Mathematics A Level 1/2 Paper 1H
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1 Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Level 1/2 Paper 1H Centre Number Sample assessment material for first teaching September 2016 Time: 2 hours Candidate Number Higher Tier Paper Reference 4MA1/1H You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Without sufficient working, correct answers may be awarded no marks. Answer the questions in the spaces provided there may be more space than you need. Calculators may be used. You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit. Information The total mark for this paper is 100. The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Advice Read each question carefully before you start to answer it. Check your answers if you have time at the end. Turn over S51832A 2016 Pearson Education Ltd. 1/2/1/ #$%&'()$')! Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs)
2 :%'#01$#'2*3$%'$3 #$%&$!$%'(#)*$"! $+$!, $-,#$.$/!$0$12$3 90$*>5&?%&#'2*$>5&#'(" 45'$)&6"%7&8)$&9$#', $.$%'$.$($+$:$;5'('$ #$¹ x = b ± 2 b 4ac 2a + % # ) * ( B()51$*(;*2("$$+$ 1 3 πr, &,5%C$?*35%;&2$*&%$&*(;*2("$$+$πrl l B()51$*(;*2@)'"?$%$+$πr, &,,5%C$?*35%;&2$*&%$&* (;*2@)'"?$%*+$,πrh r #$%"&#'("&)*+,-.*/�$1&#'23 r 4(%15)&$*30$$#*6*7'80$%*9'$% & & :%$&*(;*#%&<$='51$+$ 1 2 /#$.$%2& & *&"@*#%'&"8)$*# a b c -'"$*A5)$** = = sina sin B sinc,(3'"$*a5)$$$#, $+$%, $.$(, $0$,%(B&) ) :%$&*(;*#%'&"8)$*+$ 1 #% ) B()51$*(;*<%'31$ +$<('<$&9$B(&))$)'B%7&8$ 6'8=%5 B(&))$ )'B%7&8 B()51$*(;*3<0$%$*+$ 4 3 πrc # % 6'8=%5-5%;&2$*&%$&*(;*3<0$%$*+$Dπr, r 2 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()'')!
3 #$%&'!((')*+,)-')./++'01%#234"#5 A! G! C'))/D!E-F50!*)2!G*-'6!64*,'!6#-'!-#)'/!5)!04'!,*05#6!H!I!J!I!>! $-B4! K! Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 3 Turn over #$%&'()&')!
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earson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()*')!
5 !! "#$%&!'()$*+!,-!'(.%/!(0!1%&(2/3! 4%!56#7!8,9!0(:!%6;*!'(.3! <*%:%!=%:%!,-!1%&(2/!#2!%6;*!'(.3! "#$%&!/(&7! 3 4!(0!+*%!1%&(2/!0(:!8,3>?!%6;*3! 4%!/(&7!6&&!+*%!(+*%:!1%&(2/!6+!6!:%7);%7!5:#;%3! 4%!167%!62!(@%:6&&!5:(0#+!(0!,9A! B(:C!()+!*(=!1);*#$%&!/(&7!%6;*!:%7);%7!5:#;%!1%&(2!0(:3 8! "#$%&'()$*(+,-.%/$0(!(/.(1(2&*3.4 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 5 Turn over #$%&'()#')!
6 !! "#$!%&'$%!()*!+,-.(##$#!/,!+,)#/%&+/!/0$!12#$+/,%!,3!()4'$!#5! 6,&!-&#/!#0,7!(''!8,&%!+,)#/%&+/2,)!'2)$#5 5! 9(:! ;(+/,%2#$!3&''8!!!<=$ > B 91:!C,'D$!!!& C0,7!+'$(%!('4$1%(2+!7,%H2)45 "! "#$%&'()$*(+,-.%/$0(!(/.(1(2&*3.4 # " "64 "#$%&'()$*(+,-.%/$0(5(/.(!(2&*3.4 6 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()*')!
7 !!! ()* "#$%&' " #! 8-3&03-12!192!327.19!:;!$! <,=2!4:0/!-7>62/!&://2&1!1:!(!>,.7,;,&-71!;,.0/2>$ D92!7:/'-3!A/,&2!:;!-!',E2/!,>!/250&25!B4!FF$)G!5:33-/>$! H:/I!:01!192!7:/'-3!A/,&2!:;!192!',E2/$ +,-./-'#$! -&&0/-1234!5/-67 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&' %$&'()*+&,*-./0'1&2*!*10*3*4(,506 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5:33-/> %$&'()*+&,*-./0'1&2*7*10*3*4(,506 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 7 Turn over #$%&'()*')!
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earson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()%')! -23(%$"43,"56'7(*3&"*7"8"+%,.7/
9 #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! "#$%& '#(%&! " )*+,-+&!#$%! +%%.-+/012!3-+45! 670!3*+,-+&!87948!+!87+:0!&+30!;-9&!/-*+5,10!#"!!+53!+!80&*%*-%10!4*/7!3*+&0/0-!#! 6-*+5,10!#"!!*8!-*,7/<+5,103!+/# $ #"!=!'#(!%&!+53!#!!=#$!%&#! >+1%.1+/0!/70!+-0+!9;!/70!87+:0#!?*@0!29.-!+5840-!%9--0%/!/9!A!8*,5*;*%+5/!;*,.-08# #######################################################%& B! &%'()*+,'-+./01(2' )-617 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 9 Turn over #$%&'()*')!
10 !!! "#$%&'!%&'!()*$+),-!!!.!!/!01!.!!2!31!.!!/!31!5! "#$%&'()$*(+,-.%/$0(!!(/.(1(2&*3.4 A3!!!!AB!!!!=C!!!!A3!!!!=D!!!!AC!!!!AC!!!!=E!!!!=F!!!!AA!!!!A=!.%1! J:>6!%+(:!$+%-(!>%(?68>%++4! O)P6!%!76%(:&!,:7!-:I7!%&(Q " "!4 "#$%&'()$*(+,-.%/$0(!5(/.(6(2&* Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()$)')!
11 (a) Find an equation of the line that passes through the points ( 3, 5) and (1, 2)!! "#$%!&'()!*+,-%)!#+!./%!0')1!!2!#$!3!%!-/%)%&!4!#!*+5!%!*)%!#+.%6%),7! 8#+%!&! '/*,!%9(*.#'+!!$!3!:"!2!;!! 8#+%!& ( '/*,!%9(*.#'+''<$!2!="!3!>!?@A!B/'-!./*.!&!!#,!C%)C%+5#D(E*)!.'!& ( #$% #(% #)*+,-'.*/'0123+4*5''43'6'7,/83% Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 11!! Turn over #$%&'()$$')!
12 ! "#$!#%&'()*+,!&#(-&!%./(*,+'%(.!+0(1'!'#$!#$%)#'&!(/!&(,$!'(,+'(!23+.'&4 68!23+.'&!#+B$!+!#$%)#'!(/!3$&&!'#+.!65!<,4! C(*D!(1'!'#$!'('+3!.1,0$*!(/!23+.'& :$%)#'!;<,= #$%&'()*%+),-./&0%1))0/)2)3'+4/5 12 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()$'')!
13 ! "!#$%&'()*+'#!+',(!-'.!'!+$()&-!/0!1!!2$&#$.!'(3!'!,43&-!/0!5!!2$&#$.6! 7-$!+',(!-'.!'!8'&-!/0!,43&-!9!2$&#$!/(!&-#$$!/0!4&.!.43$.!'.!.-/,(!4(!&-$!34')#'26!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 92 5!!2! 7-$!&/&'+!'#$'!/0!&-$!+',(!'(3!&-$!8'&-!4.!9==!2 5!! 5!B!C!!D!EF!G!=! 1!!2 :',( ;4')#'2!#$%! '%%*#'&$+<!3#',( &'( &"( &%)*+,-.)/-0123*4) /83( Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 13 Turn over #$%&'()$&')!
14 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!%! #66!!!)53!$!)+0!78(5/9!85!)!-(+-10:! %#!(9!)!/)5*05/!/8!/;0!-(+-10:! <5*10!%#$!=!$&%! <5*10!$!=#$% $ $&%! >)1-.1)/0!/;0!9(?0!8@!)5*10!#$":! A(B0!)!+0)985!@8+!0)-;!9/)*0!8@!28.+!48+C(5*:! "#$% # " '()*+),!#$%! )--.+)/012!3+)45 ::::::::::::::::::::::::::::::::::::::::::::::::::::::: % &%'()*+,'-+./01(2' ) Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()$*')!
15 ! y " a = b c!!!#!$"!%&''(%)!)&!*+,-+.+%/-)!.+,0'(*1! "!#$!%&''(%)!)&!*+,-+.+%/-)!.+,0'(*1! #!#!2$!%&''(%)!)&!*+,-+.+%/-)!.+,0'(*1! 3&'4!&0)!)5(!6&7('!8&0-9!.&'!)5(!:/60(!&.!$1! ;+:(!<&0'!/-*7('!%&''(%)!)&!*+,-+.+%/-)!.+,0'(*1! =5&7!<&0'!7&'4+-,!%6(/'6< #$%&'()*%+),-./&0%1))0/)2)3'+4/5 2 x 1 a!6! =5&7!)5/)! 3 ( x 1) 3x + 2 can be written as where a and b are integers. x + b #$%&'()*%+),-./&0%1)!6)0/)7)3'+4/5 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 15 Turn over #$%&'()$#')!
16 ! "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! #! 12+!.#$%&$'!324/3!$!34,#.!(40+5! 12+!6$3+!47!*2+!(40+!#3!$!24͈*$,!(#&(,+9!(+0*&+!#9!/#*2!&$.#)3!:5;!('5!!#3!$!.#$'+*+&!47!*2+!6$3+!$0.!#$!#3!*2+!<+&*#($,!2+#%2*!47!*2+!(40+5! A$,(),$*+!*2+!3#8+!47!*2+!$0%,+!!$"5! B#<+!-4)&!$03/+&!(4&&+(*!*4!=!.+(#'$,!C,$(+5 $ "#$%&$'!#$%! $(()&$*+,-!.&$/ D &%'()*+,'-+./01(2' ) Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()$*')!
17 & & &! # #$% '()&*+,-.,/&0(120&3,.4&15&4()&67.8)&2+4(&)97,4+1:&!&;&5% '()&611.*+:,4)0&15&4()&/,<+/7/&31+:4&15&4()&67.8)&,.)&#&$%!,%& =.+4)&*12:&4()&611.*+:,4)0&15&4()&/,<+/7/&31+:4&15&4()&67.8)&2+4(&)97,4+1: & &!+%&!&;&5&>&"% & &!++%&!&;&@5% & & & &!+++%&!&;&5"% '()&67.8)&2+4(&)97,4+1:&!&;&5%&+0&4.,:051./)*&41&-+8)&4()&67.8)&2+4(& )97,4+1:$!&;&5%&A&B!C%&D)06.+C)&4()&4.,:051./,4+1:? "!?????????????????????????????&#&?????????????????????????????% #$%!?????????????????????????????&#&?????????????????????????????% #$%!?????????????????????????????&#&?????????????????????????????% #$%?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? #$% #&'()*+,'-+./01(2' )-61% Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 17 Turn over #$%&'()$*')!
18 2 2! "#$!%&'($!)*+#!$,&-+*./! y = 8x +!#-0!./$!0+-+*./-'1!2.*/+3 x! 4*/5!+#$!%.6.'5*/-+$0!.7!+#*0!0+-+*./-'1!2.*/+3! 8#.)!1.&'!).'9*/:!%;$-';13 < !=! > #$%&'()*%+),-./&0%1))0/)2)3'+4/5 18 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()$%')!
19 !! # "$$ %!# """""""""""""""""""""""""""""""""""""""! "#$ " & $#+&5+'+.)'6/7&-*8 + +&5+6')'00/0+.9+#$8 + +:+"#$ "!# +:+!# " #$ +:+"$$ " %+&5+.;/+69& ;/+0&4/+#"+5-,;+.;'.+#%+<+%"+:+"+<+# + =;93+>1+'+?/,.9)+*/.;92+.;'.+"$+&5+6')'00/0+.9+!%8 $ %&'()'*+%&'+ ',,-)'./01+2)'34 (')*$+",)-"./01*2)3"!21"4"5$-617 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) 19 Turn over #$%&'()$*')!
20 # #$%&"$&#'($)*$+,$+'-&"(#&-.$/#'-#/$-/$01 $ #$02&"$&#'($)*$&"#$/+(#$+'-&"(#&-.$/#'-#/$-/$34 $ 5-,6$&"#$/7($)*$&"#$*-'/&$42$&#'(/$)*$&"-/$+'-&"(#&-.$/#'-#/8 $%&'()#*&+#,-./'0&1##0/#2#3(+4/5 %6%78#96:#;7;<:#=>#?@@#A7:B> 20 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials (SAMs) #$%&'()')')!
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