1 / 22

Direct Proportion

S4. Direct Proportion. Direct Proportion. Direct Variation. www.mathsrevision.com. Harder Direct Variation (extension). S4. 9. Starter Questions. 8. 6. www.mathsrevision.com. Direct Proportion. Direct Proportion. S4. Learning Intention. Success Criteria.

pepper
Download Presentation

Direct Proportion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

  3. Direct Proportion Direct Proportion S4 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. Proportion S4 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. Same ratio means in proportion Proportion S4 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 www.mathsrevision.com (c) 7 golf balls for £4.20 : 10 for £6 Created by Mr. Lafferty Maths Dept.

  6. Proportion S4 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.

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

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

  9. S4 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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

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

  12. Direct Variation S4 Given that y is directly proportional to x, and when y = 20, x = 4. Find a formula connecting y and x. y Since y is directly proportional to x the formula is of the form x www.mathsrevision.com k is a constant y = kx 20 = k(4) k = 20 ÷ 4 = 5 y = 20 x =4 y = 5x

  13. Direct Variation S4 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. d Since d is directly proportional to P the formula is of the form P www.mathsrevision.com k is a constant d = kP 3 = k(2) d = 3 P = 2 k = 3 ÷ 2 = 1.5 d = 1.5P

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

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

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

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

  18. y x2 Direct Variation Harder Direct Variation S4 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 y = 40 x = 2 k = 40 ÷ 4 = 10 y = 10x2

  19. Direct Variation Harder Direct Variation S4 • Calculate y when x = 5 y = 10x2 y x2 y = 10(5)2 = 10 x 25 = 250 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  20. C √P Direct Variation Harder Direct Variation S4 • 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 www.mathsrevision.com C = 48 P = 36 k = 48 ÷ 6 = 8

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

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

More Related