p Key Stge Mthemtis Level y Level Pk C: Level 6 Stfford Burndred ISBN 1 89960 7 Pulished y Person Pulishing Limited 1997 Person Pulishing 1995 Revised Ferury 1997 A liene to opy the mteril in this pk is grnted to the purhser stritly within their shool, ollege or orgnistion. The mteril must not e reprodued in ny other form without the epress permission of Person Pulishing. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Numer nd Alger Tril nd improvement You should drw four olumns s shown elow. In the first olumn write down your guess. In the seond olumn work out the nswer using your guess. If your nswer is too ig write your guess in the too ig olumn. If your nswer is too smll write your guess in the too smll olumn. Guess Answer Too ig Too smll Question Find the vlue of orret to 1 deiml ple using tril nd improvement methods. You must not use the key on your lultor = 78. Answer You my hve used different vlues in your lultions. Guess Answer Too ig Too smll 8 is too smll. Guess higher 8 is too smll. 9 is too ig Guess etween 8 nd 9 8.5 is too smll. 9 is too ig Guess etween 8.8 nd 9 8.8 is too smll. 8.9 is too ig Guess etween 8.8 nd 8.9 8 9 8.5 8.8 8.9 8.85 6 81 7.5 77. 79.1 78.5 9 8.9 8.85 8 8.5 8.8 8.8 is too smll, 8.85 is too ig. The nswer must e etween 8.8 nd 8.85. Therefore the vlue of orret to 1 deiml ple is 8 8. Note: If the question ws Find the squre root of 78 without using the squre root key ( ) on your lultor you would use etly the sme method. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Numer nd Alger Tril nd improvement Eerises Use Tril nd Improvement methods to lulte the following. You must show ll of your working. You my use lultor ut you must not use the squre root key ( ) or the ue root key ( ). 1 Find the vlue of orret to deiml ples given = 5 Find the squre root of 0 orret to deiml ples. Find the squre root of 17 orret to deiml ples. Find the vlue of y orret to deiml ples given y = 5. 5 Find the ue root of 5 orret to deiml ples. 6 Find the vlue of orret to 1 deiml ple given = 15. 7 Find the vlue of orret to 1 deiml ple given = 8. 8 Find the et vlue of in eh of the following questions: + = 0 + = 5 + 5 = 18 d - = 1 e - = 980 f + - = 8 g - + 8 = 96 h - = 9 i + = 800 j - + = 90 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Numer nd Alger Clulting frtions nd perentges To lulte one numer s frtion of nother numer. Emple 10 people out of 5 went to work y us. Write this s frtion in its lowest terms. Without lultor 10/5 Divide top nd ottom y 5 /5 With lultor. The lultor should hve frtion key /. Clultor keys: 1 0 5 = Answer /5 / To lulte one numer s perentge of nother numer. Emple 8 people out of 800 wore glsses. Write this s perentge. Without lultor. 8/800 100 = 5.5% With lultor. Clultor keys: 8 8 0 0 % Answer 5.5% With some lultors you my hve to press = t the end. Questions 1 Find /8 of 1 A mn erns 50 per week. He reeives inrese. Wht perentge inrese is this? Answers 1 Of mens multiply /8 1 =.50 5 0 % = 1 6 % Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 5
Numer nd Alger Clulting frtions nd perentges Eerises Write the following s perentges. 1 out of 0 men hve erds. 5 people out of 0 wer hts. There re 60 girls in shool with 600 pupils. Wht perentge re oys? 8 people out of 50 people liked pop musi. 5 Find /8 of these numers: 18 0 1 d 7 e 16 f 60 g 0 h 80 i 60 6 A shop hd sle in whih ll goods were 1/ off the norml prie. Wht were the sle pries of these goods with the following norml pries? Tie 6 Shirt 1 Hndkerhief.50 d Blouse 7.50 e Skirt 6.0 f Srf 7.80 g Swet shirt 1.60 h Trousers 15.90 i Dress 1 0 7 The following list gives the mrks otined y lss of pupils in history test. The mrks re out of 80. Epress eh mrk s perentge orret to the nerest whole numer. 0 0 6 d 8 e 7 f 68 g 7 h 9 i j 5 8 A r deler ought r for 000 nd sold it for 10. Wht ws his perentge profit? Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 6
Numer nd Alger Clulting frtions nd perentges Notes nd Emples When working with perentges the totl is 100%. If we re working with prie inreses or dereses the ost prie or originl prie is 100%. Emple A mn erns 50 per week. He then reeives wge inrese. His new wge is 71. Clulte the perentge wge inrese. His wge inrese is 71-50 = 1 His originl wge is 50 1 50 The ost prie, originl prie or totl goes on the ottom line Clultor keys 1 5 0 % Your lultor should show 6. If it does not, try pressing the = key. Answer 6% Note: without lultor 1/50 100 Questions 1 A golf lu hd 100 memers. 80 of the memers were mles. Wht perentge of the memers were femle? A r ws ought for 8000 nd sold for 5000. Clulte the perentge loss. Answers 1 The question sks for the perentge of femles 100-80 = 60 60/100 Clultor keys: 6 0 1 0 0 % 0% The loss is 000. 000/8000 Clultor keys 0 0 0 8 0 0 0 % 7.5% Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 7
Numer nd Alger Clulting frtions nd perentges Eerises 1 In sle ll goods re sold t 0% off the norml prie. Clulte the sle prie of goods normlly sold t these pries. 0 00 80 d 5 e f 16 g.50 h.60 i 7.0 j 5.5 k 7.65 l 0.05 An estte gent lultes his fee for selling house y the following rules. Houses with selling prie under 50,000, selling fee % of the house prie. House with selling prie over 50,000, selling fee.75% of the house prie. Clulte the estte gent s fees for the following houses: i Selling prie 8,000 ii Selling prie 58,000 iii Selling prie 7,000 iv Selling prie 15,000 The estte gent reeived the following fees. Clulte the house pries. i 100 ii 00 iii 960 iv 05 v 870 vi 695 Two shops re selling identil television sets. The norml selling prie is 690. In AA Eletris there is sle with 1/ off everything. In Hrdy s Video nd TV store there is disount of 0%. Wht is the ost in AA Eletris? Wht is the ost in Hrdy s Video nd TV? Where should you uy the television nd how muh heper is it in this shop thn in the other shop? Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 8
Numer nd Alger Equivlenes etween deimls nd perentges Converting perentges to deimls Move the deiml point two ples to the left. 8% 8. = 0.8 0% 0. = 0.0 5% 5. = 0.05 7.% 7. = 0.7 Converting deimls to perentges Move the deiml point two ples to the right. 0.5 0.5 = 5% 0.7 0.7 = 70% 0.0 0.0 = % 0.65 0. 6 5 = 6.5% Questions 1 Convert the following perentges to deimls: 7% 6%.% Chnge these deimls to perentges: 0.5 0.08 0.06 Answers 1 0.7 0.06 0. 5% 8%.6% Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 9
Numer nd Alger Equivlenes etween deimls nd perentges Eerise 1 Write the following perentges s deimls: 8% % 6% d 6% e 80% f 5% g 5% h % i 60% j 7% k.% l 5% m 8.5% n 0% o 0.5% p 50% q.6% r 75% s 7.% t 6.8% Write the following deimls s perentges: 0.7 0.7 0.7 d 0.5 e 0.6 f 0.6 g 0.0 h 0.9 i 0.7 j 0.5 k 0.1 l 0.01 m 0.0 n 0. o 0. p.7 q.01 r.1 s 0.007 t 0.10 Complete the tle nd then memorise the following informtion if you do not lredy know these equivlenes. Frtion Deiml Perentge 1/ = 0.5 = 1/ = 0.5 = / = 0.75 = d 1/ = 0. = e / = = 66.7% f 1/8 = = 1.5% g 1/10 = = 10% h 1/100 = = 1% Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 10
Numer nd Alger Equivlenes etween deimls, frtions nd perentges Converting perentges to frtions First onvert the perentge to deiml nd then proeed s elow. Converting deimls to frtions 0. = 10 0. 7 = 7 100 One numer fter the deiml point One nought Two numers fter the deiml point Two noughts 0. 7 1 = 71 1000 0.0 = 100 Three numers fter the deiml point Three noughts Two numers fter the deiml point Two noughts Converting frtions to deimls Divide the top numer y the ottom numer. / mens = 0.75 17/0 mens 17 0 = 0.85 /0 mens 0 = 0.075 Converting frtions to perentges First onvert the frtion to deiml, then onvert the deiml to perentge. Questions 1 Convert the following deimls to frtions: 0. 0. 0.0 d 0.07 Write these frtions s deimls: /5 17/5 5/8 Answers 1 /10 =/5 /100 = 6/5 /100 = 1/50 d 7/1000 0.6 0.68 0.65 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 11
Numer nd Alger Equivlenes etween deimls, frtions nd perentges Eerise 1 Write the following deimls s frtions: 0.78 0.9 0.7 d 0.6 e 0.8 f 0.05 g 0.07 h 0.98 i 0.6 Convert the following frtions to deimls: 1/ /5 7/8 d 5/8 e /10 f 8/0 g 9/50 h 87/100 i /80 Complete this tle: Frtion Deiml Perentge 9/16 = = = 0. = = = 5.5% d = 0. = e 7/8 = = f = 0.0 = Write the following frtions s perentges: / 1/ /8 d /5 e 1/10 f 1/5 g 15/16 h 5/8 i 17/0 5 Convert the following perentges to frtions: 5% 7% 8% d 7% e 9% f.7% g 60% h 0% i 8% Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 1
Numer nd Alger Rtio 1 Questions 1 This is reipe for soup for four people. 800 wter tomtoes 100 g eef 8 g slt How muh of eh ingredient should you use for: two people si people Simplify these rtios: :18 0:5 The sle of mp is 1:1,000,000 The distne etween Longton nd Hilton is 18 m on the mp. Wht is the tul distne? The distne etween Bursley nd Highm is 1 km. Wht is the distne on the mp? Answers 1 Two people will need hlf the ingredients: 00 wter, 1 tomto, 50 g eef nd g slt Si people will need one nd hlf times the ingredients: 100 wter, tomtoes, 150 g eef, 1 g slt :18, divide oth sides y :9 0:5, divide oth sides y 15 : 1:1,000,000 mens 1 m on the mp represents 1,000,000 m on the ground 1,000,000 m = 10,000 m = 10 km Therefore 1 m on the mp represents 10 km on the ground 18 m on the mp mens (1810) km on the ground 180 km 1 km is represented y (1 10) m on the mp 1. m Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 1
Numer nd Alger Rtio 1 Eerises 1 This is reipe for Yorkshire pudding for four people: 10 g of flour 80 ml of milk eggs How muh of eh ingredient should you use for: people 6 people 10 people This is reipe to mke hot pot for four people: 0 g of eef stek 50 g of flour onions 600 g of pottoes 50 g of ue stok How muh of eh ingredient should you use for: people 6 people 10 people Simplify these rtios: :1 :8 15:9 d 10: e 18:1:9 f 150:50:50 The sle of mp is 1:100,000. Wht re the tul distnes etween the following towns? Give your nswer in kilometres. d e Ayton is 8 m from Beeton on the mp Beeton is 1 m from Ceeton on the mp Ceeton is m from Deehm on the mp Deehm is.5 m from Eford on the mp Eford is 7.6 m from Effinghm on the mp 5 These re the tul distnes etween the following towns. Wht re the distnes on the mp? Kyhm is 5 km from Elton Elton is 8. km from Emton Emton is 1.5 km from Newtown. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 1
Numer nd Alger Rtio You use rtio every dy of your life. A simple emple is mking glss of ornge sqush. You use undiluted ornge nd wter in the rtio 1 : 1 prt prts prts wter 1 prt undiluted ornge Produes 5 prts sqush Emple How mny litres of sqush n e mde with three litre ottle of undiluted ornge? The rtio is undiluted ornge wter sqush 1 : 5 one prt four prts five prts One prt is litres Therefore five prts is 5 = 15 litres Question A mn leves 5000 in his will. The money is to e divided etween his three sons Adm, Ben nd Crl in this rtio ::5. How muh does eh son reeive? Answer Adm reeives Ben reeives Crl reeives prts prts 5 prts 10 prts 10 prts is 5000 Therefore 1 prt is 500 Adm reeives prts 1000 Ben reeives prts 1500 Crl reeives 5 prts 500 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 15
Numer nd Alger Rtio Eerise 1 Epress the following s rtios in their simplest form: d A shool hs 00 oys nd 00 girls A tennis lu hs 50 femle memers nd 00 mle memers A ftory hs 900 men nd 600 women A ship hs 800 pssengers nd 160 rew Epress these sles s rtios in their simplest form: d e f The sle of mp is 1 m represents 50 m The sle of mp is 1 mm represents 1 m The sle of mp is 1 m represents 0 m The sle of mp is 5 m represents 10 m The sle of mp is 5 m represents 80 m The sle of mp is m represents 15 m In will, money is left to three dughters, Angel, Brr nd Crolyn in the rtio ::5. If the totl mount of money is 500, how muh will eh dughter reeive? A sum of money ws left to three sons Adm, Ben nd Clvin. The money ws divided in the rtio :5:6. If Adm reeived 100, how muh did the other two sons reeive? 5 Sweets were divided etween Pul, Srh nd Tony in the rtio ::5. Srh reeived 0 sweets less thn Tony. Wht ws the totl numer of sweets? How mny sweets did eh person reeive? 6 A model of siling ship ws mde. The model of the siling ship ws uilt to sle of 1:00. Complete this tle. d e Length Bredth Height of min sil Length of rudder Width of min sil Model (entimetres) 7.5 entimetres entimetres Full-sized ship (metres) 00 metres 10 metres metres Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 16
Numer nd Alger Eplore numer ptterns Emple Desrie how to find eh term in the pttern 5, 8, 11, 1, 17. Wht is the tenth term? Method: Term Find the differene 1st 5 nd 8 rd 11 th 1 5th 17 The differene is. This is wht you multiply y: 1st term is nd term is rd term is 1 = = 6 = 9 Wht do you hve to do to find the nswer? Add + = 5 6 + = 8 9 + = 11 The rule is multiply the term y, then dd. The tenth term is 10 + = Question Find the rule to produe this pttern:, 9, 16,, 0 Wht is the 0th term? Wht is the 6nd term? Answer Term Find the differene 1st nd 9 rd 16 th 7 7 7 7 5th 0 Multiply eh term y 7. 1st term is nd term is rd term is 7 1 = 7 = 6 7 = 9 Wht do you hve to do to find the nswer? Sutrt 5 7-5 = 1-5 = 9 1-5 = 16 The rule is multiply the term y 7, then sutrt 5 The 0th term is 7 0-5 = 15 The 6nd term is 7 6-5 = 59 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 17
Numer nd Alger Eplore numer ptterns Eerise Find the rule to produe eh pttern Find the 15th term Find the 17th term 1,, 6, 8, 10 6, 1, 18,, 0, 6, 9, 1, 15, 6, 10, 1, 18 5, 8, 1, 18, 6 5, 7, 9, 11, 1 7, 7, 10, 1, 16 8 -, 1, 5, 9, 1 9-5, -, 1,, 7 10 7,, 7,, 7 11 6, 11, 16, 1 1, 11, 19, 7, 5, The rules elow will produe sequenes. Produe the first five terms for eh sequene. 1 Multiply the term y then dd 1 Multiply the term y then dd 7 15 Multiply the term y then dd 1 16 Multiply the term y 6 then sutrt 1 17 Multiply the term y then sutrt 18 Multiply the term y then sutrt 10 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 18
Numer nd Alger Solving liner equtions + is the opposite of - - is the opposite of + is the opposite of is the opposite of Rules for solving equtions 1 mens The sign in front of numer is tthed to tht numer. eg - + 6 The - is tthed to the, the + is tthed to 6 Alwys keep the equls signs in stright olumns. Work down the pge not ross When you tke numer from one side of the equls to the other. + eomes - - eomes + eomes eomes 5 Do the ddition nd sutrtion prts efore the multiplition nd division. Question 1 + 5 = 8 - = -7-7y = 8 y/ = 6 5 5 + 7 = 7 6 / - 5 = 1 Answer Keep equls signs in stright olumns 1 + 5 = 8 = 8-5 = - = -7 = -7+ = -5-7y = 8 y = 8 /-7 y = - y / y y = 6 = 6 = 18 5 5 + 7 = 7 6 5 = 7-7 5 = 0 = 0 /5 = Del with the dd first Now del with the multiplition / - 5 = 1 / / = 1 + 5 = 6 = 6 = 18 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 19
Numer nd Alger Solving liner equtions Solve these equtions: 1 + = 7-5 = 8-5 = - - 8 = -1 5 + = -8 6 + 10 = - 7 = 1 8 5 = 5 9 7 = 10 8 = 16 11 6 = 1 10 = 1 8 = -8 1 5 = -0 15 7 = -1 16 - = -1 17 - = -0 18-8 = 19-5 = 0 0 - = 1 1 y + 1 = 1 + = 5 - = 7 8d -1 = 1 5 6e + = 15 6 5 + 1 = + 0 7 7 + = + 0 8 8 + 5 = +10 9 5 - = - 1 0-8 = - 1 d/ = 5 /8 = /7 = y/ = 5 6/ = 6 5/ = 0 7 / = 1 8 5/ = 15 9 / - = 0 5/ + 1 = 11 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 0
Numer nd Alger Formulting liner equtions You must understnd prolem efore you n write n eqution to solve it. Try putting numers in for the letters. This will help you to understnd wht the question is sking. Question 1 A mn uys pples t 8p eh. The totl ost is 96p. Form n eqution to show this. Solve the eqution. I think of numer N, I doule it nd dd 15. The nswer is 1. Form n eqution to show this. Solve the eqution. Answer 1 Try putting numers in for the letters. How would you work out the ost of: 5 pples 8 5 = 0 6 pples 8 6 = 8 7 pples 8 7 = 56 pples 8 = 96 The eqution is 8 = 96 8 = 96 8 = 96/8 8 = 1 Choose numers. See wht hppens: if N = + 15 = 1 if N = + 15 = if N = 5 5 + 15 = 5 Try N N + 15 = 1 The eqution is N + 15 = 1 or N + 15 = 1 N + 15 = 1 N = 1-15 N = 16 N = 16/ N = 8 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 1
Numer nd Alger Formulting liner equtions Eerise Form n eqution for eh question nd solve it. 1 Jyne uys kilogrms of sugr t 75p per kilogrm she pys 5.5. How mny kilogrms did she uy? Mr Adms works for hours per week t per hour. How mny hours does he work if he erns 1? A womn ought Y pples t 8p eh nd 1 ornges t 15p eh. She spent.5. How mny pples did she uy? John hs sweets, Dvid hs five more thn John, Pul hs twie s mny s Dvid. They hve 51 sweets ltogether. How mny sweets does John hve? 5 Here re some instrutions: Strt with numer, doule the numer, then dd. Wht is the strt numer if the result is 55? 6 The ost of hiring r is 5 plus 8p per mile. Mrs Johnson hires r nd the ost is 65. How mny miles did she trvel? 7 Mrs Shw wlks K kilometres nd runs 5K kilometres. She trvels totl of 56 kilometres. How fr did she wlk? 8 Mr Dvis is four times s old s his dughter. Si yers go he ws ten times s old. How old is Mr Dvis now? 9 A numer N is hosen. Five times the numer minus is equl to three times the numer plus 1. Wht is the numer 10 Pul nd Mrk worked s witers. Pul worked for H hours nd Mrk worked for 7H hours. The wge rte ws 5 per hour. Mrk erned 100 more thn Pul. How muh did Pul ern? Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Numer nd Alger Grphil representtion This is the y is nd the line =0 y = y = - y = 1-5 - - - -1 1 5 This is the is nd the line y=0-1 = -5 - y = - + - y = - - Question Complete this tle of vlues nd drw the grph of y = - + Note: Sometimes the question sttes drw the funtion f() = - + - - -1 0 1 y Answer If the question sks for the funtion f () = - + the tle nd grph will e the sme with f() insted of y. When = - y = -(-) + = -5 - - -1 0 1 y -5 0 0-5 y 1 - - -1 1-1 - - - Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Numer nd Alger Grphil representtion Eerise 1 You will need grph pper. Drw the -is from = -10 to = 10 Drw the y-is from y = -10 to y = 10 Drw the following lines on your grph nd lel the lines. y = 0 = 0 = d y = e = -5 f y = -7 g y = h y = - i y = + j y = - + k y = 1/ l y Complete the following tles of vlues nd then drw the grphs: y = - - - -1 0 1 y y = - - - -1 0 1 y y = 1 / - 6 - - -1 0 1 y Complete the following tles of vlues nd then drw the grphs of the following funtions: f() = - + - - -1 0 1 y f() = - 5 - - -1 0 1 y f() = + - - -1 0 1 y d f() = + + - - -1 0 1 y Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Shpe, Spe nd Mesures -D Representtions of -D Shpes -D nd -D shpes This net folds to mke ue Cue This net folds to mke uoid Cuoid This net folds to mke squre sed pyrmid Squre sed pyrmid This net folds to mke tringulr prism Tringulr prism Question Answer Drw n urte -D net of this uoid. 1 m 1 m m Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 5
Shpe, Spe nd Mesures -D Representtion of -D shpes Eerise 1 Wht -D shpe will this net form? Whih of these nets will fold to form ue? d Drw n urte -D net of this uoid. m m m Drw n urte -D net of this tringulr prism. m m 60 m 60 60 m m Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 6
Shpe, Spe nd Mesures Properties of qudrilterls Emple A qudrilterl is four sided shpe. The ngles dd up to 60. Prllelogrm Rhomus Opposite sides re prllel nd the sme length. Opposite ngles re equl. Digonls iset eh other. Rottionl symmetry order. This is prllelogrm with four equl sides. Digonls iset eh other. Rottionl symmetry order. Retngle Squre A retngle with ll sides equl length. Rottionl symmetry order. A prllelogrm with ll ngles equl (ie 90 ). Rottionl symmetry order. Trpezium Kite A qudrilterl with one pir of prllel sides. No rottionl symmetry. Two pirs of equl length sides djent to eh other. Digonls ross t right ngles. One digonl isets the other. No rottionl symmetry. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 7
Shpe, Spe nd Mesures Properties of qudrilterls Aes of symmetry Rhomus Retngle Squre Kite Prllelogrm Usully none. Trpezium Usully none. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 8
Shpe, Spe nd Mesures Properties of qudrilterls Eerise 1 Give the nme of the qudrilterl est desried y the following sttements: d e All ngles equl, opposite sides prllel All sides equl, digonls iset eh other t right ngles One pir of prllel sides Two pirs of prllel sides All ngles equl, ll sides equl Nme eh qudrilterl. d e f Find the sizes of the following ngles. 110 50 6 70 d 0 50 e Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 9
Shpe, Spe nd Mesures The Qudrilterl Gme Rules: This is gme for two plyers. You need two die. Eh plyer strts with si rhomus, five kites, four trpeziums, three prllelogrms, two retngles nd one squre. Cut out the shpes t the ottom of the pge. Choose one different numer from to 1 for eh shpe. Suppose you hoose 8 for the kite. Eh time you throw n 8 you n get rid of one kite. The first plyer to get rid of ll of their shpes wins. Use penil to omplete the tle, then you n hnge your numers for the net gme. Emple Plyer A Plyer B Qudrilterl Die totl Qudrilterl Die totl Qudrilterl Die totl Rhomus 5 Rhomus Rhomus Kite 8 Kite Kite Trpezium Trpezium Trpezium Prllelogrm 11 Prllelogrm Prllelogrm Retngle 9 Retngle Retngle Squre 7 Squre Squre Plyer A Plyer B Rhomus Rhomus Rhomus Rhomus Rhomus Rhomus Rhomus Rhomus Rhomus Rhomus Kite Kite Kite Rhomus Rhomus Kite Kite Kite Prllelogrm Prllelogrm Prllelogrm Prllelogrm Kite Kite Kite Kite Prllelogrm Squre Prllelogrm Squre Trpezium Trpezium Trpezium Trpezium Trpezium Trpezium Retngle Retngle Trpezium Retngle Retngle Trpezium Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 0
Shpe, Spe nd Mesures Regulr polygons A regulr polygon hs ll of its sides the sme length nd ll of its ngles the sme size. E I I = Interior ngles I E E I E = Eterior ngles The sum of the eterior ngles of polygon is 60 I E I E Interior ngle + eterior ngle = 180 Questions 1 Find the size of n eterior nd n interior ngle of regulr otgon. Find the size of n eterior nd n interior ngle of regulr hegon. Answers 1 I E I E E I I E E I I E I E I E An otgon hs 8 sides, 8 eterior ngles, 8 interior ngles 8 eterior ngles = 60 Therefore 1 eterior ngle = 60 = 5 8 Interior ngle + eterior ngle = 180 Interior ngle + 5 = 180 Interior ngle = 15 This question n e solved using the ove method. An lterntive method is to split the shpe into tringles. tringles re formed Therefore the sum of the interior ngles is 180 = 70 6 interior ngles = 70 1 interior ngle = 10 Interior + eterior = 180 10 + eterior = 180 Eterior = 60 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 1
Shpe, Spe nd Mesures Interseting nd prllel lines Interseting lines d + = 180 + = 180 + d = 180 Angles on stright line dd up to 180 = = d Vertilly opposite ngles re equl d + = 180 Prllel lines Look for shpes. Angles t orner of shpes re equl. or or Questions 1 Find the missing ngles: 0 d e g f Find : Find y: 110 0 50 y Answers 1 = 10, = 0, = 10, d = 0, e = 10, f = 0, g = 10. It often helps to etend the prllel lines to produe Z shpes. Try dding n etr prllel line. 70 110 70 = 70 50 50 0 0 y = 70 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Shpe, Spe nd Mesures Regulr polygons, interseting nd prllel lines Eerise 1 Find the size of eh eterior nd interior ngle of the following: d e A regulr pentgon A regulr hegon A regulr nongon (9 sides) A regulr degon (10 sides) A regulr 1 sided polygon How mny sides does regulr polygon hve if the size of eh eterior ngle is? 5 18 How mny sides does regulr polygon hve if the size of eh interior ngle is? 170 168 160 Find the ngles indited. 60 f g e d 50 y y 5 d z 110 e f 10 10 100 10 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Shpe, Spe nd Mesures Cirumferene nd re of irle, res nd volumes You must lern these formule. Cirumferene of irle = π rdius = π dimeter Cirumferene Dimeter Rdius Are of irle = π rdius rdius Volume of uoid = length width height Volume of uoid = 6 m m m = 7 m m Note: Are is in units eg m, m Volume is in units eg m, m 6 m m Questions 1 Find the irumferene nd re of irle rdius 8 m. Find the re. 8 m 5 m m 1 m m This is digrm of grden with lwn nd pth round the edge. The pth is m wide. Pth Lwn 10 m Answers 1 Cirumferene = π r Are = π r r =.1 8 =.1 8 8 = 50. m = 00.96 m Split the shpe into three prts. Are = m Find the re of the lrge retngle = 10 16 = 160 m Find the re of the smll retngle = 6 1 = 7 m Tke wy = 88 m 1 m 5 m = 5 m 16 m m m = 1 m 5 m m = 15 m Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Shpe, Spe nd Mesures Cirumferene nd re of irle, re nd volumes Eerise 1 Find the irumferene nd res of the following irles: rdius 5 m rdius 1 m rdius 7 m d rdius. m e dimeter 1 m f dimeter 0 m g dimeter 9 m h dimeter.8 m Pth Find the re of irulr pth m wide whih goes ll the wy round pond rdius 0 m. 0 m 80 m Find the distne round this yle trk. Find the re of the yle trk 1 m This is digrm of grden. 18 m Wht is the perimeter? 5 m 5 m Wht is the re? m m m 5 This is grden. It hs lwn with pth, m wide round the outside. Wht is the re of the pth? 0 m 1 m Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 5
Shpe, Spe nd Mesures Enlrgement Questions 1 Enlrge the tringle ABC y sle ftor of. Centre of enlrgement is the point (, 1). 5 1 0 1 5 R1 is n enlrgement of R. Wht re the oordintes of the entre of enlrgement? Wht is the sle ftor of the enlrgement? 10 8 6 R1 R 0 6 8 10 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 6
Shpe, Spe nd Mesures Enlrgement Answers 1 8 7 1 6 5 1 1 1 1 0 1 5 6 7 8 Count the distne from the entre of enlrgement to eh point sle ftor Point 1 up up long long Point 1 up up long 6 long Point up 6 up long 8 long 10 8 6 R1 R 0 Use ruler to join the orners. The dotted lines ross t (1,). Therefore the entre of enlrgement is the point (1,) new length Sle ftor = originl length 6 Sle ftor = = 6 8 10 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 7
Shpe, Spe nd Mesures Enlrgement Eerise 0 8 6 0 18 16 D 1 1 L 10 8 6 E 0 6 8 10 1 1 16 18 0 6 8 0 1 Enlrge L y sle ftor of, entre of enlrgement (9,18). Lel this A. Enlrge L y sle ftor of, entre of enlrgement (15,16). Lel this B. Enlrge L y sle ftor of, entre of enlrgement (1,10). Lel this C. D is n enlrgement of L. Find the entre of enlrgement nd the sle ftor. 5 E is n enlrgement of L. Find the entre of enlrgement nd the sle ftor. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 8
Hndling Dt Collet nd reord ontinuous dt in frequeny tles nd frequeny digrms Continuous dt is dt whih n hve ny vlue eg distne etween two ples, height of person. The height of person n e mesured to ny degree of ury. A person ould e 1.786 m tll. Disrete dt is dt whih n only hve ertin vlues eg the numer of people in room n only hve whole numer vlues. You nnot hve. people in room. If you re sked to ollet dt you must hoose n pproprite method. Usully survey or n eperiment. You must reord your dt nd then present it in tles, digrms nd grphs. Questions The following re the times tken y 0 people to omplete jigsw. The times re in minutes. 8.6, 8., 8.1, 0.1, 6.0, 7., 6.01, 5.,.6, 9.97, 18.6, 0.00,.7, 8.6, 0.01, 19.99, 7.6, 16., 8.7, 1.58 Reord the informtion in frequeny tle. Choose suitle equl lss intervls. Show this informtion in frequeny digrm. Answers Minutes Minutes Tlly Frequeny 0-10 0 - under 10 I I A ommon error is: 10-0 10 - under 0 I I I I 0-0 0 - under 0 I I I I I I 7 0 - under 0 I I I I Where would you reord 0? 0 - under 50 I I I In the 10-0 or 0-0? 7 6 5 Frequeny 1 0 10 0 0 0 50 Time in minutes Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 9
Hndling Dt Collet nd reord ontinuous dt in frequeny tles nd frequeny digrms Eerise 1 The dt elow shows the height of 0 hildren in lss. Height is in entimetres. Choose four suitle equl lss intervls. Reord the informtion in frequeny tle. Show the informtion in frequeny digrm. 17 18 16 150 16 156 18 19 156 159 168 157 16 15 16 19 15 167 19 10 The dt elow shows the mss of 0 dults. Mss is in kilogrms. Choose suitle equl lss intervls. Reord the informtion in frequeny tle. Show the informtion in frequeny digrm. 80 6 58 7 9 6 7 68 8 6 58 5 7 60 58 71 6 61 59 71 The dt elow shows the distne 1 pupils trvel to shool. The distne is in kilometres. Choose suitle equl lss intervls. Reord the informtion in frequeny tle. Show the informtion in frequeny digrm. 0 78 0 1 8 1 68 1 0 1 1 1 7 1 6 1 1 0 87 Collet dt for the following: The height of eh pupil in your lss. The mss of eh pupil in your lss. The irumferene of eh pupils wrist. 5 A tsk of your own hoosing eg the time tken to omplete tsk. Reord the informtion. Present the informtion in frequeny tle. Show the informtion in frequeny digrm. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 0
0 KS Mthemtis C: Level 6 Hndling Dt Construting pie hrts Question Thirty people were sked wht sort of holidy they would hoose. 5 sid mountin resort, 10 sid eh holidy, 7 sid n tivity holidy nd 8 sid ruise. Show this informtion in pie hrt. Answer There re 60 in irle. The pie hrt must represent 0 people. 60 0 = 1. Therefore 1 represents 1 person. Holidy hoie Mountin resort Beh holidy Ativity holidy Cruise Frequeny 5 10 7 8 Multiply y 1 1 1 1 1 Angle t the entre of the pie hrt 60 10 8 96 How to drw the pie hrt 1 Drw irle. Drw line from the entre to the edge. 60 Ple the protrtor on the irle. Ple the entre of the protrtor on the entre of the irle. Mke sure 0 is on the line. Mesure the ngle, 60. 180 Drw line from the entre to the edge t 60. Lel the setor mountin resort write 60. Mountin resort 60 0 Move the protrtor s shown. Mesure 10. Drw line from the entre to the edge. 10 5 Repet for 8. Chek the remining ngle is 96. Lel eh setor. Beh holidy Ativity holidy 10 60 8 96 Mountin resort Cruise Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 1
Hndling Dt Construting pie hrts Eerise 1 Drw pie hrt to show this informtion: Fvourite type of musi Pop Clssil Country Soul Frequeny 8 8 5 9 Angle t the entre of the irle Drw pie hrt to show this informtion: Shoe size 5 6 7 Frequeny 6 8 7 6 Angle t the entre of the irle Drw pie hrt to show this informtion: Vehiles pssing shool Frequeny Angle t the entre of the irle Crs Vns Lorries Buses 18 8 Drw pie hrt to show this informtion: Pupils trnsport to shool Frequeny Angle t the entre of the irle Bus Cr Cyle Wlk 15 8 6 7 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Hndling Dt Stter digrms A stter digrm is used to ompre two sets of results. Height Time spent t work House numer Mss Time spent t home Clssroom numer This digrm shows positive orreltion This digrm shows negtive orreltion This digrm shows no orreltion A positive orreltion indites tht s one quntity inreses so does the other quntity. The digrm shows tht in generl tller people re hevier. A negtive orreltion indites tht s one quntity inreses the other quntity dereses. The digrm shows tht in generl the more time person spends t work, the less time he spends t home. No orreltion indites tht there is no reltionship etween the two quntities. The digrm shows tht pupil s house numer hs no onnetion with the pupil s lssroom numer. Question Desrie the type of orreltion shown y this stter digrm. Eplin the reson for this orreltion. Sweets eten Answers Negtive orreltion. Numer of fillings Sweets n use hrm to teeth. Therefore in generl the more sweets person ets, the more fillings will e required. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Hndling Dt Stter digrms Eerise 1 Desrie the type of orreltion shown y this stter digrm. 100 Wht n you sy out pupils mrks in English nd Mths? English mrk 0 Mths mrk Desrie the type of orreltion shown y this stter digrm. Eplin the reson for this orreltion. Height Lst digit of house numer Desrie the type of orreltion shown y this stter digrm. Eplin the reson for this orreltion. Cigrettes smoked per dy Age t deth Ple some rosses on this stter digrm to show the type of orreltion you would epet. Does this stter digrm show positive, negtive or no orreltion? Temperture Eplin the reson for this orreltion. Ie-rems sold Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568
Hndling Dt Proility Questions 1 Drw tree digrm to show ll of the possile outomes when two oins re tossed. Complete this tle to show ll of the possile outomes when throwing two die. 1 5 6 1 5 6 How mny different wys n two die lnd? Wht is the proility of doule? The proility of new light ul not working is 0.0. Wht is the proility of new light ul working? Answers 1 First oin H T Seond oin H T H T Outomes HH HT TH TT 1 5 6 1 5 6 7 5 6 7 8 5 6 7 8 9 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 1 6 wys There re 6 doules There re 6 different wys Proility = 6/6 = 1/6 A light ul n either work or not work totl proility is 1. Proility of working + proility of not working = 1.? + 0.0 = 1 Proility of working = 1-0.0 Proility of working = 0.97 Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 5
Hndling Dt Proility Eerises 1 In Sotlnd jury n find defendnt not guilty, not proven or guilty. Two ses re held. Drw tree digrm to show ll of the possile outomes. Trffi lights n show red or green. Eh dy Mrs Sims drives through two sets of trffi lights. Drw tree digrm to show the outome. A drwing pin n lnd point up or point down. Two drwing pins re dropped onto the floor. List ll of the possile outomes. Dvid n fford to uy one n of drink nd one g of risps. List ll of his possile hoies. Bon flvour risps Plin risps 5 Andre hs two die. One is si sided nd one is four sided. Complete this tle to show ll of the possile totls. How mny different wys n the die lnd? Wht is the proility of soring i 6, ii 7? 1 1 5 6 8 7 6 This is g of ounters. Wht is the proility of hoosing lue ounter? Wht is the proility of not hoosing lue ounter? y p y p p p y y y = yellow = lue p = pink 7 The proility of r reking down is 0.0. Wht is the proility of it not reking down? Eplin how you worked out the nswer. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 6
Ativity nd Investigtion Bloks Building loks or ues will e useful for mking the shpes. Shpe 1 Shpe Shpe Results tle Continue the shpes. Reord you results in tle Height 1 Bloks 1 Numer of loks 1 6 6 How mny loks for height of 10, 0, 100? Try to find rule for height of H. Now try [drw results tle] How mny loks for height of 16, 0, 00? Find rule for height of H. Now try How mny loks for height of 10, 15, 100? Find rule for height of H. d Investigte other shpes suh s: Now try pyrmids. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 5
Ativity nd Investigtion Dimonds Rules: You will need squred pper or grph pper. Stge 1 Stge Strt with 1 squre in the entre of your pper. Add new squres to the first squre. Eh new squre must touh the previous squre long one side only. 1 1 Corret only one side only Wrong Two sides re touhing 1 This is how the pttern strts. At stge dimond is produed. 5 5 1 5 5 Mke opy of this nd fill it in s fr s stge 9. Now you re redy to drw some dimond ptterns. You will need some grph pper. Size A with mm squres is est. Use four or eight different olours eg red, lue, yellow, green. Colour eh stge eg stge 1 red, lue, yellow, green, 5 red, 6 lue, et. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 55
Ativity nd Investigtion You n mke more interesting ptterns y hnging the olours fter eh dimond shpe. It is est to use four or eight different olour. Now you must investigte the ptterns. Look t wht hppens for the first few stges. Stge Squres 1 1 1 5 6 1 et Cn you predit the stges when dimond shpes pper? Cn you find rules for eh stge? Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 56
Ativity nd Investigtion The Symmetry Puzzle Cut out the strips elow. Ple them on the piture ove so tht the piture hs rottionl symmetry order. Pemrokeshire e-portl Liene ep 1Aug10 Person Pulishing, Chesterton Mill, Frenh s Rod, Cmridge CB NP Tel 01 50555 F 01 568 57