Created by Mr. Lafferty Maths Dept.

Slides:

Advertisements

Similar presentations

Describe the relationship between x and y.

Advertisements

Fill in missing numbers or operations

Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = x 1 = x 1 = 12 X 2 1.

Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = ÷ 1 = ÷ 1 = 12 ÷ 2 2 ÷ 2 =

Created by Mr.Lafferty Maths Dept

Warm up Complete the analogies: 5 is to 25 as 6 is to ___________ 7 is to 77 as 11 is to ___________ ¼ is to ½ as.25 is to ____________

GCSE Higher Revision Starters 11 Module 3 and 5 Revision.

Algebraic Operations Factors / HCF Common Factors

Created by Mr. Lafferty Maths Dept.

1-Jun-14Created by Mr. Lafferty Maths Dept. Hourly Rates / Wages Wages / Hourly Rates Wages & Salaries Weekly / Monthly Wages Annual.

Money Compound Interest

Created by Mr.Lafferty Maths Dept

© Richard A. Medeiros 2004 x y Function Machine Function Machine next.

Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept

Surds Simplifying a Surd Rationalising a Surd Conjugate Pairs

Simple Linear Patterns Harder Linear Patterns Triangular Numbers Square Numbers MTH 2-13a & MTH 3-13a Simple Linear Patterns using diagrams and tables.

Look at This PowerPoint for help on you times tables

What is it and how do I know when I see it?

12-Jun-14Created by Mr.Lafferty Maths Dept Money Revision Money Level 1 Foreign Exchange Rates Converting Back to £s Level 2.

Equations & Inequalities

13-Jun-14Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem Finding the length of the smaller side Length of line using Pythagoras.

Level 3 Areas of Simple Shapes

Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept.

Types of Numbers Multiples and LCM Factors and HCF Prime numbers

Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic Int.

24-Aug-14Compiled by Mr. Lafferty Maths Dept. Money Simple Interest Simple Bills & VAT Electricity Bills National 4 NUM 1.2.

Straight Line Graphs The gradient Vertical ÷ Horizontal Basic Lines

25-Aug-14Created by Mr. Lafferty1 Statistics Mean Mean from a Frequency Table Range of a Set of Data Median and Mode Grouped Frequency.

Created by Mr. Lafferty Maths Dept

Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.

Equations & Inequalities

Mathematical Similarity

25-Aug-14Created by Mr. Lafferty Multiples and LCM Factors and HCF Types of Numbers Prime numbers Prime Decomposition.

Graphing y = nx2 Lesson

Least Common Multiples and Greatest Common Factors

14-Dec-14 Created by Mr Lafferty Maths Dept What do you see ? The Colour Quiz Look at the chart and say the colour, not the word.

18-Dec-14Created by Mr.Lafferty Math Dept Revising Basic Angles Naming Angles Calculating Missing angles Angles in a Triangle Corresponding.

19-Dec-14Created by Mr. Lafferty Maths Dept. Simplifying Ratios Ratio Calculations Ratios MNU 3-08a MNU 4-08a.

MNU 3-03a 15-Jan-15Created by Mr. Lafferty Maths Dept. Revision Level E Add & Subtract Decimals Decimals Multiplying by 2 Simple.

15-Jan-15Created by Mr. Lafferty Maths Dept Integers – Positive and Negative Add /Sub using Thermometer Integers Add / Sub Integers.

Calculating Percentages

13-Apr-15Created by Mr. Lafferty Maths Department Solving Sim. Equations Graphically Solving Simple Sim. Equations by Substitution Simultaneous Equations.

17-Apr-15Created by Mr. Lafferty Maths Dept Ordering integers Integers Add / Sub Mathematically Letters and Numbers Multiplying Integers.

Level 4 Mathematical Similarity Calculating Scale Factor Similar Triangles Parallel Line Triangles Scale Factor in 2D (Area) Scale.

Inverse Proportion X y Inverse Proportion

16-May-15Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Variation Harder Direct Variation (extension) Direct Proportion.

18-May-15Created by Mr. Lafferty Maths Dept. Coordinates Plotting Coordinates Coordinates Different Grids Proper Names Extending.

9-Jun-15Created by Mr. Lafferty Maths Dept. Simplifying Ratios Ratio Calculations Proportional Division S4 Ratio.

Created by Mr. Rate and Proportion Rates and Finding Rates Wednesday, June.

MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Simplifying Ratios Ratio Calculations Ratio & Proportion Direct Proportion.

Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.

Simple Linear Patterns using diagrams and tables

Direct Proportion Direct Proportion Graphs Direct Proportion formula and calculations Inverse Direct Proportion Direct Proportion Other Direct Proportion.

Direct Proportion Inverse Proportion Direct Proportion (Variation) Graph Direct Variation Direct Proportion Inverse Proportion (Variation) Graph Inverse.

Level D 9-Oct-15Created by Mr. Lafferty Maths Dept. Coordinates Reading and Plotting Coordinates Proper Names Grids Fun Grids.

MNU 3-08a 7-Dec-15Created by Mr. Lafferty Maths Dept. Proportion Proportion Direct Proportion Graph of Direct Proportion Proportional.

N5 Num 25-Dec-15Created by Mr. Lafferty Maths Dept. Ratio & Proportion Indirect Proportion Ratio Calculations Direct Proportion Sharing.

4-Mar-16 Starter Questions Starter Questions. 4-Mar-16 Ratio & Proportion The table below shows the cost of packets of “Biscuits”. Direct Proportion Graphs.

Num 4-Mar-16Created by Mr. Lafferty Maths Dept. Ratio Simplifying Ratio Ratio Calculations Ratio Direct Proportion Proportion per.

Created by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.

Fraction & Percentages

Direct Proportion Direct Proportion Inverse Proportion

Direct Proportion Direct Proportion Direct Proportion Graphs

Presentation transcript:

Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Direct Proportion Graphs Direct Proportion formula and calculations www.mathsrevision.com Other Direct Proportion formula Inverse Direct Proportion 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Starter Questions 9 8 6 www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 : www.mathsrevision.com 4 eggs, 8g butter, 80 ml of milk. (b) Simply half original amounts: 1 eggs, 2g butter, 20 ml of milk. 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Now try Exercise 1 Ch8 (page 101) www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 ? 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion Graphs 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. 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion KeyPoint Two quantities which are in Direct Proportion Graphs KeyPoint Two quantities which are in Direct Proportion always lie on a straight line passing through the origin. www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Graphs Example : Plot the points in the table below. Are they in Direct Proportion? X 1 2 3 4 y 6 9 12 www.mathsrevision.com We plot the points (1,3) , (2,6) , (3,9) , (4,12) 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com Direct Proportion Graphs y 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 2-Apr-17 Created by Mr. Lafferty Maths Dept. x 1 2 3 4

Direct Proportion www.mathsrevision.com Direct Proportion Graphs y 12 Find the formula connecting y and x. 11 10 9 Formula has the form : 8 7 y = kx 6 www.mathsrevision.com 5 Gradient = 3 4 Formula is : y = 3x 3 2 1 2-Apr-17 Created by Mr. Lafferty Maths Dept. x 1 2 3 4

Direct Proportion Key point of Ex 2 www.mathsrevision.com 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

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

Created by Mr. Lafferty Maths Dept. Starter Questions 9 8 6 www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Formula Exercise 3 Ch8 (page 105) www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com 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 y x www.mathsrevision.com y = kx2 40 = k(2)2 k = 40 ÷ 4 = 10 y = 10x2 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Direct Proportion Harder Direct Proportion Formula Calculate y when x = 5 y = 10x2 y = 10(5)2 = 10 x 25 = 250 y x www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Direct Proportion www.mathsrevision.com 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 y x k = 48 ÷ 6 = 8 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Direct Proportion Harder Direct Proportion Formula How much will 100 pages cost. www.mathsrevision.com y x 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Direct Proportion Harder Direct Proportion Formula Exercise 4B Ch8 (page 106) www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www.mathsrevision.com X 1 2 4 8 y 80 40 20 10 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 y x X 1 2 4 8 y 80 40 20 10 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www.mathsrevision.com 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 y x Men Hours 3  8 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 y x 15  120 ÷ 15 = 8 months 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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 y x 10  256 ÷ 10 = 25.6 mins 2-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Inverse Proportion Inverse Proportion Exercise 5 Ch8 (page 108) www.mathsrevision.com 2-Apr-17 Created by Mr. Lafferty Maths Dept.