Edexcel GCSE Maths Foundation Skills Book Ratio, proportion and rates of change 1

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1 Guidane on the use of odes for this mark sheme ethod mark A C P ao oe ft Auray mark ark awarded independent of method Communiation mark Proof, proess or justifiation mark Corret answer only Or equivalent Follow through Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 1

2 Question Working Answer ark AO Notes Grade 1 kg = 000 g for method of finding how many lots of 0 minutes = 0 = 10 min 10 min = hours 0 mins Plus 0 mins rest give hours 0 min So if it is put on at 6:0 pm it will e ready at 9:0 pm. No, she needs to put it on earlier. are needed ao for method of finding total time ao ft No and a lear summing up of why it won t e ready = 60 = 0 0 = 0 She spends 0 on lothes 0 a = 0.17 (to dp) = 0.8 = 8% Or 10 = 1 1 = 0.8 = 8%(to dp) = 7. = 8 to nearest ar are red 8% Yes for adding ratios to for proess of finding the share ao for proess of finding part of a ratio answer orret to sf or more for diving y showing nearest whole numer is more than d 17% green + % red Total % Less than half the ars are aounted for, so there ould e one third silver. 10 = 0 whih is a whole numer. No, she is not right. Yes, he ould e right. adding oth together in some way for no with justifiation for proess looking at how many availale to e silver for yes with suitale justifiation 8 One day is 60 = 10 minutes 10 = 88 minutes This is less than 60 minutes. 60 minutes is longer. finding a day in minutes. dividing total minutes y ao Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange

3 a 1%, y dividing y 100 Then multiply that figure y the perentage needed. E.g. find 8% of 100 = =.6 So 8% of is.6 C for proess of finding a perentage for first example for seond example 6 a 0% is 10% or so need to divide 10 y 10 then multiply y Or divide y. Look for ommon fators. When there are no ommon fators, it s in its simplest form. for lear explanation for lear explanation for lear explanation e.g. start with the ratio 1 : 18 Common fators are, and 6 Dividing the ration y 6 gives : and have no ommon fators, so you know that it is in its simplest form. for having a satisfatory example for the aompanying explanation 7 7 = So parts = = 0 So one part = 0 So Peter got 0 = for proess of sorting the ratios for finding parts = 10 dividing y ao ao Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange

4 8 a Corret = = > 0.6 for orret for lear explanation 9 a 8 = 16 pupils liked footall est 8 = 1 liked tennis 8 8 = 18 liked athletis Total = 6 alane = 8 6 = Corret 100% = 60% Not orret = = 11. liked swimming 6 A for orret with lear justifiation for not orret for lear explanation for proess of finding eah part for eah orret sport found for orret proess leading to = So of total = 10 1 of total = 10 = 0 So total = 0 = for omining frations for reognising is 10 for proess of getting from to the whole for orret answer alongside justifiation 10 1 mm 1. = 18.7 mm = 19 mm to next whole numer 19 mm 1. =.7 mm = mm to next whole numer mm 1. = 0 mm 0 mm 1. = 7. mm = 8 mm to next whole numer 8 mm 1. = 7. mm = 8 mm to next whole numer 1 mm, 19 mm, mm, 0 mm, 8 mm, 8 mm 8 for method of inreasing y % for 19 for method of ontinuing in same way for for 0 for 8 for 8 for omplete orret solution Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange

5 11 One years interest is = 0 Numer of years needed to get 160 in interest =. years interest is 0 = 00 Next whole year aove is. years for finding one years interest ao for setting up equation for numer of years for. ao 1 Ratio of areas of small to large is 1 : of small square is shaded. 7 As a fration of the larger square, this is 7 1 = 1 Total shaded is = = proess of sorting ratio for explanation of eah part 1 7 finding fration in small square ao adding the two frations ao 1 If Anna starts with fare of x New fare is x 1.1 = 1.1x A redution of 1% on that will give negotiated fare as 1.1x 0.8 = 0.977x No, she is etter off. 7 proess of stating a starting fare, say x finding 1% inrease ao method of reduing new fare y 1% finding 1% redution. ao No with lear justifiation 1 Pens-R-Us Pay for 0 get 10 free Cost = 0 udget Stationery Numer of pens ( + ) = So pay for 0 and get 1 free. Cost is the same. udget Stationery has the etter deal as Sian will get pens for the same prie as 0 at Pens-R-Us for proess for ost at Pens-R-Us ao for method at udget Stationery ao orret final statement. Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange

6 1 Pay for 1000 ml and get 100 ml Ratio in ml, pay : free 1000: 00 : 1 uy one get one free Ratio in ml, pay : free 00 : 00 1 : 1 So uy one get one free is the etter deal. uy one get one free is the etter deal as you get a higher ratio of shampoo free. for proess of finding ratio for usale ratio for proess of finding ratio answer in a suitale form to ompare for uy one get one free with explanation 16 a 1 : 6 6 : 1 eause 1 : 6 = 6 : 6 ( 6) No for proess of finding eah ratio in its unitary form as a method of omparison, oe d Or 6 : 1 = 1 : : 9 ( 19) 1 : 1 19 : 19 ( 6) : G : : 10 6 : 1 (1 pupils) 7 : 17. (not possile!) 8 : 0 (8 pupils) 19 : 9 ( 19) 1 : No, eause the units must e the same in order to ompare. No, to retain this ratio requires oys and girls eah time, so 7 pupils. This means that there an only e multiples of 7 pupils in the lu. is not a multiple of 7 for alulation showing a multipliative anelling down for an understanding of sale and equivalene of units for referene to multiples of 7 17 a Paks of : 90 = 0 0 paks 1.0 = Paks of 1: 90 1 = 6 6 paks = 0 Paks of : 90 is not divisile y. 6 paks of 1 for orret omination to 90 for orret ost uy get one free on paks of = 10 1 = free = 10 1 = free So new ost = 0 Or ( 1)+ ( 1) = = 0 No, still selet 6 paks of 1 ut it now osts less! for a method for alulating of the ost for orret justifiation of hoie Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 6

7 18 Appropriate workings related to their question. 19 a : W : women so the total memer ship is: 1 : 1 60 : Total memership = 60 + = 8 e.g. A shop inreased its pries y 10%. When an item osts 100, how muh more does it osts after the prie inrease? for larity of question for multiplying y 1 oe for 8 memers in total R : S : J = : : + + = = 8.0 Shaun pays 8.0 =.0.0 for division of 8 y 10 for orret multipliation 8.0 oe 0 a = 1 Own question like the one in part a For example: a tennis lu has 0 male memers. The ratio of women to men is 6 :. ow many female memers are there? 6 for orret type of question for proess of setting up equation = 8 0 = 10 hours 10 hours ao osts osts = 1.68 to dp =1. The inrease in ost is proportionally more than the inrease in attery life. for division of more expensive ost y heaper ost for use of omparison to justify = = 90 = 17.0 Redution is: = for multiplying heaper ost y and dividing y ao Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 7

8 1 a 90 = 0 minutes = 1.p per minute 80 = 00 minutes = 1.6p per minute 80 = 00 minutes = 1p per min heapest Or = 69 minutes per = 6 minutes per = 100 minutes per 1 est value est uy is pak for 80 minutes for method of multiplying up for total minutes and then division to identify either ost per minute or time per for orret workings in first of the three ases for the orret working in the seond two ases 80 minutes is not long enough = = = They will get more. for explanation of possile reasons not to hoose the est uy for multipliations for sutration ft ao Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 8

9 a 8 kg = 8000 g = kg = 000 g = (to nearest whole numer) kg = 000 g =100 7 kg = 7000 g = 8 for proess of division to see how many athes of 1 isuits an e made with eah ingredients for, 100 and 8 So the limiting value is the amount of iing sugar. Therefore she an make 8 = 67 isuits. Numer of pakets = 67 1 = =.99 = = 11 disounted =. to dp 11. = 7.9 Total sales = = Total osts = = 8 % profit = ( )/ % = 8.9% = 71 0% disount = =.80 Or = = 71.0 a So she an make omplete paks of 1 isuits. 9% profit to the nearest integer. e is overpaying y.80 Disagree; he would pay the shop more than he needs to. A 0.8 = 8 for orret identifiation of limiting value for orret ost of three-quarters of isuits for use of 0.8 multiplier ao for division of total sales y total ost (ft) for orret % with rounding for proess: multiplying y 1. to find ost with VAT for multiplying y 0.8 to find 0% redued prie (ft) for sutrating to find overpayment for demonstrating over-payment with explanation for orret formula A = 0.8 for orret rearrangement of y 0.8 Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 9

10 6 a A = A 1. = A. No: an inrease to A of 0% followed y another inrease of 0% gives.a. Douling would e A A.A for lear explanation with alulated justifiation oe 7 a A = 0.9A A = 0.9A A 6 7 = 996 If the original ost is A, the ost after a disount of % is 0.7A to pay VAT at 0% gives a new prie of 0.9A. If VAT is added first, the prie is 1.A. A % redution fives a new prie of 0.9A. eause multipliation is ommutative, the pries are the same. It makes no differene. for method of setting up oth equations for lear explanation with alulated justifiation oe for multipliation and rearrangement A = ao A 1.0 = 6.0 A = for multipliation y 1.0 and rearrangement. ao A 1.07 = 97.6 A = for multipliation y 1.07 and rearrangement ao d e For an original amount A, the multiplier is for a perentage inrease or derease, and the new value is C A = C 8 Current osts are 1.0/mile and 0p/minute Competitive priing struture: answers will vary. A = C 1 ultiplier (x) x > 1 inrease 0< x <1 derease 8 for orret explanation either in words or y a general formula, provided the variales are defined for larity that a derease will have a multiplier etween 0 and 1 and inrease will have a multiplier greater than 1 ( a multiplier of 1 will not hange the value) for proess of finding harges for working out urrent prie struture Time taken minutes minutes 10 minutes 1 minutes 1 minutes Distane 1 mile miles miles miles 6 miles Total harge (A) Total harge () for a orret alulation of a priing struture that has an element of ompetition. The suggestion () ompetes for short distanes, mathes for mid distanes and is not ompetitive for longer journeys Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 10

11 9 a Travel 0 miles in minutes minutes = hour orret explanation with alulation that indiates 10 miles every 1 minutes implies 0 miles every 60 minutes oe 0 = 0 = 10 = 0 mph as required lear explanation of given result Not hanging minutes into hours for stating a ommon misoneption Units of speed = units of distane units of time for orretly stating the relationship etween speed, distane and time 0 A retangle 1 m m Area = m A retangle m 8 m Area = m Length sale fator = Area sale fator = 16 ( ) Area = 16 = m m for proess of trial and improvement ao =. Length sale fator is. Volume sale fator is (.) = = 78.1 litres 78.1 litres Length sale fator = 0 1 = 0 Volume sale fator = 0 = = m ( 100 or for m ) = 1.1 m for alulation of length sale fator. for alulation of volume sale fator. ao for alulation of length sale fator for alulation of volume sale fator 1.1 m for orret onversion to ui metres ao Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 11

12 In year = 0 Interest = 0 So total at end of year 1 = = 80 Year = 7.0 Interest = 7.0 At end of year = = Year =.61 (anks round down) Interest =.61 At end of year = = for showing the onept of ompound interest. for any suitale method of alulating total at end of year 1 ao for any suitale method of alulating total at end of year (ft) for any suitale method of alulating total at end of year (ft) ao (aept 871.8). for larity of explanation through set out of alulations Let starting amount e Then 0.8 n < Divide oth sides y 0.8 n < 0. Trial and improvement 0.8 = 0.6 not yet 0.8 = 0.1 not yet 0.8 = now less than a half weeks for hoosing a starting a position, either a variale like or a speifi amount like 100 for working through the weeks in some way for proess of finding amounts for weeks and to show the point at whih the ank aount first dips elow 0% of the original alane ao OR starting with a given amount Say = = = = 0.96 Edexel GCSE aths Foundation Skills ook Ratio, proportion and rates of hange 1