by Mr. Lafferty Maths Dept.

  14. y x Direct Proportion Direct Proportion Graphs 12 Plotting the points (1,3) , (2,6) , (3,9) , (4,12) 11 10 9 8 7 Since we have a straight line passing through the origin x and y are in Direct Proportion. 6 www.mathsrevision.com 5 4 3 2 1 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4

  15. y x Direct Proportion Direct Proportion Graphs 12 Find the formula connecting y and x. 11 10 9 8 Formula has the form : 7 y = kx 6 www.mathsrevision.com 5 Gradient = 3 4 Formula is : y = 3x 3 2 1 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4

  16. Direct Proportion Direct Proportion Graphs Key point of Ex 2 Fill in table Find gradient from graph www.mathsrevision.com Write down formula using knowledge from straight line chapter Created by Mr. Lafferty Maths Dept.

  17. Direct Proportion Direct Proportion Now try Exercise 2 Ch8 (page 104) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  18. Starter Questions 9 8 6 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  19. Direct Proportion Direct Proportion Formula Learning Intention Success Criteria 1. Understand the process for calculating direct proportion formula. • 1. To explain how to work out Direct Proportion formula. 2. Calculate gradient from information given. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  20. Direct Proportion Direct Proportion Formula • Given that y is directly proportional to x, • and when y = 20, x = 4. • Find a formula connecting y and x Since y is directly proportional to x the formula is of the form k is the gradient www.mathsrevision.com y = kx 20 = k(4) k = 20 ÷ 4 = 5 y = 5x Created by Mr. Lafferty Maths Dept.

  21. Direct Proportion Direct Proportion Formula • The number of dollars (d) varies directly as the • number of £’s (P). You get 3 dollars for £2. • Find a formula connecting d and P. Since d is directly proportional to P the formula is of the form k is the gradient www.mathsrevision.com d = kP 3 = k(2) k = 3 ÷ 2 = 1.5 d = 1.5P Created by Mr. Lafferty Maths Dept.

  22. Direct Proportion Direct Proportion Formula • How much will I get for £20 d = 1.5P d = 1.5 x 20 = 30 dollars www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  23. Direct Proportion Direct Proportion Formula Exercise 3 Ch8 (page 105) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  24. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  25. Direct Proportion Harder Direct Proportion Formula Learning Intention Success Criteria 1. Understand the process for calculating direct proportion formula. • 1. To explain how to work out harder Direct Proportion formula. 2. Calculate k for harder direct proportion formula. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  26. y x Direct Proportion Harder Direct Proportion Formula • Given that y is directly proportional to the square of x, and when y = 40, x = 2. • Find a formula connecting y and x when . Since y is directly proportional to x squared the formula is of the form www.mathsrevision.com y = kx2 40 = k(2)2 k = 40 ÷ 4 = 10 y = 10x2 Created by Mr. Lafferty Maths Dept.

  27. y x Direct Proportion Harder Direct Proportion Formula • Calculate y when x = 5 y = 10x2 y = 10(5)2 = 10 x 25 = 250 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  28. y x Direct Proportion Harder Direct Proportion Formula • The cost (C) of producing a football magazine • varies as the square root of the number of • pages (P). Given 36 pages cost 45p to produce. • Find a formula connecting C and P. Since C is directly proportional to “square root of” P the formula is of the form www.mathsrevision.com k = 48 ÷ 6 = 8 Created by Mr. Lafferty Maths Dept.

  29. y x Direct Proportion Harder Direct Proportion Formula • How much will 100 pages cost. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  30. Direct Proportion Harder Direct Proportion Formula Exercise 4B Ch8 (page 106) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  31. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  32. Inverse Proportion Inverse Proportion Learning Intention Success Criteria 1. Understand the idea of Inverse Proportion. • 1. To explain the term Inverse Proportion. 2. Solve simple inverse Proportion problems. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  33. y x Inverse Proportion Inverse Proportion Inverse Proportion is when one quantity increases and the other decreases. The two quantities are said to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other. Example : Fill in the following table given x and y are inversely proportional. www.mathsrevision.com 40 20 10 Created by Mr. Lafferty Maths Dept.

  34. y x Inverse Proportion Inverse Proportion Inverse Proportion is the when one quantity increases and the other decreases. The two quantities are said to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other. Example : If it takes 3 men 8 hours to build a wall. How long will it take 4 men. (Less time !!) www.mathsrevision.com Men Hours 3  8 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours Created by Mr. Lafferty Maths Dept.

  35. y x Inverse Proportion Inverse Proportion Example : It takes 10 men 12 months to build a house. How long should it take 15 men. Men Months 10  12 www.mathsrevision.com 1  12 x 10 = 120 15  120 ÷ 15 = 8 months Created by Mr. Lafferty Maths Dept.

  36. y x Inverse Proportion Inverse Proportion Example : At 8 m/s a journey takes 32 minutes. How long should it take at 10 m/s. Speed Time 8  32 mins www.mathsrevision.com 1  32 x 8 = 256 mins 10  256 ÷ 10 = 25.6 mins Created by Mr. Lafferty Maths Dept.

  37. Inverse Proportion Inverse Proportion Exercise 5 Ch8 (page 108) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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