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Pearson Edexce!lnternationa! GCSE

Centre Number Candidate Number

You must have:Ruler graduated in centimetres and millimetres, protractor, compasses,pen, HB pencil, eraser, calculator. Tracing paper may be used.

Mathematics ALevel 1/2Paper 2H

Y. i-L LJ' \ {,

Higher TierThursday 7 June 2A18 - MorningTime:2 hours

Paper Reference

4MA1IzH

P54695A0201 8 Pearson Education Ltd.

1/1/1/

lnstructionso Use black ink or ball-point pen.o Fill in the boxes at the top of this page with your name,

centre number and candidate number.o Answer all questions.o without sufficient working, correct answers may be awarded no marks.o Answer the questions in the spaces provided

- there may be more space than you need.a Calculators may be used.o You must NOT write anything on the formulae page.

Anything you write on the formulae page will gain NO credit.

lnformationo The total mark for this paper is 100.r The marks for each question are shown in brackets

- use this as a guide as to how much time to spend an each question.

Advice

a Read each question carefully before you start to answer it.o Check your answers if you have time at the end.

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@Pearson

lnternational GCSE Mathematics

Formulae sheet - Higher Tier

X

,:. ,:l

,,/ i.,

,.#/.'6'*{

,ffit'.%,

'.. *4\',)nrt

*T

*,.'

FW

t..:t' '

a.. ,/,'.,'/,''

.-\.., ,/,,' ''/''/.'.::,

,a ./,/' r'.'..,ffi.,

W,/..N.',

::a& .'.Yl

/,ffi..'

&*/g.

,r.'rw,t

.t. ..//,,t/

Arithmetic series

Sum to n terms. .S :'t1 lZa+(n-t)dl

Area of trapezium : l@ * U),

,<o>lAFThe quadratic equation

The solutions of nx2 + bx + c: 0 wherea = 0 are given by:

Trigonometry In any triangle ABC

SineR.ule o = b - 'sinl sinB sinC

Cosine Rule a2 : b2 + c2 -2bccosA

Area of triangle : ! ab sin C

.l

Volume of cone : ' tr:ha.l

Curved surface area of cone

Volume of prism: area of cross section x length

length

Volume of cylinder : rrzhCurved surface areaof cylinder : 2xrh

Volume of sphere : !*'3

Surface area of sphere : 4Tr2

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{v./. &; :.

AnswerALL TWENTY THREE questions.

Write your answers in the spaces provided.

lbu rnust write down all the stages in your working.

1 (a) Make rz the subject of the fbrmula M: ac - hd

l"i ** L3 ts\,

{\-\ 1 :': c},

;\ \*-

?- C*

(b) Sotve the inequality 5x - 4 < 39

d*tr *- b;i.

>- :t- i*--

{ .*-.-)+

.3_

j-i +- L*I

t. L{-3

d.- t"{-'-3i(--'

r -"'->./ \<\.-.. ) s*'

(c) Factorise fully l\e'J'' - 12e3./'

/ 2-l-{*,r-L - \Lq.:'(.-5i'-Zo))1

(Total for Question 1 is 6 marks)

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2 Work out the difference between the largest share and the smallest share when 3450 yenis divided in the ratios 2:6 :V 2+4"--1 = t S

3 r+Sa + tS : 23c'

2x23c = +6 G

-?a.23o = i6tc

t6ro*'*6a

I t, S<3 yen

(Total for Question 2 is 3 marks)

3 Gopal is paid 20000 rupees each month.Jamuna is paid 19200 rupees each month.

Gopal and Jamuna are both given an increase in their monthly pay.After the increase, they are both paid the same amount each month.

Gopal was given an increase of }Yo I . O XWork out the percentage increase that Jamuna was given.

ZOc;o€' x l-Ott = Z l6Os

l q zoc 2g :C : 216o q-

€ .e LI6O G= I-l-zS

laZo c

1\,4.^\h-irll='^ l" lz-s:, I tZ, S.7-

lz-€ "n

(Total for Question 3 is 4 marks)

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:'rl.:::.,

v'r/ tt.1.'. ,'..' 4 Showthat :.j-1l=tI7856

zt ):

(Tqt?l fqr Qlprfiqr I F I na{\q)

5

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5 In the diagram below, P and Q are points on a circle with cente O.

Diagram NOTaccurately drawn

QT is a tangent to the circle.Angle OP): 19"

Work out the size of angle PQT.Give a reason for each stage of your working.

Z- C'G.P= !:* ( t-sc-'Scc-1',e-s a P<R, ]

I C QA-* aCo (o-^*t *- ;'<br^'e€-rrr

LPGJI*?cl c*

f od.L; c..ctr --l-,.*.c\)

l8 ':=, 72-*

-1 Z'qt:*:e:r Q:estion5is3marks)

;/ ,/.Y.!

,/,":.':.'!.'

":'t'\.y',".)x,.,.

a. ,l\

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The diagram shows two cylinders, A and B.

0.56 ni

A

c'54

XgS*

x=:St-6

Diagram NOTaccurately drawn

Cylinder A has height 1.6m and radius 0.56m.

(a) Work out the curved surface area of cylinder A.Give your answer in m2 correct to 3 significant figures.

C=. ]{-xd:TI-r. l.lz

Arv-*= t?-lt-2.< t'6

s-6 L71

Cylinder B is mathematically similar to cylinder A.The height of cylinder B is 0.6m.

(b) Work out the radius of cylinder B.

=- l -tZaT

I c."^-.-=ot -)

Gr?t}. .'Jrectrang{.e )

s -6s{ i'z1d1

x./o'( \[- \

L r-6 ,l

t'\S<-a\e- "{-'., ctcr'

)

c -2*l\

c-2_1. *{22

_ _I!ot"l for Question 6 is 4 marks)

7

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The students in Class A and in Class B take the same examination.

There are 28 students in Class A and 32 students in Class B.The mean score for all the students in both classes is 72.6The mean score for the students in Class A is 75

(a) Work out the mean score for the students in Class B.

A+c Iz-& t- 32-) >.rz'6 /{r 3 s6tot*[

A rzr.<=r^!-, = -7 S ".2 B a Z t OC, o,r-rcr-['a-f

E ff\Pr+rr !' 3s( -2) czc - ZZS4

B MzM' e -7O -s32_

11 o:5{e}

The lowest score in Class A is 39The range of scores for Class A is 57The lowest score in Class B is 33The range of scores for Class B is 60

(b) Find the range of scores for all the students in both classes.

A

s3 r-6 c-,

[Z-^o

)q3

f- tctl- : 9<-3S

63t4 t1"3 j

(Total for Question 7 is 7 marks)

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,'x,it ,':'..)i...:':v)

#:.8*)/.'

tuw&i.

'Y//

,w€.

\eilWfr#\F,W

/"YY '

ir.,#.,..:::w';|',,:.,1.'l...:*/:'t,I: "..,.,;t

8

Diagram NOTaccurately drawn

Work out the value of x.Give your answer comect to 3 significant figures. Sct+ Tafr

t2- 6

C?=LSzlZC - +6 S-l

20'5(Total for

-Qg_gg-t'ion 8 is 3 marks)

9 Solve the simultaneous equations

yry:157x-5y:3

><sShow clear algebraic working.

Sr + 53=-7S-I= S:3 : 3

Ar@ (2 :c- :

5F=

ls

-rI6-s

6'S + \3

E-s 6-qQ-s

9 is 3 marks)

c-n

(Total for

v:

9

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8lo 1 :2'

(a) Find the value of n. S) 3a-) 2*+4:

Z' -r-l.L

tLL--n: ........ ... . ..1

txt

(13*)o x 135: l3r

(b) Find the value of ft.

-z+ <- ,-l'1t3 -'r. l3 a 13

k: .-- I t11i\x.a !

g-ojll &r Q-qeqtienJg is J_nlrkq)

10

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\.. .,', :,,

g,'u*/.:*A\68;'t&t

iK.v*ffi

'-.a,r.j,,.;

w'&';

\&@./7

'/ il.'ajYffi

.:?:al!r{Wb/

.:w./.'w

.@,ffi

'ba{W

'1& /.#

1#i);v,/

.,//.:: ..,

,.,,1i:,.,

')1.r/

/t

A solid metal sphere has radius I .5 cm.The mass of the sphere is 109.5 grams.

Work out the density of the sphere"Give your answer correct to 3 significant figures.

t+,""2..J

I Liq. €

cilI -:-r- .

lr--2-*

+''= -*--2<_

I I*>.J

3x- 1.5- : {;}*:'.-^-t.i i*...,1

')j

*7 .*t -s z.-'c

-*l '-l 5-- gtcm3

(Total fo r QF es !i:_o": )):;3 yt;I"il.

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t2

Diagram NOTaccurately drawn

A

The diagram shows a hexagon ABCDEF.BC is parallel to ED.

Work out the size of the obtuse angle DEF.

t-

{-

--"\t-{. i-)\-

,: --\'-_(' \ ,)\-__ .

t 2 i5 f tL l**\-: + {- {_u'r\ L--e"'* r- \u'. \ /

l 3 5'*' ( iult--ru:,'. u-] g-tl' \t-.) \

I Lz'r(* l

L.. *r*;".--'1 t--1.{z --.-J

,"' ,-*-e. -'L r.:; (, a-=', r---i | .- s .-.r-{ t:i;''^'' ) -.. -.- \--.

4 Y-. I -?c" *' i /-t*"

Sd:r, "r a t f th.+'+* r+- z-** I :3 :

**.

(Total fgr Question 12 is 5 m,ar_lls)

E 42"

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:flk*K

\. &&ltu4

ffi:,F

/..k':''4"J

,,tll''''.

Feiix has l0 cards.There are 5 red cards, 4 blue cards and I green card.

Felix takes at random one of the cards.He does not replace the card.Felix then takes at random a second card.

(a) Complete the probability tree diagram.

First card Second card

red

blue y

green

red #

blue .*

green

red

blue

green

(b) Work out the probability that Felix takes at least one blue card and no green card.

13

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+*t

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! i-: <:JiL' r,.

"? iar

--" &..4* i

t**t '.."+

2.. c-)

.:|'v- ji -

*1

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<'"-1 ,-'; \.

{33

_" _ _ " (:!o!:)_!:.:"_9t"*p,Ji-"-t-*9":r F*w:yA*** " -- "

€il c,

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M (a) Complete the table of values for y : x3 - 2x2 - 3x + 4

t_;i;

,:l . .,1.

'.,../;,'

fi:

t'*'*1.

w""(H,

@'r'

B'q.:fu..

L*t=-.

(b) on the grid, draw the graph of y : x3 -2x2- 3x * 4 for values ofx from _2to 3

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,l'*a ,'

,,1:(::. ,"' ,'

,/ . ,/:',,L',:

'/'.'':'.

P54695A01424

.&.,'' &&3/'

. ':;&;.

'w\w'/. .4.6

W

./r&:'..fnLIA/,:/.

(c) By drawing a suitable straight line on the grid,find estimates for the solutions of the equationGive your solutions correct to I decimal place.

-Dr"***

*r'gr.a*:L-.. \l ,;' ":X- *?"'-:*'"-)

x3-2x2-x+I:o

3

.t1 -':-

?,.-.: _-/-4t1

\,

+3

t-i r, r-'r{.

lrl*1_f ..- _^ -r'i--i

-(r-7-.c*;-

\ .,L- L:ilL

+-'

e : 8.31 correct to 2 decimal places

f :0.65 correct to 2 decimal places

Work out the lower bound for the value of e - f

\_:)q r: -- *'- J

-F--yj"Ilp:-9y:yli":,-!.!--b-[":p-r-r-$)

t*f, f:*-t '

jr: **r.-r'cj

,, ilI

ll!I

Show your working clearly. r e----_

' I *'v\ v'Lo'tot''d

q". - -?rq {.5

I

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(a) Find a formula for R in terms of /.

zA+<.

2- = [2--*

ab t =ZJC ? Yu-

V-.2-5Q= "2-2-st

#'l

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P54695A01624

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Given also that R: *(b) show that / is inversely proportional to Jx for / > 0

2.s+t -: 8S>c

L- r625;t-

i t<-t-\ 2.S, =s-It I

:-)-vr--

.S J=

q2t

(Tqtrl -rqr Qq-$tigq 16 ry 5 qrqrh ) "

17

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l7 !:x3-2x2-15;r+5dv(a) Find:dx

oq:3>:a u-,;.-rsC is the curve with equation y : x3 - 2x2 - 15x + 5

(b) work out the range of values of x for which c has a negative gradient.

O1-"

ds-

\,

'At2

-# tt.nr."' f,^ 3 F-i, tt

3J- k--r< ls(3'.+s)(e. - =)

S sE- -^ 33

s- -3

lsc',

{4}

(Total for Question 17 is 6 marks)

.,s3

t8

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/")L>

',rI

tg'".. ./.:

v

,r44w'

tu\, ./,

w//1ffi:l

w

A triangle has sides of length 8cm, l0cm and l4cm.

Work out the size of the largest angle of the triangle.Give your answer correct to I decimal place.

{-)C, c'"'r I k*c---r

t **"" 'y]

. -{- .{.,lcr_:l{'j \ L-t' 3,*

\'.\,./

A-4\

\tt

;-f,..-t / n(*u-.5 / -

l-'+lC,t- {t+.?-

$r.-\2 >r':fn l*'l

t

\.(: i --s' o

Gqqlfqr 9,leqtlq! .19 !! l nlrlil) _

J l-.I qjLr-{Ee...S L

l

\'Ltt t \_-

1LLbt -f L

Z-'a u

\,,,

Y t*\'S3{

-")^4_--

--{.-

Llr

r r\L, ( L-*..: /1

srpc,5it;"s rt*q-

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19 The diagram shows a triangular prism.

Diagram NOTaccurately drawn

AF: l0cm, AB:24cm and BC: Scm.Angle MB : angle ADC: angle BCD : 90"

Wbrk out the size of the angle between the line BE and the plane ABCD.Give your answer correct to I decimal place.

D68cr"^

A

DB= 8.{E<h

)C : ta--t-' ( lo8.,18

I "[ia- - 2 t-s<R

t-6(Total for Question 19 is 3 marks)

24cm

2-W- '\

20

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20 The histogram shows information about the bith weights of some babies.

s'e

t+€>

Frequenc&,density

2o

tTlol4-;r- I' \J-0 0.=2345#.f's- wei:lt (ks'ffi"

,,^*--<i-tr^ 1-<_lo._rr r-'Chttr -6 of these babies had a birth weight less than 2.5kg or greater than 4kg.

work out the number of babies who had a birth weight between 2.5kg and 4 kg.

2 )2-srp--J S

4,*- >< C -S t-ilc2<J = 63x : €,

E=2-<€,. < t- lCt+t*- -Sq\4c'<- f-" f.a.*-?-

Gs-t)* (o .r-y>< +-) Y(u-z>. s<,1

+ (o.Yx3 o)

+2_

t+z(ToFJ for Questigl?0 is 3 marks)_

"_"....".""'___-

4., .",.'.4/ ',//t..:,

^;1,/

21

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2t (a) Show that J+s + Jn = sJiShow your working clearly.

f,{--{T r ,fC>- d:s

= 3is + Z {g : S.Js*

)(b) Express -; " in the form

vJ-rp+Ja

I"ff#fi1liiffir:;il:,] 2-_ ,.(gj1]'f 3 - t ( {3:-+-l )

= 2G'Y2- -= Z{€1 2-

3 +{5-.lT* {

le! + d3..t U\

9bt

(c) Express x' + 6Jix - 1 in the form (x + a)2 + fiShow your working clearly.

,/ ^L

= t.-F + 3{- ) -rat?-(=*;s-f,) - ia

__. (Total for Question 21 is 6 marks) __----

22

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Diagram NOTaccurately drawn

A, D, B and E are points on a circle, centre O.AFBC, OEC and OFD are straight lines.

AF:7 cm, FB: 4cm, BC : 5cm, FD:2cnn and CE: xcm.

Work out the value of x.Show your working clearly.

(Total for Qrfegjion 22 is,9 marks) ._*--.

?u--"*j**- *:*"-:;' (

--'"t- L

23

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23 The sum of the first 48 terms of an arithmetic series is 4 times the surn of the first36 terms of the same series.

Find the sum of the first 30 terms of this series.

S^ ? + (Z* r*(^ -1) "t)Sq* 2-+ (Z* -r- Lr--l d )

+- 3 =J)S=s j,.} (Z-^

z+ (t^ {- +*l'*) ': Lrx' }g (z--€sr)

t+8- -t- | | 2-ACIt ':. I L+Lt- 61- f

+ l3A2.c,\.

r3:13.d_*q(

2Stc'c"\

l-/

I+--.Scl

3 (:l ( Z1< *t + .-SC!-r-- 2*n, "'\ I2-\

tSzq Cr/-i

TOTAL FOR PAPER IS 1OO MARKS

23 is 5 marks

24

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