*GMT41* *24GMT4101* Mathematics. Unit T4 (With calculator) Higher Tier [GMT41] WEDNESDAY 6 JUNE 9.15 am am. 2 hours.
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1 entre Numer ndidte Numer Mtemtics Generl ertificte Secondry Eduction 0 Unit T4 (Wit clcultor) Higer Tier [GMT4] WEDNESDAY 6 JUNE 9.5 m.5 m *GMT4* *GMT4* TIME ours. INSTRUTIONS TO ANDIDATES Write your entre Numer nd ndidte Numer in te spces provided t te top tis pge. Write your nswers in te spces provided in tis question pper. omplete in lue or lck ink only. Do not write in pencil or wit gel pen. Answer ll fourteen questions. Any working sould e clerly sown in te spces provided ce mrks my e wrded for prtilly correct solutions. You my use clcultor for tis pper. INFORMATION FOR ANDIDATES Te totl mrk for tis pper is 00. Figures in rckets printed down te rigt-nd side pges indicte te mrks wrded to ec question or prt question. Functionl Elements will e ssessed in tis pper. Qulity written communiction will e ssessed in questions nd 7. You sould ve clcultor, ruler, compsses nd protrctor. Te Formul Seet is overlef. 745 *4GMT40* *4GMT40*
2 Formul Formul Formul Formul Formul Formul Formul Formul Formul Seet Seet Formul Seet Formul Formul Seet Seet Formul Formul Seet Seet rossross + ) trpezium trpezium ( + ( ) ross ross ross + trpezium trpezium prism prism cross cross ) (+ + +( )+)) trpezium ( ) trpezium trpezium ( + ( ) ross ross trpezium prism cross ( trpezium trpezium ( prism prism cross cross + ( )+ ) (+ trpezium ( + ) ) trpezium trpezium prism prism cross cross ( )+ ) trpezium ( + cross cross cross cross cross cross cross B BB B c c c c c c c A A AA A A A B B B Surfce Surfce Surfce Surfce 4πr 4πr 4πr 4πr Surfce Surfce 4πr 4πr l l l r r r r r r r 0,0,re re 0,given re given yy y given 0, re 0,given re given y y 0, re 0, given re given y y Qudrtic Qudrtic Eqution Eqution Qudrtic Eqution Qudrtic Qudrtic Eqution Eqution xx Qudrtic Qudrtic Eqution Te solutions Te solutions Eqution x x c c 0c 0 0 xx x x Te solutions Te solutions Te solutions xx c 0c 0 xx Te solutions Te solutions 0,given x x c 0c 0 0, re re given y y given 0,0, re re 0,given re given yy y 0, re 0,given re given y y ± ± 4 c c 4c44 c x x x± ±± 4c x x ± ± 4c 4 c [Turn [Turn over over x x [Turn over [Turn [Turn over over [Turn [Turn over over πr πr πr πr πr 34 πr πr 33 Surfce Surfce 4πr 4πr Surfce 4πr Surfce Surfce 4πr 4πr Surfce Surfce 4πr 4πr Surfce 4πr l l l l r r r r r r r prism prism cross cross prism cross prism prism cross cross prism prism cross cross cone cone3 πr 3πr πr cone πr cone cone3 πr 3 3 πr cone cone3 πr 3 urved urved surfce surfce cone cone πrl πrl InInny In tringle ny tringle AB AB urved surfce cone urved surfce cone urved surfce cone πrlπrlπrl ny tringle AB In ny In tringle ny tringle AB AB urved urved surfce surfce cone cone πrl πrl In ny In tringle ny tringle ABAB tringle tringle tringle tringle tringle tringle tringle cc c Sine Sine rule :rule c c Sine rule : :: A Sine Sine rule :rule AB Bcc Sine Sine rule :rule : B A B A A B A B B A oe oe rule: rule: + + c + c cc cos c Acos A Formu oe rule: cos A Formul oe oe rule: rule: + cc+ c c cos c Acos AFormul oe oe rule:rule: + c + c c cos cacos Formul A Formu Formul Formu trpezium trpezium ( + ( ) + ) + trpezium ) trpezium trpezium ( + ( ) + ) ( trpezium trpezium ( + )+ ) ( Surfce Surfce AB Surfce Surfce Surfce InIn ny In tringle ny tringle AB Surfce Surfce ny tringle AB In ny In tringle ny tringle AB AB In ny In tringle ny tringle AB AB πr cone cone 3 πr πr 3 πr cone cone cone 3 πr 3 cone cone 3 πr 33πr urved urved surfce surfce cone cone πrlπrl πrl urved surfce cone urved urved surfce surfce cone cone πrl πrl urved urved surfce surfce cone cone πrl πrl l l l l l l l Qudrtic Qudrtic eqution: eqution: prism cross ccross c prism cross Qudrtic eqution: Qudrtic Qudrtic eqution: eqution: prism cross c c Sine Sine Rule: Rule: prism prism c cross Qudrtic Qudrtic eqution: eqution: Sine Rule: c c Sine Sine Rule: Rule: prism Aprism cross cross A B B Sine Sine Rule: Rule: A++ B 0, 0, Ax Ax B+ B x Te solutions Te solutions x + c 0, c 0, A+x Ax B 0,0, 0, Tesolutions solutions x +c cb+ 0,c0, Te Te solutions x ++ 0, +x x Te solutions Te solutions x +x x + + x c + 0, c 0, 0, 0, c cc cos oe oe Rule: Rule: c Acos cc cc cos A A 4c cos c Acos A oe ±oe ±oe ±Rule: Rule: 4Rule: c c c 4 oe oe Rule: Rule: c c c cos c A cos A x x ± ± c c 4 4 In ny In tringle ny tringle AB AB x xin AB x ± Inny ±ny tringle In 4tringle ctringle 4 cab ny AB x x In ny ny ABAB tringle In tringle tringle tringle tringle [Turn tringle tringle tringle [Turn over over over tringle tringle tringle tringle [Turn [Turn [Turn over over tringle tringle tringle tringle [Turn[Turn over over *4GMT40* *4GMT40*
3 Qulity written communiction will e ssessed in tis question. Sow your working. Exminer Only Mrks Remrk () In oug estte 5 6 te ouses ve grge. In tree out every four grges tere is cr prked. Tere re 5 crs in totl prked in grge. Find te numer ouses tt ve no grge. Answer [3] () An empty tnk is in te spe cuoid s sown wit mesurements.4 m,. m nd 0.8 m ll to te nerest 0 cm. Wt is te smllest possile volume te tnk? Answer m 3 [3] Totl Question 745 [Turn over *4GMT403* *4GMT403*
4 0 employees in wreouse were sked ow fr tey trvelled to work ec dy. Te tle sows teir responses. Exminer Only Mrks Remrk Distnce (km) Frequency (numer people) Distnce () umultive frequency 0 d d d d 0 0 d d d d d 45 5 () omplete te cumultive frequency tle ove. [] () Drw te cumultive frequency grp on te grid opposite. [3] (c) Use your grp to find (i) te medin, Answer km [] (ii) te percentge employees wo trvel more tn 8 km to work ec dy. Answer % [] 745 *4GMT404* *4GMT404*
5 (d) Te minimum distnce trvelled y ny employee ws km nd te mximum distnce trvelled ws 44 km. Exminer Only Mrks Remrk Drw ox plot elow to illustrte te dt for ll 0 employees. [3] Totl Question 745 [Turn over *4GMT405* *4GMT405*
6 3 () Find te lest common multiple (LM) 60 nd 3. Exminer Only Mrks Remrk Answer [] () M is te point (, 4). N is te point (5, 8). Find te MN, correct to deciml plces. Answer [3] 745 *4GMT406* *4GMT406*
7 (c) Exminer Only Mrks Remrk O is te rdius te se te cone. OD is te eigt te cone. O 5 5 cm. D 5 cm. lculte te ngle DO. Answer [3] Totl Question [Turn over *4GMT407* *4GMT407*
8 4 () Solve te simultneous equtions 5x y 5 3 x 3y 5 9 Exminer Only Mrks Remrk A solution y tril nd improvement will not e ccepted. Answer x 5 [] Answer y 5 [4] () Fctorise fully (i) 9xy y Answer [] (ii) g 9 Answer [] Totl Question *4GMT408* *4GMT408*
9 5 () P, Q, R nd S re points on te circumference circle, centre O. Te ngle PSR is 48 Exminer Only Mrks Remrk lculte (i) te ngle PQR, Answer [] (ii) te reflex ngle POR. Answer [] 745 [Turn over *4GMT409* *4GMT409*
10 () Exminer Only Mrks Remrk RT is tngent to te circle, centre O. Write down te size ngle SRT. Give reson for your nswer. Answer ecuse [] Totl Question *4GMT40* *4GMT40*
11 6 () (i) Find te eqution te line troug te points (0, ) nd (3, 3). Exminer Only Mrks Remrk Answer [3] (ii) Find te eqution te line wic is perpendiculr to te line y 5 3x 4 nd psses troug te point (0, 7). Answer [] 745 [Turn over *4GMT4* *4GMT4*
12 () Solve te eqution Exminer Only Mrks Remrk 3x5 x A solution y tril nd improvement will not e ccepted. Answer x 5 [4] Totl Question *4GMT4* *4GMT4*
13 Qulity written communiction will e ssessed in tis question. 7 () In forest, te wrden wises to estimte te numer rits. He ctces nd mrks 40 rits nd releses tem gin. Exminer Only Mrks Remrk Te next dy e ctces 80 rits nd finds 3 te mrked ones mong tese. Estimte te numer rits in te forest. Sow your work clerly. Answer [3] () Ligtup clim tt te lifetime teir ligt uls is over 00 ours. (i) Explin wy it is necessry to use smpling to find te lifetime te ligt uls. [] (ii) Descrie suitle smpling metod for testing te lifetime te ligt uls. [] 745 [Turn over *4GMT43* *4GMT43*
14 (c) In ospitl 840 ptients were treted for tonsillitis during one yer. Some informtion on te gender nd ge groups tese ptients is sown in te tle elow. Exminer Only Mrks Remrk Under Over 50 Mle Femle 43 Te ospitl wises to interview some te ptients. Tey tke strtified smple 80 ptients. (i) How mny ptients in te smple sould e mles under 5? Answer [] (ii) In te smple tken tere were 5 femles over 50. Estimte te numer femles over 50 wo were treted for tonsillitis in te ospitl. Answer [] Totl Question *4GMT44* *4GMT44*
15 8 Exminer Only Mrks Remrk Sip P is 6 km from ligtouse L on ering 07 Sip Q is 45 km from L on ering 4 lculte () te distnce etween P nd Q, Answer km [3] () te tringle LPQ, Answer [3] 745 [Turn over *4GMT45* *4GMT45*
16 (c) te ering P from Q. Exminer Only Mrks Remrk Answer [3] Totl Question *4GMT46* *4GMT46*
17 9 Te force F exerted y mgnet on metl utton is inversely proportionl to te squre te distnce d te mgnet from te utton. Exminer Only Mrks Remrk Wen d 5 8 cm, F 5.5 newtons. lculte te distnce from te mgnet wen te force on te utton is 6.4 newtons. Answer cm [5] Totl Question [Turn over *4GMT47* *4GMT47*
18 0 () Expnd nd simplify ( 3)(3 ) Exminer Only Mrks Remrk Answer [3] () Solve te qudrtic eqution giving your nswer correct to deciml plces. Answer [3] Totl Question *4GMT48* *4GMT48*
19 () Fctorise 6 x x x Exminer Only Mrks Remrk Answer [3] () Solve 7 5 3x x 5 4 A solution y tril nd improvement will not e ccepted. Answer [7] Totl Question 745 [Turn over *4GMT49* *4GMT49*
20 Te tle records te weigt, in grms, some te 350 prcels wic pss troug post fice during week. Exminer Only Mrks Remrk Weigt (w grms) Frequency 0 w w w w w w w *4GMT40* *4GMT40*
21 Te istogrm illustrtes te weigts some te prcels. Exminer Only Mrks Remrk () omplete te frequency density on te grid. [] () Use te dt in te tle to complete te istogrm. [] (c) Use te dt in te istogrm to complete te tle. [] (d) Estimte te medin weigt te 350 prcels. Answer g [] Totl Question 745 [Turn over *4GMT4* *4GMT4*
22 3 Exminer Only Mrks Remrk A verticl telegrp pole TP stnds t te corner P orizontl field PQRS. PQRS is rectngle 60 m nd redt 5 m. Te eigt te pole is 0 m. lculte te ngle elevtion te top te pole, T, from R. Answer [3] Totl Question *4GMT4* *4GMT4*
23 4 () lculte, sowing ll your working, te vlue 8 3 Exminer Only Mrks Remrk Answer [] () Find te vlue n for wic 9 n 5 3 Answer n 5 [] (c) c Find possile vlues,, c. Answer 5 5 c 5 [4] THIS IS THE END OF THE QUESTION PAPER Totl Question *4GMT43* *4GMT43*
24 DO NOT WRITE ON THIS PAGE For Exminer s use only Question Numer QW Totl Mrks Mrks Exminer Numer Permission to reproduce ll copyrigt mteril s een pplied for. In some cses, efforts to contct copyrigt olders my ve een unsuccessful nd EA will e ppy to rectify ny omissions cknowledgement in future if notified. 745 *4GMT44* *4GMT44*
*GMT62* *20GMT6201* Mathematics. Unit T6 Paper 2 (With calculator) Higher Tier [GMT62] MONDAY 11 JUNE 3.00 pm 4.15 pm. 1 hour 15 minutes.
![*GMT62* *20GMT6201* Mathematics. Unit T6 Paper 2 (With calculator) Higher Tier [GMT62] MONDAY 11 JUNE 3.00 pm 4.15 pm. 1 hour 15 minutes.](/thumbs/87/96675469.jpg "*GMT62* *20GMT6201* Mathematics. Unit T6 Paper 2 (With calculator) Higher Tier [GMT62] MONDAY 11 JUNE 3.00 pm 4.15 pm. 1 hour 15 minutes.")
entre Numer ndidte Numer Mtemtis Generl ertifite Seondry Edution 0 Unit T6 Pper (Wit lultor) Higer Tier [GMT6] MONDAY JUNE 3.00 pm4.5 pm *GMT6* *GMT6* TIME our 5 minutes. INSTRUTIONS TO ANDIDATES Write
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