1. 16-May-15Created by Mr. Lafferty Maths Dept. Direct Proportion www.mathsrevision.com Direct Variation Harder Direct Variation (extension) Direct Proportion S4

2. 16-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 9 6 8 S4

3. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.To explain the term Direct Proportion. 1. Understand the idea of Direct Proportion. Direct Proportion 2. Solve simple Direct Proportional problems. Direct Proportion S4

4. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion “.. When you double the number of cakes you double the cost.” CakesCost Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT Proportion, if : Example :The cost of 6 cakes is £4.20. find the cost of 5 cakes. 6  4.20 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50 Write down two quantities that are in direct proportion. S4

5. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion Example : Which of these pairs are in proportion. (a)3 driving lessons for £60 : 5 for £90 (b)5 cakes for £3: 1 cake for 60p (c)7 golf balls for £4.20: 10 for £6 Same ratio means in proportion S4

6. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion £$ Example :On holiday I exchanged £30 for $45. How many $ will I get for £50. 30  45 1  45 ÷ 3 0 = 1.5 50  1.5 x 50 = $75 What name do we give to this value Exchange rate S4

7. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Proportion PencilsCost Example :300 pencils cost £6. How much will 200 cost. 300  £6.00 100  £6.00 ÷ 3 = £2.00 200  £2.00 x 2 = £4.00 S4

8. 16-May-15Created by Mr. Lafferty Maths Dept. Now try Ex 1 Ch17 (page 187) www.mathsrevision.com Proportion S4

9. 16-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com S4

10. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain what direct variation is and how to work out simple direct variation formulae. 1. Understand the process for calculating direct variation formulae. Direct Variation 2. Calculate the constant k from information given and write down formula. S4

11. 16-May-15 www.mathsrevision.com Variation If you double the number of cakes you double the cost Variation is the ALGEBRA form of Proportion. S4 If you treble the number of cakes you treble the cost If you half the number of cakes you half the cost We say the cost (C) VARIES as the number (n) of cakes Mathematically we say, It should be obvious that if you increase the number of cakes you buy from a shop then you increase the cost. Not a formula ! Formula !

12. 16-May-15 www.mathsrevision.com Direct Variation 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 y = kx k is a constant 20 = k(4) k = 20 ÷ 4 = 5 y = 5x y = 20 x =4 y x S4

13. www.mathsrevision.com Direct Variation 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 d = kP k is a constant 3 = k(2) k = 3 ÷ 2 = 1.5 d = 1.5P d = 3 P = 2 d P S4

14. d = 1.5 x 20 = 30 dollars 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Direct Variation Q. How much will I get for £20 d = 1.5P d P S4

15. 16-May-15Created by Mr. Lafferty Maths Dept. Now try Ex 2 Ch17 (page 188) www.mathsrevision.com Direct Variation

16. 16-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com S4

17. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain how to work out harder variation formulae. 1. Understand the process for calculating direct variation formulae. Direct Variation 2. Calculate the constant k from information given and write down formula and use it to solve problems. S4 Harder Direct Variation

18. 16-May-15 www.mathsrevision.com Direct Variation 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 y = kx 2 40 = k(2) 2 k = 40 ÷ 4 = 10 y = 10x 2 y x2x2 y = 40 x = 2 Harder Direct Variation S4

19. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Direct Variation Q. Calculate y when x = 5 y = 10x 2 y = 10(5) 2 = 10 x 25 = 250 y x2x2 Harder Direct Variation S4

20. 16-May-15 www.mathsrevision.com Direct Variation Q. The cost (C) of producing a football magazine varies as the square root of the number of pages (P). Given 36 pages cost 48p 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 k = 48 ÷ 6 = 8 C √P C = 48 P = 36 Harder Direct Variation S4

21. 16-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Direct Variation Q. How much will 100 pages cost. C √P Harder Direct Variation S4

22. 16-May-15Created by Mr. Lafferty Maths Dept. Now try Worksheet www.mathsrevision.com Direct Variation Harder Direct Variation S4