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

  • Direct ProportionInverse ProportionDirect Proportion (Variation) GraphDirect VariationDirect Proportion Inverse Proportion (Variation) GraphInverse VariationJoint Variation

    Created by Mr. Lafferty Maths Dept.

  • Understanding FormulaeThe Circumference of circle is given by the formula :C = DWhat happens to the Circumference if we double the diameterC = (2D)New D = 2DThe Circumference doublesIn real-life we often want to see what effect changing the value of one of the variables has on the subject.= 2D

    Created by Mr. Lafferty Maths Dept.

  • Learning IntentionSuccess CriteriaTo explain the term Direct Proportion.1. Understand the idea of Direct Proportion.Direct Proportion2. Solve simple Direct Proportional problems.Direct Proportion

    Created by Mr. Lafferty Maths Dept.

  • *Direct Proportion .. When you double the number of cakes you double the cost.CakesCost Two quantities, (for example, number of cakes and totalcost) are said to be in DIRECT Proportion, if :Direct ProportionExample : The cost of 6 cakes is 4.20. find the cost of 5 cakes.6 4.20 14.20 6 = 0.70 50.70 x 5 = 3.50 Write down two quantities that are in direct proportion.Easier methodCakesPence6420 5

    Are we expecting more or less(less)

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionDirect ProportionExample : 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 6Same ratio means in proportion

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionDirect ProportionWhich graph is a direct proportion graph ?

    Created by Mr. Lafferty Maths Dept.

  • Learning IntentionSuccess Criteria1. To explain the term Inverse Proportion.1. Understand the idea of Inverse Proportion.Inverse Proportion2. Solve simple inverse Proportion problems.Inverse Proportion

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionInverse Proportion is when one quantity increasesand 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 yare inversely proportional.Inverse Proportion102040Notice xxy = 80Hence inverse proportion

    X1248y80

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionMenHours Inverse Proportion is the when one quantity increasesand 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 !!)3 8 13 x 8 = 24 hours 424 4 = 6 hours Inverse ProportionEasier methodWorkers Hours38 4

    Are we expecting more or less(less)

    Created by Mr. Lafferty Maths Dept.

  • *Inverse ProportionMenMonths Example : It takes 10 men 12 months to build a house.How long should it take 8 men.10 12 112 x 10 = 120 8120 8 = 15 months Inverse ProportionEasier methodWorkersmonths 1012 8

    Are we expecting more or less(more)

    Created by Mr. Lafferty Maths Dept.

  • 12288 12 = 24 mins 132 x 9 = 288 mins 9 32 mins *Inverse ProportionSpeedTime Example : At 9 m/s a journey takes 32 minutes.How long should it take at 12 m/s.Inverse ProportionEasier methodSpeedminutes 932 12

    Are we expecting more or less(less)

    Created by Mr. Lafferty Maths Dept.

  • Learning IntentionSuccess Criteria1. To explain how Direct Direct Proportion Graph is always a straight line.1. Understand that Direct Proportion Graph is a straight line.Direct Proportion2. Construct Direct Proportion Graphs.Direct Proportion Graphs

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionThe table below shows the cost of packets of Biscuits.Direct Proportion GraphsWe can construct a graph to represent this data.What type of graph do we expect ?Notice C P = 20Hence direct proportion

    Created by Mr. Lafferty Maths Dept.

  • *Created by Mr. Lafferty Maths Dept.Direct Proportion GraphsNotice that the points lie on a straight line passing through the originSo direct proportionC PC = k Pk = 40 2 = 20C = 20 P

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionDirect Proportion GraphsKeyPointTwo quantities which are in Direct Proportionalways lie on a straight linepassing through the origin.

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionEx: Plot the points in the table below. Show that they are in Direct Proportion.Find the formula connecting D and W ?Direct Proportion GraphsWe plot the points (1,3) , (2,6) , (3,9) , (4,12)

    W1234D36912

    Created by Mr. Lafferty Maths Dept.

  • 1Direct ProportionPlotting the points

    (1,3) , (2,6) , (3,9) , (4,12)Direct Proportion Graphs0123410111223456789Since we have a straight linepassing through the originD and W are in Direct Proportion.

    Created by Mr. Lafferty Maths Dept.

  • 1Direct ProportionFinding the formula connecting D and W we have.Direct Proportion Graphs0123410111223456789D WConstant k = 6 2 = 3Formula is : D= 3WD = kWD = 6W = 2

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionDirect Proportion Graphs1. Fill in table and construct graph2. Find the constant of proportion (the k value) Write down formula

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionQThe distance it takes a car to brake depends on how fast it is going.

    The table shows the braking distance for various speeds.Direct Proportion GraphsDoes the distance D vary directly as speed S ?Explain your answer

    S10203040D5204580

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  • The table shows S2 and D

    Fill in the missing S2 values.Direct ProportionDirect Proportion GraphsDoes D vary directly as speed S2 ?Explain your answer1004009001600

    S2S10203040D5204580

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionFind a formula connecting D and S2. Direct Proportion GraphsD S2Constant k = 5 100 = 0.05Formula is : D= 0.05S2D = kS2D = 5S2 = 100

    Created by Mr. Lafferty Maths Dept.

  • Learning IntentionSuccess Criteria1. To explain how the shape and construction of a Inverse Proportion Graph.1. Understand the shape of a Inverse Proportion Graph .Inverse Proportion2. Construct Inverse Proportion Graph and find its formula.Inverse Proportion Graphs

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionThe table below shows how the total prize money of 1800 is to be shared depending on how many winners.Inverse Proportion GraphsWe can construct a graph to represent this data.What type of graph do we expect ?Notice W x P = 1800Hence inverse proportion

    Winners W12345Prize P1800900600450360

    Created by Mr. Lafferty Maths Dept.

  • Direct Proportion GraphsNotice that the points lie on a decreasing curveso inverse proportionInverse Proportion

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionInverse Proportion GraphsKeyPointTwo quantities which are in Inverse Proportionalways lie on a decrease curve

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionEx: Plot the points in the table below. Show that they are in Inverse Proportion.Find the formula connecting V and N ?Inverse Proportion GraphsWe plot the points (1,1200) , (2,600) etc...

    N12345V1200600400300240

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionPlotting the points

    (1,1200) , (2,600) , (3,400) (4,300) , (5, 240)Inverse Proportion Graphs0123410001200200400600800Since the points lie on adecreasing curveV and N are in Inverse Proportion.5

    Created by Mr. Lafferty Maths Dept.

  • Inverse ProportionFinding the formula connecting V and N we have.Inverse Proportion Graphs k = VN = 1200 x 1 = 1200V = 1200N = 101234100012002004006008005N

    Created by Mr. Lafferty Maths Dept.

  • Direct ProportionDirect Proportion Graphs1. Fill in table and construct graph2. Find the constant of proportion (the k value) Write down formula

    Created by Mr. Lafferty Maths Dept.

  • Learning IntentionSuccess Criteria1. To explain how to work out direct variation formula.1. Understand the process for calculating direct variation formula.Direct Variation2. Calculate the constant k from information given and write down formula.

    Created by Mr. Lafferty Maths Dept.

  • Direct VariationGiven 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 formy = kxk is a constant20 = k(4)k = 20 4 = 5y = 5xy = 20x =4

    Created by Mr. Lafferty Maths Dept.

  • Direct VariationThe 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 formd = kPk is a constant3 = k(2)k = 3 2 = 1.5d = 1.5Pd = 3P = 2

    Created by Mr. Lafferty Maths Dept.

  • d = 1.5 x 20 = 30 dollarsDirect Variation How much will I get for 20d = 1.5P

    Created by Mr. Lafferty Maths Dept.

  • Direct VariationGiven that y is directly proportional to the square of x, and when y = 40, x = 2. Find a formula connecting y and x .Since y is directly proportional to x squaredthe formula is of the formy = kx240 = k(2)2k = 40 4 = 10y = 10x2y = 40x = 2Harder Direct Variation

    Created by Mr. Lafferty Maths Dept.

  • Direct Variation Calculate y when x = 5y = 10x2y = 10(5)2 = 10 x 25 = 250Harder Direct Variation

    Created by Mr. Lafferty Maths Dept.

  • Direct Variation The cost (C) of produc