Direct Proportion www mathsrevision com S 4 Direct

Direct Proportion www. mathsrevision. com S 4 Direct Proportion Direct Variation Harder Direct Variation 04 -Dec-20 Created by Mr. Lafferty Maths Dept. (extension)

Starter Questions www. mathsrevision. com S 4 9 8 6 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain the term Direct Proportion. 1. Understand the idea of Direct Proportion. 2. Solve simple Direct Proportional problems. 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Proportion www. mathsrevision. com S 4 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. Cakes Cost 6 4. 20 Write down two quantities that are 1 4. 20 ÷ 6 = 0. 70 in direct proportion. 04 -Dec-20 5 Created by Mr. Lafferty Maths Dept. 0. 70 x 5 = £ 3. 50

Same ratio means in Proportion proportion www. mathsrevision. com S 4 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 60 p (c) 7 golf balls for £ 4. 20 : 10 for £ 6 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Proportion www. mathsrevision. com S 4 Example : On holiday I exchanged £ 30 for $45. How many $ will I get for £ 50. £ 30 1 50 04 -Dec-20 What name do we give to this Exchange value $ rate 45 45 ÷ 30 = 1. 5 x 50 = $75 Created by Mr. Lafferty Maths Dept.

Proportion www. mathsrevision. com S 4 Example : 300 pencils cost £ 6. How much will 200 cost. Pencils 300 100 200 04 -Dec-20 Cost £ 6. 00 ÷ 3 = £ 2. 00 x 2 = £ 4. 00 Created by Mr. Lafferty Maths Dept.

Proportion www. mathsrevision. com S 4 Now try Ex 1 Ch 17 (page 187) 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 4 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Direct Variation www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain what direct variation is and how to work out simple direct variation formulae. 04 -Dec-20 1. Understand the process for calculating direct variation formulae. 2. Calculate the constant k from information given and write down formula. Created by Mr. Lafferty Maths Dept.

Variation www. mathsrevision. com S 4 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 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 Mathematically formula ! we say, 04 -Dec-20

Direct Variation www. mathsrevision. com S 4 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 y = kx k is a x 04 -Dec-20 20 = k(4) y = 20 k = 20 ÷ 4 = 5 x =4 y = 5 x constant

Direct Variation www. mathsrevision. com S 4 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 d = k. P P 3 = k(2) d = 3 k = 3 ÷ 2 = 1. 5 P=2 d = 1. 5 P k is a constant

Direct Variation www. mathsrevision. com S 4 Q. How much will I get for £ 20 d d = 1. 5 P P 04 -Dec-20 d = 1. 5 x 20 = 30 dollars Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Direct Variation Now try Ex 2 Ch 17 (page 188) 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 4 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Direct Variation Harder Direct Variation www. mathsrevision. com S 4 Learning Intention Success Criteria 1. To explain how to work out harder variation formulae. 1. Understand the process for calculating direct variation formulae. 2. Calculate the constant k from information given and write down formula and use it to solve problems. 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Direct Variation Harder Direct Variation www. mathsrevision. com S 4 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 y = kx 2 04 -Dec-20 40 = k(2)2 y = 40 k = 40 ÷ 4 = 10 x=2 y = 10 x 2

Direct Variation Harder Direct Variation www. mathsrevision. com S 4 Q. Calculate y when x = 5 y = 10 x 2 y x 2 04 -Dec-20 y = 10(5)2 = 10 x 25 = 250 Created by Mr. Lafferty Maths Dept.

Direct Variation Harder Direct Variation S 4 www. mathsrevision. com Q. The cost (C) of producing a football magazine varies as the square root of the number of pages (P). Given 36 pages cost 48 p 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 C √P 04 -Dec-20 C = 48 P = 36 k = 48 ÷ 6 = 8

Direct Variation Harder Direct Variation www. mathsrevision. com S 4 Q. How much will 100 pages cost. C √P 04 -Dec-20 Created by Mr. Lafferty Maths Dept.

Direct Variation Harder Direct Variation www. mathsrevision. com S 4 Now try Worksheet 04 -Dec-20 Created by Mr. Lafferty Maths Dept.