Homework. Revising sequences. a Start. b Start. c Start. Write down. Write down 3. Write down. Multiply by 3. Add on 4. Subtract 5.

Transcription

1 A.HW evising sequences Here re three flow chrts. Follow the instructions to generte sequence from ech flow chrt. Strt Strt c Strt Write down 7 Write down Write down 5 Add on 4 Multiply y Sutrct 5 Write down your nswer Write down your nswer Write down your nswer No Is it more thn 0? No Is it more thn 00? No Is the nswer negtive? Yes Yes Yes Stop Stop Stop Drw flow chrt for generting ech of the following sequences: 6, 0, 4, 8, 0.5, 0.75,,.5,.5 c 6, 8, 4,,, 0.5

2 A.HW Generting sequences The nth term of sequence is given. Write down the first five terms of ech sequence. Descrie ech sequence using term-to-term rule. The first one is done for you. 5n + n c d 00 0n n e 4n = = 5 + = = = 8 The first term is 8, then dd 5. f n + Mtch ech sequence to its correct term-to-term nd position-to-term rule. Sequences Term-to-term rules Position-to-term rules 4, 8,, 6, 0,... First term 0 Sutrct 5 T(n) = n +, 4, 5, 6, 7,... First term Add 5 T(n) = 0n +5, 8,, 8,,... First term 4 Add 4 T(n) = 4n 5, 5, 45, 55, 65,... First term Add T(n) = 5 5n 0, 5, 0, 5, 0,... First term 5 Add 0 T(n) = 5n Find three different sequences tht strt with,, Descrie ech of the sequences using term-to-term rule.

3 A.HW Descriing sequences A pond is surrounded y squre concrete sls s shown elow: Investigte the numer of squre concrete sls surrounding rectngulr ponds of different sizes. For exmple: A y 4 pond needs 6 sls A y pond needs sls 4 Write rule, using words or letters, for the numer of sls you will need for ny size pond. Explin why your rule works.

4 A.HW evising functions Complete these function mchines nd mtch ech one with one of the functions in the oxes. (There re two spre functions.) i Input N Output O 7 Functions + 5 O N = + 4 ii Input N Output O O = 5N O = N + 4 iii Input N + 4 Output O O = 5(N + ) iv Input N Output O O = N O =N +5 v Input N + 4 Output O O =(N +5) For the two spre functions, drw the function mchines. Use ny two of these functions in this function mchine: c Input N Which order of functions gives the iggest output? Which order of functions gives the smllest output? Are there ny comintions tht give the sme outputs? Output O

5 A.HW Drwing grphs from functions For the function y = x + 5: Drw the function mchine. Use the function mchine to generte coordinte pirs. Input x 5 5 Output y???? Coordinte pirs (, ) (, ) (, ) (, ) c d Copy the grid onto squred pper nd plot these points. Join the points with stright line. Lel the liner function y = x + 5. Use the line to find: i the output when the input is x = ii the input when the output is y = y x 4 6 For the eqution y = x 4: Copy nd complete the tle of results. x y 7 0 c Plot the coordinte pirs on to grid of suitle size. Join up the points nd lel the line. Which of the following equtions would e prllel to the line in question? y = x + y = x + y = 4x + y = + x

6 A.HW el-life grphs One dy in 004 the exchnge rte for (sterling) to euros ws =.6 euros. Copy the xes for the conversion grph for to euros. Plot the conversion grph using these conversions s strting point: 0 = 0 euros 00 = 60 euros 00 = 0 euros Use your conversion grph to convert the following: c d e f 5 into euros 60 into euros 0 into euros 40 euros into pounds 80 euros into pounds 00 euros into pounds. (sterling) Euros The grph shows the height of the wter in the sink s Dvid did the wshing up. C D Height of wter A B E Time Descrie wht my e hppening t points A, B, C, D nd E.

7 N.HW Adding nd sutrcting frctions ememer: You cn compre frctions when they hve the sme denomintor. Smmy sys tht this 5 6 rectngle with 0 squres cn e split into the following frction sum: c d Copy the 5 6 grid nd show tht this is not true. Work out the frction sum. (ememer tht, 5, 6 nd 5 ll divide into 0!) Write down wht you think the frction sum should e chnged to in order to e correct. Find frction sum for the 5 6 grid tht contins i ii frctions frctions.

8 N.HW Multiplying y frctions Work out ech of the following. The first two re done for you. = 7 = 7 = 7 = 6 7 c 6 = d 5 = e g i 8 5 = f 4 = 6 = h 7 = 5 = j 8 = Put the pproprite < (less thn) or > (greter thn) sign etween these sttements. (Use the frction wll to help you.) The first question is done for you > c d 5 4 e 4 8 f 6 5 g 8 6 h 5 7 i 5 6 j 6 k l 7 5

9 N.HW Dividing y frctions ememer: When you divide n mount y frction less thn, the result will e lrger. Copy nd complete these frction division spider digrms. The ules without numers re for your own exmples

10 N.4HW Finding percentges In these numer pyrmids, two oxes next to ech other dd up to mke the ox on top. Copy nd complete this numer pyrmid using percentge sttements. Insted of writing just the numer, write percentge sttement with the vlue of tht numer. One ox is done for you s n exmple. 0% of 70 Hint: 0% of 0= 0% of 0= = 7 7 = 0% of 70 0% of 0 0% of 0 5% of 40 0% of 0 Copy nd complete this numer pyrmid. Write percentge sttements so tht strting from the ottom, the oxes dd up to give the finl nswer 00 t the top. Note: There re mny nswers to this question. 00 Hint: Strt y writing two percentges in these oxes whose nswers dd to 00.

11 N.5HW Frctions, decimls nd percentges Wht frction of 0 hours is hours? Express your nswer in its simplest form. Wht percentge of 5 hours is 5 minutes? Jim mkes fruit sqush out of fruit juice nd lemonde. If 40% is fruit juice, wht frction is lemonde? Express your nswer in its simplest form. 4 0 of whole-ft milk is ft. Wht percentge of whole-ft milk is not ft? 5 A shop is offering 5% off in sle. Express this discount s frction in its simplest form. 6 This r chrt shows the results of survey out how students trvel to school. 40 c Wht percentge trvel y us? Wht frction wlk or come y cr? (Express your nswer in its simplest form.) Wht frction use wheels s method of trnsport? (Express your nswer in its simplest form.) Percentge of pupils Cycle Wlk Cr Bus 7 This pie chrt shows students fvourite fizzy drink flvours. 80 students liked ornge. Estimte how mny students liked: Col Ornge Col Lemon. Other Lemon

12 N.6HW Percentge chnge Copy nd complete the tle y choosing from the percentge increses nd new mounts shown in the clouds. The first one hs een done for you. Percentge increse New mount 75% 0% 0% % 5% 60% 5% Amount % increse New mount 40 0% ememer: To find the new mount, dd the increse on to the originl mount.

13 N.7HW Using rtio ememer: You cn simplify rtio y dividing ech prt y the sme numer. For exmple 4: = : 7 cn e shred etween two or three people in different rtios. Copy nd complete this spider digrm for shring 7 in ech rtio. : : 6 : : : 4 : 48 : : : 4 : 5 7 : 0 : 6 : : : 4 : 9 : 8 : 45 5 : 8 : 6 : 0 : Mke up your own spider digrm for 40.

14 N.8HW Direct proportion Copy nd complete these direct proportion tles. gllon = 8 pints Gllons Pints 8 40 litre =.76 pints Litres 7 5 Pints c kilogrm =. pounds Kilogrms 77 Pounds Use conversion of your own to complete this tle. = A 5 g jr of coffee costs.75. A 40 g jr of the sme coffee costs Work out the cost of 00 g of coffee for: Hint: Use the unitry method i the 5 g jr find the cost of g. ii the 40 g jr. Which jr represents the est vlue? Explin your nswer using your clcultions for prt.

15 N.9HW Order of opertions Comine the four digits using ny of the opertions to mke these totls. Write out your methods using rckets where you need to c 4 d 0 e 8 Work out the four clcultions in ech grid nd find which clcultion is the odd one out ( + 5) ( ) (4 + 5) (8 ) ( ) c d 5 6 ( + ) ( 4) (7 ) + (6 5 + (4 )) Mke the numer 00, using ech of the digits to 9 just once, ll in the correct order. Here is one method: = 00 ememer to insert rckets if you re using or s well s + or.

16 A.HW Using letter symols Design set of dominoes to help prctise simplifying expressions. For exmple: st domino The nswer to your lst domino goes here to mke the loop complete! It simplifies to: nd domino It simplifies to: = Wht does = = = simplify to? Wht does I H I simplify to? + + rd domino It simplifies to: 4I + H Wht does + F F F simplify to? + 4th domino It simplifies to: Wht does p 4 + m + m simplify to? etc. Continue these dominoes or mke up your own. Ply gme of dominoes with prtner.

17 A.HW Arithmetic in lger Find the vlue of ech expression in this spider digrm when x = 5. w (4x + ) c 4x d 4x 0 6 v 4x + u 4x + 4x 0 4x e f x s x + 0 x t (x + 0) x = 5 g x h 4(x ) i (x ) p 9x + 5 o 9x j x m x r 9x 5 5 q 9x 5 k x + 5 l x 0 n x + 5 Mke up your own spider digrm for someone else to complete. Mke sure you hve the nswers worked out s well!

18 A.HW Solving liner equtions Copy nd complete the crossword with the solutions to the equtions elow. Some of the clues hve een done for you. 4 d e c 5 f g h j i m n k q p s r v t u Across Down + 6 = = c = 45 e + 4 = 0 d + 45 = 00 f + 4 = 5 h + 0 = 9 (g ) = 90 i + 50 = 95 4j + = 90 k = m = 80 p = 500 (n + ) = 0 u + 4 = 70 q = 80 t + 00 = 000 r + 4 = 4 s 50 = 00 v 9 = 0

19 A.4HW Blncing liner equtions In two-wy flow digrm, you rech the sme finish numer F, whichever route you follow. x s x For exmple: Using the left pth s x s Using the right pth s x s +4 + F +4 s + 4 s + + So, F = s + 4 = s + Tke off s from oth sides s s 4 = s + Tke off from oth sides = s So, s = nd F = s + = 0. Find s nd F in these two-wy flow digrms y forming equtions. s s c s x x x8 x0 x x5 + F F + + F 6 d s e s f s x7 x5 x4 x5 x x 0 F + + F +6 F +5

20 A.5HW Solving proportionl prolems These pictures elow re ll enlrgements, or reductions, of the first picture. Some re not in the sme proportion. Work out which pictures re not in the sme proportion y drwing grph on xes like this. cm 6 cm Length (cm) O N Width (cm) 8 cm 8 cm.5 cm cm 0 cm 5 cm cm 0 cm 40 cm 6 cm 4.5 cm 5 cm 0 cm 8 cm Chllenge: Find the reltionship etween the length nd width of the photogrphs tht re in the sme proportion, nd write this s formul.

21 A.6HW Sustitution ememer: The order of opertions is: Brckets Indices Division Multipliction Addition Sutrction Secret codes! Find the vlue of ech expression when r =, s = nd t = 4. Then use the code elow to chnge your nswers to letters. t 5r 6s + r + s t(r + s) + r (r + s) r(s + t) t + r + s t t + s r t sr + c r s r(t + ) 5t + d (s + ) r + t s 4 rt + rs r+ t + t + r t + s Code A B C D E F G H I J K L M N O P Q S T U V W X Y Z Wht does the messge sy? Mke up your own secret messge y writing expressions with the letter, nd c, where = 4, = nd c = 5.

22 S.HW Geometricl lnguge Copy nd complete ech of these sentences. lines intersect t right ngles. lines re lwys equidistnt. c A prllelogrm is mde up of two pirs of lines. d A shpe hs equl sides nd equl ngles. Choose from this list: equl regulr prllel isosceles perpendiculr e A rhomus cn e mde using two tringles. Find the vlue of the unknown ngle in these digrms. 7 = > errnge the letters to give mthemticl term. LLALAPE GONOPLY c TOUNCENG d ALUGE e PONNAGET 4 Drw nd cut out two congruent right-ngled tringles: Drw digrms to show ll the shpes you cn mke y joining the tringles together. Nme ech shpe you mke.

23 S.HW Properties of tringles Drw these tringles on n isometric grid. equilterl isosceles c sclene d right-ngled Mrk the equl ngles nd equl sides on your digrms. Find the unknown ngles. c 4 57 > = 6 08? d e f 60 D A i C j i i g h i n k k l 0 l m n 00 j k G H F H I I 50

24 S.HW Lines nd ngles Copy this digrm which shows three sets of three prllel lines. Using three different colours, colour ngles tht re equl in size. Which ngle is verticlly opposite? Which ngle is lternte to? c e c Which ngle is lternte to c? d Which ngle is corresponding to e? e Which ngle is corresponding to f? f d Find the unknown ngles. Give reson in ech cse. c c 4 d d f g e 0 f e h 55 r s t

25 S.4HW Clssifying qudrilterls Drw these qudrilterls on isometric pper. One is impossile which one? squre rectngle c rhomus d prllelogrm e kite f trpezium g isosceles trpezium h rrowhed i n irregulr qudrilterl On ech digrm mrk: equl ngles equl sides prllel lines perpendiculr lines ( ). Drw the shpes h from queston on plin pper. c d e Drw in the two digonls for ech shpe Which shpes hve perpendiculr digonls? Which shpes hve digonls tht isect ech other? Which shpes hve perpendiculr digonls tht isect ech other? Copy nd complete this tle, writing qudrilterls from question in the correct plce. All 4 ngles re equl Not ll 4 ngles re equl All 4 sides re equl Not ll 4 sides re equl 4 On y grids on squre dotty pper, drw 6 different qudrilterls. None of the qudrilterls should e congruent. For exmple, squre: Nme the type of qudrilterl in ech cse.

26 S.5HW Properties of qudrilterls ememer: The sum of ngles in qudrilterl is 60. Find the unknown ngles. Give reson in ech cse. 9 c 5 05? 5 = > e 0 f B B 70 B B A 0 0 Find the unknown ngles in these tesselltions. > = 4 > 0 c d 45 B B C A A 0 0

27 S.6HW Constructing perpendiculrs You wnt to swim cross the pool from A to the side BC. Copy the digrm nd drw your pth from A so tht you swim the shortest distnce possile. A B C Drw line BC so tht BC = 0 cm. Mrk point A out 5 cm from the line BC. A 5 cm Construct the shortest line from A to the line BC. B C Drw line AB so tht AB = 0 cm. Mrk point P so tht AP = 4 cm. Construct the perpendiculr from the point P. A 4 cm P B 4 Construct this kite using compsses. Clculte the re of the kite. Hint: Drw DB first nd then construct AC. cm D cm A 6 cm B cm Hint: Are of tringle = D> se (>) height (D) C 5 Using compsses, construct the tringle ABC. Write the type of tringle. c Clculte or mesure the ngles t A nd C. A 6 cm C 6 cm B

28 S.7HW Constructing tringles Accurtely construct these tringles. Give the type of tringle for ech one. ASA ASA cm 6 cm 45 c SAS 6 cm d SAS 8 cm 60 6 cm 40 6 cm e SSS f SSS 5 cm cm cm 4 cm 4 cm 5 cm Accurtely construct this net of squred-sed pyrmid. 8 cm 8 cm 8 cm 5 cm 8 cm 5 cm 5 cm 8 cm 5 cm 8 cm 8 cm 8 cm Accurtely construct these qudrilterls. cm cm 5 cm 5 cm 60 0 cm 60 5 cm 6 cm 5 cm

29 S.8HW Loci Drw the locus of ech sitution. If possile, descrie the pth using mthemticl terms. clock pendulum roller coster c ll going into sket in sketll d child on see-sw e child on slide Hint: Using mthemticl terms, pth is n rc of circle. Drw line AB, so tht AB = 5 cm. Construct the perpendiculr isector of AB. A 5 cm B Lel the point t the intersection of AB nd the isector s M. Mesure AM. Drw line AB, so tht AB = 7 cm. Construct the locus of the points tht re equidistnt from A nd B. 4 Drw point O. Drw the locus of the point X, which moves so tht the distnce OX is lwys 4 cm. 5 Construct, using compsses on plin pper, these coordinte xes: O N 4

30 S.9HW More loci Use protrctor to drw n ngle of 70º. Construct the ngle isector. Mesure nd lel the two new ngles. Drw verticl nd horizontl lines tht intersect t right ngles. c Construct the ngle isector for ech ngle. Lel your digrm N, NE, E, SE, S, SW, W, NW in clockwise direction. Use protrctor to drw n ngle of 0º. Construct the ngle isector. Mesure nd lel the two new ngles. 0 ememer: In LOGO you specify distnce in mm nd ngles in degrees. FOWAD 60 mens forwrd 60 mm or 6 cm. LEFT 90 mens turn left through 90º. 4 Write LOGO commnds to drw these shpes. c 5 Drw line AB, with AB = 8 cm. Drw the locus of the points tht re lwys cm wy from the line.

31 D.HW The hndling dt cycle Wht is primry dt? Give n exmple of primry dt. Wht is secondry dt? Give n exmple of secondry dt. Here re some ides for hndling dt projects. Suggest set of dt tht could e included in ech project, nd stte whether it is primry or secondry dt. Explin how mny dt vlues you would expect there to e in ech set. c d Jn wnted to investigte wht temperture people let their te cool down to efore they strted drinking it. Solomon wnted to know whether the rce times in his school s sports dys hd improved over the yers. Fund decided to see whether people could predict whether coin would lnd on heds or tils. Siân wnted to know wht were the most populr holidy destintions for people in the UK, nd how mny people in her school hd visited them. e Peter decided to find out wht percentge of Yer 9 students hd television in their edroom.

32 D.HW Clculting sttistics Crl looked t this set of dt. Computer network performnce numer of errors in 0-dy period esults for 5 different computer networks Crl sid: The esiest verge to work out is the mode, which is 0 errors. Explin why the mode would not e good verge to use in this cse. Zoë compred the prices of five second-hnd crs dvertised in her locl newspper c Explin why you could not find the mode of these prices. Explin why the men would not give very representtive impression of the prices of the crs. Work out the medin nd the rnge of the prices. onnie mesured the heights of 0 people in her clss. Heights of 0 people in centimetres Copy nd complete the frequency tle for this set of heights. Use your completed tle to work out the modl clss for the heights. Height, D cm 40 h < h < h < h < h < 90 Frequency

33 D.HW Constructing pie chrts ememer: There re 60º in circle. To find the ngles in pie chrt: Work out the totl numer of items. Work out the ngle for one item. Multiply the ngle for one item y the numer of items in ech ctegory in turn. The tle shows the numers of drinks dispensed y vending mchine one lunchtime. Drink Te Coffee Hot chocolte Soup Numer Drw pie chrt to show this dt. A school secretry checked the numer of pcks of pper in the office stock cupord. The tle shows the numer of pcks of ech colour. Colour White Ple lue Drk lue Yellow Numer Drw pie chrt for this dt.

34 D.4HW Selecting nd drwing chrts Dvid is doing project on recycling. He records the numer of ottles put into ottle nk in hlf-hour period. Bottle colour Green Brown Cler Blue Numer 5 9 Show this informtion s r chrt. This tle shows the heights of trees in smll wood. Height (m) 0 D < 5 5 D < 0 0 D < 5 5 D < 0 0 D < 5 Frequency Drw frequency digrm to represent this dt. ememer: A frequency digrm is like r chrt, ut it hs no gps etween the rs.

35 D.5HW Interpreting grphs nd sttistics This popultion pyrmid shows the ge distriution of the popultion of Grethmpton. Age Mle Femle How mny mles re ged 40 or less ged etween nd 60? How mny femles re ged 0 or less ged etween 5 nd 80? In Grethmpton everyone over 60 is retired. How mny people in Grethmpton re retired? How mny more femles thn mles re retired? 4 Wht is the mximum possile numer of teengers in Grethmpton? 5 Everyone ged 60 hs jo. How mny people hve jo? 6 How mny more people hve jo thn re retired?

36 D.6HW Compring distriutions The tles show the verge monthly rinfll, nd the verge mximum tempertures, for two different plces: Chittgong (in Bngldesh) nd Deth Vlley (in the USA). Chittgong Deth Vlley Averge mximum temp. ( C) Averge rinfll (mm) Jn Fe Mr Apr My Jun Jul Aug Sep Oct Nov Dec Averge mximum temp. ( C) Averge rinfll (mm) Copy these xes on to grph pper. Drw line grphs to show the verge monthly tempertures in oth plces. You could drw oth grphs on the sme xes. For ech plce work out: the men temperture the rnge of the temperture. Write your nswers in tle like this: Temp C Jn Fe Mr Apr My Jun Jul Chittgong Deth Vlley Aug Sep Oct Months Nov Dec Temperture Men nge For ech plce work out: the totl rinfll the men rinfll c the rnge of the rinfll. Write your nswers in tle similr to the one in question. 4 Write prgrph compring the tempertures for the two plces. Write prgrph compring the rinfll for the two plces.

37 S.HW Coordintes Copy these xes on to squred pper. Plot nd join up the points. Write down the letter formed in ech cse. (, ) (, ) (0, ) (, ) (, ) (0, 0) (, ) (, ) c (, ) (0, ) (, ) (, 0) (, 0) y 0 x Copy these xes nd plot the points shown. Write down, if possile, the coordintes of the extr point tht will mke: prllelogrm n isosceles trpezium c kite d rhomus y 0 x Copy these xes. Plot the pirs of points nd find the midpoints of the lines joining them. (6, 0) nd (6, 4) (, 6) nd (6, 6) c (0, ) nd (4, 5) d (, 4) nd (5, 0) e (, ) nd (, ) y x ememer: To find the midpoint of line, you find the men of the coordintes of the endpoints. The x-coordinte of the midpoint is the men of the x-coordintes. The y-coordinte of the midpoint is the men of the y-coordintes. 4 Check your nswers to question y finding the midpoints y clcultion.

38 S.HW Are of tringle ememer: Are of rectngle = length width Are of tringle = se height The height must e perpendiculr to the se. Clculte the re of ech of these tringles. c d e f 4 cm m 0 mm 7 cm m mm Drw tringle with n re of cm. Clculte the re of ech of these shpes. 4 cm 4 cm 5 cm 5 cm 5 cm 5 cm 8 cm 5 cm 0 cm 4 The re of this isosceles right-ngled tringle is 8 cm. Clculte the se nd perpendiculr height.

39 S.HW Are of prllelogrm nd trpezium ememer: Are of tringle = se height The height must e perpendiculr to the se. Are of prllelogrm = se height Are of trpezium = ( + ) + h h Clculte the re of ech of these prllelogrms. c d 4 mm 9 mm 0 cm 5 cm Clculte the re of prllelogrm A. Clculte the re of tringle B. c Clculte the re of tringle C. d Add your nswers for the res of A, B nd C. e Check your nswer to d y clculting the re of the lrge tringle. A B C Clculte the re of ech of these trpeziums. cm cm cm 6 cm 5 cm 7 cm 4 Clculte the re of the trpezium using the trpezium formul. Clculte the re of tringle A. c Clculte the re of prllelogrm B. d Add your nswers for the res of A nd B. Check your nswer it should e the sme s your nswer to prt. A B

40 S.4HW Mesuring volume ememer: Volume of cuoid = length width height height width length Give n oject tht would hve its volume mesured in: cm m All these shpes re mde from centimetre cues. Find the volume of ech shpe. c d e All these shpes re mde from centimetre cues. Write down the length, width, height nd volume for ech cuoid. c 4 Clculte the volume of ech of these cuoids. cm cm c m cm m m 5 cm 4 cm cm 5 Find the length of the side of ech of these cues. c Volume = 7 cm Volume = 000 cm Volume = 75 cm

41 S.5HW Surfce re ememer: Volume of cuoid = length width height The surfce re of cuoid is the re of its net. Copy these nets on to squred pper nd cut them out. Fold ech net into -D shpe. For ech shpe find: i the totl surfce re ii the dimensions iii the volume. Clculte the totl surfce re nd volume of ech cuoid. 0 cm 0 cm cm cm 5 cm cm There re two different cuoids with volume of 0 cm. Find the dimensions of ech cuoid. Clculte the totl surfce re of ech cuoid. 4 Clculte the totl surfce re of this cue. Find the dimensions of the cue. c Clculte the volume of the cue. Are of top is 9 cm Are of end is 9 cm Are of side is 9 cm

42 S.6HW Units of mesurement ememer: pint 600 ml foot 0 cm gllon 4 litres kg. l yrd metre yrd = feet 5 miles 8 kilometres Suggest n pproprite metric nd imperil unit to mesure: the height of house the cpcity of swimming pool c the mss of cr d the distnce run in mrthon e the length of swimming pool f your own mss. Put ech pir of quntities in order of size, smllest first. hour, minute grm, l c metre, yrd d litre, gllon e metre, foot In 00 the men s record for running the 500 m ws minutes 6 seconds. Chnge 500 metres into kilometres. Chnge the record time into seconds. 4 A ox contins 750 g of cerel. Chnge this mss into kg. 5 A mug holds 50 ml of wter. How mny mugs re needed to mke one litre? 6 Pottoes used to e sold in ls. If one l cost 60p, wht would e the pproximte cost of kg? 7 It is 40 km from Mnchester to Liverpool. Wht is this distnce in miles? 8 If pint of lemonde costs, wht would you expect to py for litre of the sme lemonde?

43 N.HW Powers nd roots Work out the nswers to: 5 6 c d e 6 f 7 g 4 h 5 j 64 k 000 i 64 l 9 Hints: 5 = 5 5 = 6 6 = = = 5 5 = Use your nswers to question to help you work out: c 00 d 0 e 600 f 70 g 400 h i 6400 j k l 900 A well-known squre numer fct is tht + 4 = 5. Copy nd complete these squre numer fcts. 6 + = 0 + = 4 In question the numer fct ws + = c. However, there re mny squre numers, tht dd up to cue numer, for exmple + = c. Copy nd complete these = + = c + 0 = 0 d + = 5

44 N.HW Powers of 0 Copy this numer ldder with 5 spces. Now work out the nswers to ech of these questions nd write the nswers in the correct order on copy of the numer ldder. lrgest smllest Now mke up your own ten questions to fill 0-spce numer ldder. Write your questions nd their nswers in copy of the numer ldder in the correct order. lrgest smllest

45 N.HW ounding A recurring deciml goes on forever. You put dot over the strt of the numers tht repet. Using clcultor, = = This cn e written s s 09 recurs. Copy nd complete this tle. Frction Clcultor disply ecurring nottion ounded to dp dp Copy this tle. Use clcultor to find five recurring decimls of your own. ecord the informtion in the tle. Frction Clcultor disply ecurring nottion ounded to dp dp

46 N.4HW Addition nd sutrction Numer of visitors to sttely home ech month Month Jn Fe Mr Apr My Jun Jul Aug Sep Oct Nov Dec Adult visitors Child visitors How mny people visited in April nd Octoer, in totl? Hint: People includes dults nd children. Clculte the totl numer of dult visitors for the summer months: June, July nd August. Clculte the totl numer of child visitors for the winter months: Decemer, Jnury nd Ferury. 4 How mny more dult visitors were there in Septemer thn in Octoer? 5 How mny more child visitors were there in July thn in Decemer? 6 Which month hd most visitors? How mny visitors ws this? Hint: Include dults nd children 7 Which month hd lest visitors? How mny visitors ws this?

47 N.5HW Mentl multipliction nd division It is esy to doule: = 6 Multiplying y 4 is esy too: 4 = 6 4 = 6 = = 4 Copy nd complete these prime fctor tree digrms = 6 = Use your digrms from question to help you work out: 8 6 c 5 8 d e 0.8 f 6 g.6 4 h Now dpt your method to help you work out: c 7. 8 d 4.6.6

48 N.6HW Written multipliction ememer: For the clcultion 9 79 Lst digit check It ends in 9 so the nswer will end in 7. Estimtion It is roughly = 400 Hint: 9 = 7 Look t these numers Three of them multiply together like this: = 4 55 Identify the three correct numers using written clcultions. Use the methods of lst digit check nd estimtion to help you. In her homework Shni clcultes:. X 67 = Do written clcultion to check whether Shni s nswer is correct. Write down four other clcultions tht equl Here is one:. 670.

49 N.7HW Written division Exmple To work out 04 Estimte: 00 0 = 60 Work out roughly wht the nswer is: 50 = = The nswer is etween 50 nd = 00, so sutrct this from 04 to find wht s left: = 04 Write out the times tle: = = 44 = 66 4 = 88 5 = 0 04 = = = 54 reminder 6 Here re 0 division questions. i 04 ii 84 5 iii iv 86 v vi 96 vii viii 99 ix 89 4 x 089 Without doing the clcultions, identify those tht will leve reminder. Explin how you know. Hint: Do not do the division. Choose five of the questions nd work them out using written method. ememer to do n estimte first. Which of the 0 numers eing divided is squre numer?

50 N.8HW Clcultor methods Some of the numers in the cloud re the nswers to the questions elow. A numer my e used more thn once! You cn use clcultor to help you. Which numer dded to 7.7 mkes 49.8? Which two numers hve product of 8.095? Wht is 00.4 divided y to mke 7.? 4 The difference etween which two numers is 4.0? 5 Which numer is the squre root of ? 6 Which numer is missing from this clcultion? =.7 7 Wht re the two numers missing in this clcultion? + = Which two numers hve squre roots tht sum to 7.5?

51 A4.HW Finding fctors, multiples nd primes Lern these divisiility tests. Divisile y ule the lst digit ends in 0,, 4, 6, 8 the sum of the digits is divisile y 4 the lst two digits re divisile y 4 5 the lst digit is 0 or 5 6 it is divisile y nd 8 hlf of it is divisile y 4 9 the sum of the digits is divisile y 9 Use the divisiility tests to work out nd explin which of these two-digit numers re prime c 5 d 9 e 6 f 7 To work out if numer is divisile y two-digit numer, you cn pply two of the divisiility tests ove. For exmple: Divisile y ule the numer is divisile y nd 4, the sum of the digits is divisile y nd the lst two digits re divisile y 4 Hint: nd 4 re fctors of. Write rule to test if numer is divisile y: 8 0 c 48 Which of these numers re multiples of, 5, 8, 0 or 48? 80 0 c 6 d Find the highest common fctor (HCF) of: 9 nd 4 nd 6 c 8 nd 0 d 48 nd 7 Hint: List the fctors of ech numer. 5 Find the lowest common multiple (LCM) of: 4 nd 6 8 nd 7 c nd 5 d 6 nd 6 Hint: List the multiples of ech numer.

52 A4.HW Using prime fctors By writing ech numer s product of its prime fctors, find the HCF nd LCM of the following pirs of numers. The first one is done for you. nd = = 8 = = Write the fctors in Venn digrm: 8 HCF = = 6 LCM = = 6 6 nd 54 c 6 nd 64 d 65 nd 6 e 75 nd 64 f 80 nd 4 Chllenge Explin why the method works for finding HCF nd LCM.

53 A4.HW Using index nottion ememer: 7 = 49 nd 49 = 7 7 = 4 nd 4 = 7 Work out the vlue of ech power or root contined in the ox. Write your nswers, with their letters, in order strting with the smllest. Wht do the letters spell? A 00 C E 8 5 A 64 D 5 Q 4 B 7 S 5 E S U 9 S 8 N 4 U 6

54 A4.4HW Solving prolems involving indices Copy nd complete this tle of powers of : Power of Vlue You cn mke 5 y dding powers of : 0 + = + 4 = 5 You cn mke 4 y dding powers of : = = 4 Write ddition sums using powers of for these numers: 7 c 00 d 50 e 46 f 6 g 7 h 8 Hint: Use your tle from question to help you. Write five clcultions of your own, using powers of. Wht is the lrgest numer you cn mke?

55 A4.5HW Plotting liner grphs Copy nd complete the tle of vlues for the function y = x +. c d e x y 0 Write down the coordinte pirs. Copy the grid nd plot the coordinte pirs. Join the coordinte pirs nd extend to the edges of the grid. The following coordintes lie on the stright line y = x +. Use the grph to complete the coordintes. Use the rule y = x + to check tht the coordintes in prt d fit the function. y x (x, 6) ( 4, y) (x, 0) Drw the grphs of y = x + nd y = x for x vlues to on suitle size grid. Hint: Look for the smllest nd lrgest y vlues. Write down the coordintes of the point where the two lines cross. Check tht these coordintes fit oth functions.

56 A4.6HW Stright-line grphs ememer: The eqution of digonl stright line is y = mx + c. m is the grdient, c is the y-intercept. Copy the xes on to squred pper. Sketch or plot the following stright-line grphs on your xes. y = x + y = 4 y = x + 0 y = x 8 y = y = x Shde in the shpe tht the lines enclose in the centre of your grph. Wht kind of shpe is it? Mtch ech function to its grph. y = x y = x c y = x + y x Grph Grph Grph

57 A4.7HW ecognising stright-line grphs Dominoes Mke set of 6 dominoes so tht when they re plyed they mke complete loop. The loop hs een strted for you. You decide which grph goes here! O = N O 5 4 N 4 5 O = N + O 5 4 N 4 5 O = N O 5 4 N 4 5 You decide which eqution goes here! Ply gme of dominoes with prtner.

58 A4.8HW Using grphs Give n explntion for the shpe of the following grphs from A to F. Ech explntion hs een strted for you. Temperture of th wter Weight of g of sweets Temperture A B C D E F Weight A B C D E F Time Time A: Hot wter tp is running ut is not hot yet. A: No sweets re tken from the g. B: Hot wter tp is running nd it s hot. B: A few sweets re tken out. C: C: The continer elow is eing stedily filled with wter. Which of the grphs shows the reltionship etween time nd height of wter in the continer? c Height of wter Height of wter Height of wter Time Explin your choice. Time Time

59 A4.9HW Interpreting distnce time grphs This is distnce time grph for Eline nd her friend s trip to the shops. c d e How long did it tke them to get to the shops? How long were they t the shops? Ws the journey ck from the shops fster or slower thn the journey there? How long were they trvelling for? How long were they wy from home in totl? shops home :00 :0 :00 :0 :00 :0 :00 This grph shows Miss Millwrd s journey to work. work home 7:00 7:5 7:0 7:45 8:00 8:5 Descrie her journey in words. Drw distnce time grph, on copy of the grid opposite, for Birminghm the following trin journey: A: Trin leves London t 6 pm Coventry B: Trin stops t Milton Keynes t 6.0 pm C: Trin leves Milton Keynes t 6.45 pm D: Trin stops t Coventry t 7.5 pm Milton Keynes London 6:00 E: Trin leves Coventry t 7.45 pm F: Trin rrives in Birminghm t 8.5 pm 7:00 8:00 9:00 c Which prt of the journey ws the fstest nd which the slowest? For how long ws the trin sttionry?

60 D.HW evising proility Drw nd lel proility scle. Use these lels. Certin 0.5 Impossile 0 Evens chnce Amit nd Denise ech uy n Indin snck pck with the contents shown. Indin snck pck smoss 4 hjis 4 pkors Amit picks snck t rndom from his pck. Find the proility tht he picks: c hji smos hji or pkor. Denise ets three of the pkors from her pck. She then picks nother snck t rndom. d Find the proility tht she picks smos. Wht is the proility of rolling six on n ordinry dice? c Stephen rolls dice 48 times nd gets sixes. Wht is the proility of rolling six on Stephen s dice? Do you think Stephen s dice is fir? Explin your nswer.

61 D.HW The proility of n event not occurring ememer: If you know tht the proility of n event occurring is p, then the proility of the event not occurring is p. The proility of Sushm completing her homework in 5 minutes is Work out the proility tht she does not complete her homework in 5 minutes. The tle shows the proility, p, of some events. Copy the tle nd complete it to show the proility tht ech event does not occur, p. p p 0.6 5% % 9 Here re 0 crds: The crds re shuffled nd spred fce down. One crd is picked t rndom. Give your nswers to the following questions s percentges. Wht is the proility tht the crd picked is tringle? Wht is the proility tht the crd picked is hert? c Wht is the proility tht the crd picked is not tringle? d Wht is the proility tht the crd picked is not squre?

62 D.HW Smple spce digrms A crd is picked from pck of plying crds nd coin is tossed. The possile outcomes for the coin re: The possile outcomes for the crds re: Heds Tils Spdes Clus Herts Dimonds Copy nd complete this smple spce digrm to show the possile outcomes. Crd suit Spdes Herts (He) Clus Dimonds Heds Tils (H, S) (H, He) Use your smple spce digrm to work out the proility tht: c d the coin will show Tils the crd will show Clus the coin will show Heds nd the crd will show Dimond. These two fir spinners re spun together. The scores on the spinners re dded together. Drw smple spce digrm to show the possile outcomes Use your digrm to find the proility tht the totl will e n odd numer. Hint: The squre spinner hs four outcomes Citlin nd Sion ech hve three numer crds. They ech pick one of their crds t rndom, nd they dd the numers on the two crds. 4 5 Drw smple spce digrm to show the possile totls. Use your smple spce digrm to work out the proility tht the totl is: exctly c less thn 5 d n even numer e more thn 8.

63 D.4HW Experimentl proility The cricket tems in legue collect the results for their first 50 mtches in seson. Home win 5 Awy win 5 Use these results to estimte the proility in future cricket mtches of: home win n wy win. For the next 50 mtches the results were Home win 9 Awy win Comine oth sets of results to estimte the proility in future cricket mtches of: c d home win n wy win. Clire sys: `When I drop piece of tost, the proility of it lnding utter side down is 75%. Descrie n experiment you could do to test whether Clire s estimte of the proility is correct.

64 S.HW Berings This mp shows mountins in the Lke District. Scfell Pike is the highest mountin in Englnd. N Pillr Steeple 84 Hycock Kirk Fell 80 Sethwite Glrmr 78 Setlln 69 Whin igg Wst Wter Whilln Beck Gret End Scfell Sc Pike Fell Allen Crgs 785 Esk Huse 759 Bow Fell 90 Crinkle Crgs Esk Scle cm = km km Write down the nmes of the mountins tht re on these erings from Scfell Pike. 04º º c 8º d 77º e 08º Write down the erings of these mountins from Scfell Pike. Gret End Bow Fell c Whin igg d Hycock e Pillr Estimte the distnce, in km, from Scfell Pike to: Sc Fell Bow Fell c Glrmr d Kirk Fell e Sethwite 4 It is impossile to see Whin igg from Scfell Pike, even on fine dy. Why?

65 S.HW Descriing trnsformtions Write down the trnsltion tht moves the shded fce to: c d e A B C D E O D E B A C N eflect ech shpe in the mirror line. Nme the new shpe formed. Mrk the equl ngles nd equl sides on the new shpe. c d e Copy these shpes on to squred pper. otte ech shpe out the dot (.) through 80º. Nme the new shpe formed y dding the shpe nd rottion together. Mrk the equl ngles nd equl sides on the new shpe. c d e

66 S.HW Comining trnsformtions Copy the digrm on to squred pper. Trnslte the lck shpe y right. Lel the new shpe A. up Trnslte the shpe A y right. down Lel the new shpe B. c Wht single trnsformtion moves the lck shpe directly to the shpe B? Copy this rrowhed on to squred pper nd cut it out. c Use repeted 80º rottions out the midpoints of the sides to tessellte the rrowhed. epet this process for prllelogrm. Copy this digrm on to squred pper. c otte the lck shpe through 90º clockwise out the dot. Lel the new shpe A. otte the shpe A through 90º clockwise out the dot. Lel the new shpe B. Wht single trnsformtion moves the lck shpe directly to the shpe B?

67 S.4HW Symmetries of polygons Copy ech shpe. Drw in ny lines of symmetry. i ii iii iv v vi vii Stte the order of rottionl symmetry for ech shpe. c d e How mny lines of symmetry hs regulr decgon? Wht is the order of rottionl symmetry for regulr decgon? 4 An equilterl tringle hs rottionl symmetry of order. Wht geometricl properties does this men the tringle hs?

68 S.5HW Enlrgements Find the scle fctor of these enlrgements. c Copy these shpes on to squred pper. Drw the enlrged shpe. c d scle fctor scle fctor scle fctor scle fctor The shded shpes re enlrged to give shpes A, B nd C. C B 4 cm B C A cm cm A cm Copy nd complete these tles. Shpe Scle fctor Perimeter Shpe Scle fctor Perimeter Shded squre 4 cm Shded pentgon 5 cm Squre A Pentgon A Squre B Pentgon B Squre C Pentgon C

69 S.6HW Scle drwings Express these rtios in their simplest form: 4 kg: kg 9 cm: cm c 0 ml:45 ml d 8 m: m e 6 mm:4 mm f 4 cm: m g 500 g: kg h 40 sec: min i 0 cl: l j 5 kg:500 g Hint: Mke sure tht the numers re in the sme units. Mesure the length of these lines. Use the scle to clculte the ctul distnce tht ech line represents. cm represents m cm represents km c cm represents.5 km d cm represents 0 m e cm represents 0 m Convert the scles in question into rtios. 4 A model ot is uilt using scle of :0. Copy nd complete this tle. Mesurement Width Length Numer of portholes Model ot el ot 50 cm 900 cm 5 Mke scle drwing of your edroom, including the furniture. Choose suitle scle.

70 P.HW Mking sense of the prolem Jnine is tiling her throom using mosic tiles. She hs different sized tiles. 5 cm cm cm cm cm 5 cm On the wll she hs mrked out n re 0 cm y 0 cm. How mny of the 5 cm y 5 cm tiles will cover the re? How mny of the cm y cm tiles will cover the re? Jnine puts three tiles on the wll like this: c d Cn Jnine completely fill the 0 cm y 0 cm re without cutting ny tiles? Explin how you got your nswer. Jnine sees some cm y cm tiles in ctlogue. Wht is the minimum numer of cm y cm tiles she needs to order to fill her 0 cm y 0 cm re strting with the pttern of lrger tiles shown ove?

71 P.HW eding tles nd digrms This tle shows cinem s prices. Tuesdy All dys except Tuesdy Adult Child (6 or under) Senior citizen (60 or over) Mrs Johnson (ged ), her mother (ged 6) nd her two children (ged 7 nd 5) go to the cinem on Tuesdy. How much does it cost them? Sophie (7), Tom (5) nd Cherry (6) go to the cinem on Wednesdy. How much does it cost them? Smir did survey in his school. He sked students Do you like school dinners? This tle shows his results. Yes No Don t know Yer 7 8 Yer Yer How mny students from Yer 8 took prt in the survey? In totl, how mny more students sid No thn sid Yes?

72 P.HW Using strtegy Srh hs in her nk ccount. Trcy hs 7.5 less thn Srh. How much does Srh hve in her ccount? Jodie wnts to uy Hi-Fi system. 400 It costs 400. There re two wys she cn py. FF EV. PLAY STOP < > Py now nd get 5% off! Py 8.50 per week for 5 weeks How much will she sve if she pys now, with 5% off? Butcher s lock worktops cost per squre metre. How much would it cost to cover this workspce? m 6.4 m Hricot ens cost.40 per kg. How much would.6 kg of hricot ens cost? c The rtio of the height of Pul to the height of Shoi is 6: 5. If Shoi is.6 m, how tll is Pul? d Brown crpets cost.70 per squre metre. How much would it cost to crpet n re of 9.8 m with rown crpet?

73 P.4HW Proportionl resoning The lel on tin of spghetti hoops shows this informtion. Averge vlues per 00 g Energy 6 Cls Protein.7 g Crohydrte g Ft 0. g Hint for questions nd : First find the vlues for one grm. Work out how much energy, protein, crohydrte nd ft is provided y 40 g tin of spghetti hoops. Give your nswers to one deciml plce whenever necessry. The lel on jr of myonnise shows this informtion. 00 g typiclly provides Energy 7 Cls Protein. g Crohydrte. g Ft 6 g A recipe for potto sld requires 65 g of myonnise. Work out how much energy, protein, crohydrte nd ft is provide y 65 g of myonnise. Give your nswer to one deciml plce wherever necessry. Jim is on specil diet tht mens he should not hve more thn 4 g of slt in one mel. He wnts to hve pizz, ice crem nd soft drink for dinner. Slt.5 g Slt g Slt. g Cn he hve 00 g pizz, 00 g ice crem nd 50 ml lemonde? Suggest different portion sizes tht Jim could hve to fit his diet.

74 P.5HW Geometricl resoning The digrm shows shpe ABC. A C B To wht fmily of polygons does this shpe elong? Wht is the specil nme for this shpe? Which sides hve the sme length? 4 Wht do you know out ngles A, B nd C? 5 Side BA is opposite vertex C. Which side is opposite vertex A? 6 Wht is the size of ngle B? 7 Wht nme is given to ngles B nd C? 8 How mny lines of reflection does the shpe hve? 9 Wht is the order of rottionl symmetry of the shpe? 0 How mny digonls does the shpe hve? How mny vertices does the shpe hve? Suppose you cut off ngle A with horizontl cut. Wht is the nme of the new polygon? If you fold the corner of ngle A down onto the point hlfwy long the side BC, wht is the nme of the new shpe you hve? 4 Which vertices would you hve to cut off with stright cut in order for the new polygon to e hexgon? 5 Imgine shpe the sme s ABC ut igger. Are the shpes similr or congruent?

75 P.6HW Checking results For ll the following questions, rememer to check your results. Find the sum of 55 nd 7. Find the difference etween 9 nd 4. c Clculte the product of 7 nd 9. Find x when 5x = m + 6 = 8 Find m. 4 Four people mesured the length of plying field. Which mesurement is most pproprite? m 9546 cm 0. m 5 m Explin why you chose your nswer. 5 Copy nd complete this mgic squre. Every row, column nd digonl should dd to the sme totl. 7 5 Cn you fill it in with different numers, to mke nother mgic squre?

76 A5.HW Equtions, formule nd functions ememer: You solve n eqution y keeping it lnced. x + = 7 x = 7 x = 5 x = 5 x = 5 Solve these equtions: m = 7 4p 0 = c 7t + = 4 Write n eqution for this prolem: Four pcks of chewing gum nd 40p r of chocolte cost 0p in totl. Hint: Use x for the cost of one pck of chewing gum. Solve your eqution to find the cost of pck of chewing gum. Work out the vlues of the unknown in these digrms: x x x 5 y 4y + x + 4 Sustitute the vlue x = into the expression x + 5. Sustitute the vlue z = 4 into the expression z + 5.

77 A5.HW Using rckets ememer: To expnd rckets, you multiply ech term inside the rckets y the term outside. ( + c) = + c ( c) = c Expnd the following rckets. (n + 4) 5(x ) c 4(p + 6) d (e + ) e 0( + ) Expnd the rckets nd simplify the expressions. 0 + (x + ) (p + ) + 4(q + 4) c e + (e 4) + d 4(x ) x + 5 e 4(x + y) (x + y) Find ll the different expressions for the re of the shded region in ech of these shpes nd show tht they re ll equivlent: c 0 d 0 0 e c 5 d 5 f 4 8 0

78 A5.HW Solving equtions Cross numer puzzle Copy the grid. Solve the puzzle using the solutions to the equtions elow. Some of the clues hve een completed for you. c d e f 4 g h j i m n k q p s r v t u Across Down = ( + ) = (c 4) = 0 (e + 6) = 40 d = 4 5(f ) = 4(f + ) h = 48 g = 8 i = 7(j 5) = 6 (k + ) = k 4 m = 44 p = 4480 (n + ) = 90 t = 4(q + ) = 60 4(u ) = (u + 0) r = s = 0.5 4(v + ) = 6v 44

79 A5.4HW Equtions involving frctions Exmples Solve: x 5 = 6 x = 4 x 5 = 6 = 4 x x = 5 6 = 4x x = 0 4 = x x = Solve ech eqution elow nd use this code to chnge your nswers to letters. A B C D E F G H I J K L M N O P Q S T U V W X Y Z c x = 6.5 x x = d x + e x = 0 f g i k = 5 = x + 5 = 0 x = h (x + ) = x = j x 4 = 8 5 x = 5 l (x + ) = 0 m x = 0 n o 6(x ) = p q x + = 5 4 x + = 5 x = Mke up your own questions to complete the sentence.

80 A5.5HW Using formule A compny is designing new pckging for their new rnd of sweets. They need to work out which of the following cuoids gives the mximum volume. Using the formul for the volume: V = lwh where l = length, w = width, h = height find the volume of ech cuoid elow: i ii iii 0 cm cm cm cm cm cm 6 cm iv 7 cm cm cm 6 cm 4 cm Which ox would you dvise the compny to use? Work out the re of crdord needed to mke ech of the oxes. Hint: Find the re of the net of ech cuoid. Hve you chnged your mind out which ox you would dvise the compny to use? Explin your nswer. 4 Write formul for working out the surfce re of cuoid.

81 A5.6HW Solving equtions using grphs There re two specil offers on the sme phone tht Emily likes ut in two different shops. N OVA P H ON E S 0 to uy the phone plus 0 per month for unlimited clls P-Moile 5 to uy the phone plus per month for unlimited clls Copy nd complete ech formul. (C = cost, m = numer of months) Nov Phones: C = + m P-Moile: C = + m Copy nd complete the tles of vlues: Nov Phones: m C P-Moile: m 0 C Drw grph for ech shop with oth lines plotted on the sme grph. 4 When do oth moile phone offers cost the sme mount? 5 If you wnted to keep the moile phone for only 6 months, would you uy it from Nov Phones or P-Moile? Why? Cost y If you wnted to keep the moile phone for t lest yer, where would you uy it from? Why? Months x

82 D.HW Collecting nd orgnising dt Becky s clss re strting work on hndling dt project. The theme is Trnsport. They hve to choose their own questions to investigte. Becky s techer gve them this dvice efore strting: ememer these things: Pick question tht is interesting nd importnt. Try to turn your question into specific hypothesis, which you cn test. Pln the dt collection. Decide which dt you will need. Is it primry or secondry dt? How will you collect nd orgnise your dt? How will you use the dt? Do one of the tsks descried elow. Tsk If you hve strted work on your own hndling dt project, write up pln for your own project. (You my lredy hve strted on this in clss.) You cn use the notes ove to help. Tsk If you hve not strted work on your own project, use the notes ove to help you write pln for project on the theme of Trnsport.

83 D.HW Clculting sttistics The frequency tle elow shows the results of survey out the numer of DVDs group of 0 people rented from video store in month. DVDs Frequency Work out the men, medin, mode nd rnge of the numer of DVDs rented. Hint: Men = totl numer of DVDs totl numer of people To work out the medin (middle numer), first write the numer of DVDs in order of size: 0, 0, 0, 0, 0, 0, 0,,,,,,,, The heights of 0 students in clss re shown in the frequency tle. Height, D cm 50 D < D < D < D < D < 75 Frequency c Which ctegory would height of exctly 60 cm e recorded in? Write down the modl clss for the distriution. Copy nd complete the frequency digrm for the dt in the tle. Frequency Height (cm)

84 D.HW Using n ssumed men ememer: To find men using n ssumed men: Assume men. Find the difference of the ssumed men from ech dt vlue. Find the men of the differences. Add the ssumed men ck on. You cn use the formul: Totl numer of differences Men = Assumed men + Numer of items The tle shows the ge t which people pssed their driving test. Age (yers) Difference from 7 0 Copy nd complete the tle to show the differences from 7 yers. Work out the men ge of the people. Adm recorded the times tken (in seconds) for people to complete tsk. In the second row of the tle he strted to work out the difference from 60 seconds for ech time. Time (s) Difference from 60 s c d e Copy nd complete the tle. Work out ll the differences from 60 seconds. Work out the sum of the positive differences: Work out the sum of the negtive differences: + Add your nswers to nd c to find the totl of ll the differences. Use this formul to clculte the men time: Totl of ll the differences Men time = 60 + Numer of items