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Pearson EdexcelLevel 1/Level 2 GCSE (9-1 )

MathematicsPaper 3 (Calculator)

Higher TierWednesday B November 2017 - Morning i Paoer Rererence

Time: t hour 30 minutes | 1 MA 1 l3HYou must have: Ruler graduated in centimetres and millimetres,protractor, pair of compasses, pen, HB pencil, eraser, calculator.Tracing paper may be used.

t*:"1fl"1,t6/6/6/7/2/2/

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@

lnstructionso Use black ink or ball-point pen.. Fil! in the boxes at the top of this page with your name/

centre number and candidate number.Answer all questions.

Answer the questions in the spaces provided

- there may be more space than you need.

You must show all your working.Diagrams are NOT accurately drawn, unless otherwise indicated.Calculators may be used.lf your calculator does not have a z button, take the value of n to be3.142 unless the question instructs otherwise.

lnformationo The total mark for this paper is B0

o 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

a Read each question carefully before you start to answer it.o Keep an eye on the time.o Try to answer every question.a Check your answers if you have time at the end.

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AnswerALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 The table shows information about the heights of 80 children.

130<ft<140

140<1,<150

, 150 1, < 160

160<ft<170' t7o < /? < 180

(a) Find the class interval that contains the median.

! of f,o= +o

Frequency

4

ll24

22

t9

(b) Draw a frequency polygon for the information in the table.

Frequency

_l

:G*dohvo fiqwYtl--\' t hrstsl1s ( hetghti

3q J6 ( <-+ofrpt

I'vTEQVTL

16o<^ll"O

(Total for Question I is 3 marks)

Sra*rortr furuE

o(AqlntBenr aEN

M,DPorrJTSoF 6*es

Height (ft cm)

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3

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In London, 1 litre of petrol costs 108.9pIn New York, I US gallon of petrol costs $2.83

I US gallon = 3.785 litresf,l : $1.46

In which city is petrol better value for money, London or New York?You must show your working.

Lonao.r ll,lra -*f .Otq

-Ir. ton"lor-. ,l- casls

$ 6.,o2 Fv eq.[[o r-r

C" NY ,f on[y trrsf $ l'4 t-'." lrlY ri LretFor_rr4luc.

. x 3.-785 = t +. t2t 865 Fr aqil

)rr.*a= { b.or7q*1

(Total for Question 2 is 3 marks)

3 A gold bar.has a mass of 12.5 kg.

The density of gold is 19.3 g/"m'

Work out the volume of the gold bar.

Give your answer correct to@

Vol = rltqss

Cler...e,}qonvQ,tgfons: | 2, 5 *, lOoO s lzso 3"eP-s

: t{SOO 3 6q,71668rq . 6

(Total for Qyestiol3 -is 3 lnarlrs]

;l'+6

Vo [,r nn.

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4 There are only blue pens, green pens and red pens in a box.

The ratio of the number of blue pens to the number of green pens is 2 : 5The ratio of the number of green pens to the number of red pens is 4 : I

There are less than 100 pens in the box.

What is the greatest possible number of red pens in the box?

blua '. quen-#2-: s+: to6: rs

Q+h-o.

5 (a) Find the value of the Eqiprocal of 1.6Give your answer as a decimal.

Jess rounds a number, x, to one decimal place.The result is 9.8

(b) Write down the error interval for x.

qte^, 14..(+:lg LLt2 : 3

=J_t-6

= O,6aS

q,7ss )<< q.s5

(Total for Question 5 is 3

Saynenu*tltafof q{ee-n,

1.+: 6o:tS

1-8 5

T;tr%,,tr;r ffiflt ilt lilltffi ilil flilt ]ilil ilt llilt lill il1il llil llltP 4I314 A 0 4 2 0

t-

6 Here is a rectangle.x +-I

The length of the rectangle is 7 cm longer than the width of the rectangle.

4 of these rectangles are used to make this 8-sided shape.

*+1-T_ = 7

a+7The perimeter of the 8-sided shape is 70cm.

Work out the area of the 8-sided shape.

,(+L+-l+x+-?+)t+?+t +Xt? +I +7+)S+l =5670a(?.S

€N*42=8x =

X=

x=f,.$ k,ns = ro -S r 3 .s = J6-lso,il

Skop e [T'o s =+x= t+-Z

--::

36"7Szcwl

t+ rorhan3las

rue|&Lglq{&n 6 is s qtrEl:

Ifl]tiltilt liltillt ilil flil]l]tiltllil lilfl ilIililililt5

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Work out (13.8 x 107) x (5.4 x lQ-tz)Give your answer as ang$rtnYlgej:, = 7.+SZx lO+

=sr|?t+s 2_

ffi tl

0 apl t;r(n zqn s

= 0,0007+s L(Total for Question 7 is 2 marks)

t 'ltG nurn

Z-l

-tm

I

(n

Eff!

t-;

d.:

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8 When a drawing pin is dropped it can land point down or point up.

Lucy, Mel and Tom each dropped the drawing pin a number of times.

The table shows the number of times the drawing pin landed point down and the numberof times the drawing pin larrded point up for each person.

Lucy Mel Tom

point down 31 53 16 i O O

point up 14 27 g 5A

.tat{^t +5 + 8O -F -25 =l5O-Rachael is going to drop the drawing pin once.

(a) Whose results will give the best estimate for the probability that the drawing pin willland point up?Give a reason for your answer.

l'hr-[ Stues l*to la:sf eshrnal4 beccut;tt;- sha tla rea &tz

drdr^J.,^t Pr,rr #he ltqg numbe r o{ lbqStuart is going to drop the drawing pin twice.

(b) Use all the results in the table to work out an estimate for the probability that the

drawing pin will land point up the first time and point down the second time.

Usc13 4[ [ +ho ra sl,lfS , T*te- P,,^ po rrlte-d doq IOO hrno s

t44a ?r^ pnied u? 50 hmr5

t?lat :lSO l1aro,^rSP (p,^ ,p), ,*{;, = *? t,.,n do^r,i = 99-- = zrso 3

Pip,,l up t g,noto^,^'l 3 i x ? =,3--(ffitat16r Question 8 is 3 marks)

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7

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Jack bought a new boat for f12500

The value, € 4 of Jack's boat at the end of n years is given by the formula

V: 12500 x (0.85),,

(a) At the end of how many years was the value of Jack's boat first less than 50% of thevalue of the boat when it was new?

o l.t"t( o+ boc^fs Yolva = * aZSO

ttr2s6= tzsoox o'8Sn

o,S = 0.glno Os,nj1 .fr.,.ia-l ar^d ,ryrProvernafr, Vy d^trerelf

yatrds €br ^ .

0,853=O,6t+---. (bob,q) 5Yn'^ t_u \t' . uolue LESS

A savings account pays interest at arate of Ro/o per year.Jack invests f,5500 in the account for one year.

At the end of the year, Jack pays tax on the interest at a rate of 40yo.After paying tax, he gets f79.20

(b) Work out the value of R.

lnfeasf = t z?'20 qftu +oZ Lt*t off.

6oZ =t71 'aot% = f t.3z

too'/o =l tSz

t32 = 55OD x (0,o?+ = 2

/xroov2. +7"

.

-

-_

Gg,lqlfqf Qqqstion ?_lp 5 qrarks)

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o

2 4/"!-1 |

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There are only blue counters, yellow counters, green counters and red counters in a bag.A counter is taken at random from the bag.

The table shows the probabilities of getting a blue counter or a yellow counter or a green counter.

(a) Work out the probability of getting a red counter.

{4

1*zLu

5L

?

oLJ

€_qr-h c*llorl,r-. mus-f be a ,^t-{note_ nu m*_r o€

(ot nvparly cxclvsrirc. e,'tc-*ls, probab'i'hnn ADO U? tO 1

I - (o-zro.3S + o-+\ = o'oS.. O...'. OS

t, Itel

(b) What is the least possible number of counters in the bag?You must give a reason for your answer.

I

{o-

G q,t teost .?O counlers rn b.qto hataa a O.OS chorrce e*fleth^g t f<d.

o.os = ,-fr 12- /t,rt,st Itorl.c

(Total for Question L0 is 3 marks)

yellow

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7

9

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The cumulative frequency graph shows information about the weights of 60 potatoes.

ll ?ob

) 6t3

40

Cumulativefrequency

30

30 40 s0 5?60 70 I

Weight (g)

(a) Use the graph to find an estimate for the median weight.

Jamil says,

"80 - 40 : 40 so the range of the weights is 40 g."

(b) Is Jamil correct?You must give a reason for your answer.

Hu m',gh+ d b" leacor*$e +he

o( Y+\e nnrh ruor1ht co vld tne

5?*

r14x rucr1ht could be rzss ttan tO

less klra^ l+O.

-l

10

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tu

u:

Fzul*-

=t*L

o

UJ!c

*t:ZrltFE.tst-ozo'a

ur

tn

ZIII

F

fr

(c) show that less than25Yo of the potatoes have a weight greater than 65 g'

?:s'/o "l 60 : lS goheJtDe S

I t oota.va t\ ri less Hton I-So/o€

See graPh

i:i

(roldtqr"Qqqsjio! 11 is 1 ryqlk!) *--

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I

t2 Alan has two spinners, spinner A and spinner B.Each spinner can land on only red or white.

The probability that spinner A will land on red is 0.25The probability that spinner B will land on red is 0.6

The probability tree diagram shows this information.

Spinner A Spinner B

red ?LetL)

white ? (A, [d )Alan spins spinner A once and he spins spinner B once.He does this a number of times.

The number of times both spinners land on red is 24

Work out an estimate for the number of times both spinners land on white.

R f Ar R.) . o.zS x 0.6 = o.! S (av hmes)

?(u/u):o.7Sxo-t{ 3O'3\ ,

Oo.,bl. probah,l'lq ;

6+ UIN *npornYb l.tQ

So zx{)ecF sp,na er b i

[a nd a^ i+ tl-rr rjr

2x&Q = +gg: ,e-l-F4 ,

LFg

12

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lrl&t4

F4;

=bZLJ

IJJ

{n

F4lllts0c

ozoc

{UJ

afl

+

tuF.

ex

F$ar

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13 Write xz + 6x - 7 in the form

lunr | ,/eLvatc+z

(r+ 3) +0

(**3)aq -vt^--J

4 ho ntan\t-r hon bradtels<-xponJo A N

(x + a)z + b where a andb are integers.

*7 r.*j )'= y-"o6r+Q

I for Ouestion 13 irs 2 marks

14 Cone A and cone B are mathematically similar'The ratio of the volume of cone A to the volume of cone B is 27 : 8

The surface area ofeone A is 297 erfi

Show that the surface area of conq B is 132 cm2

gs

' volvmascale'btjpr

sf=

5 u r6at0

A/^Q ator- A G*B

3,q 1

i,f3 =

: S.A (&"e 6

r SFz

U

t'5

= 6",$grea x 3r"Olt q

3.s?5 ,

)"r'l

a(L4fcr^. k-€o,clo r

zr's

* -(Tq1a^!*for

Qugrtion 14 iqlgg.tr) - -Af e-A

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15 (a) Show that the equation x3 +'|x - 5 : 0

rub L= / O jt

7xo -S

st,b x:l fj+7*l -5

has a solution betweenx : 0 and.r : I

= - 5 \ a,or. cy.4.r1q1 shor^rSt-!---

=*2 tZr - gtzta.t +$-e' Xra1ln eroSscS

llna x 4o4s ba?woettl"l-

ahertcQ' asol-hsv'r

i?r

(b) Show that the equation x3 + 7x- 5 - 0 can be amanged to give *: fi1

lc3+?rc-S =6rJ*t

a_

x(r5 t7*z + tx-)

5

btaelu-t tA

(rL * 1.)

5\

sq':*

1a +?rq

(c) Starting with x, : 1, use the iteration formula xn+t

an estimate for the solution of x3 + 7x - 5 : 0

5=O

= O.(o.ozsz+ ?

5x3

6t65327

= 0,b-?ouq,63co I

o_ :6-?O-au83OO

i,Lt

three times to findxz +7n

62Sxr

7z-

lo + -l

5

(o.eress27.--)i:

{Ji

oowt ttOuruglTIESE

NornBros t

t-a.Ji orrf c,l.lilililrJltl|tllulfiuilltJiluilil]tllil]illllillJlilililffi 'f,i,fi],,*. '_l

t-

(d) By substituting your answer to part (c) into x3 + 7x - 5,

comment on the accuracy of your estimate for the solution to x3 + 7x - 5 : 0

16 The petrol consumption of a car, in litres per 100 kilometres, is given by the formula

100 x Number of litres of petrol usedPetrol consumption :

Number of kilometres travelled

Nathan's car travelled 148 kilometres, correct to 3 significant figures.The car used 11.8 litres of petrol, correct to 3 significant figures.

Nathan says,

"My car used less than 8 litres of petrol per 100 kilometres."

w

t"L+?, sl-owQr

b orrncll.

r+e-5

tt-8sPPNtDOurrO.

tt.1sl-c.rrlelb6und

0pw

Nothan cor,,td bo wrry baco,ttse trv'?(W bou$ $ 0vo!8 l'kaS '._.1

(Total for Question 16 is 3 marks)

,-3,( o, o?o,ue6 Boo !) F 7n(a, b ?0,+u3 3oo t) : S

= : 5. Lt t *7 x[CJ- " =

Thr's B{vtk occvraf,e because

Could Nathan be wrong?You must show how you get your answer.

tOex [,t'roSeU*r)

Wupkr)

=t0Ox It'?Er+8.5

= V, 4wWs7

) ' ilOc ,.Iryq= r:.rror)

hrn (oourar)

= ilqo--ry- 1-li?5t+7'S

= g. b336?s

@_,OO5,LLqLfB

ans Ler Ls closa lo zud'''(Total for Question 15 is O ,rru.t rl

,(uL"r-3.863

n I [ / \. rvv^lqrlcJtl

i#r"p fn ^

( [","'r) = -ffi{e p, op(M,bouncl rrt r;s5fij

15I

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I

17 ABC and ADC are triangles.

?o. tu-ayrone'/1rU/T\ '\i,

A^AlatrcJiuoengLav\d b

The area of triangle ADC is 56m2

Work out the length of AB.Give your answer correct to I decimal place.

@ Us,"q Cosne Auh ID 6,rcI AC.g

N_' = : Jz r eC r:

2*tl ^Cp ^G

S {0SL

M- = aq2 -il33l 7o2 *, f--

AC = tf.o 4t4036 LL . v !

,A f)hr>

o A &<a of l"i""E/*,

i " ill x (D S,,r ( {C5) = 56.

- 5.Bta5qeattSxCE - SL,,, { \\t1 i :-

\, l.CD = to-S+oq qSs+l

Srn a+3

AB

AC':_

Stn ;r?\, xSrrr 46UL

= l1'oqi1036$ xS,.,tl-B$ut J! I

lL|, 3 E S 63 z(g

|L.! crap) @d^ ot@{,

Xi,L . LL.t").....m

(Total for Question 17 is 5 marks)

6;-Ui't/--e'=bt* t- 2bc(o. A^i

16

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lilt

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18 Here is a speed-time graph for a train.

:+-

rl1,L\

F{",.gi

5fiE

:::i

Areq kageaorng, b+u)Lh=b(SY0xS= t?'5n-

hca llrarlelrurf'l= lca*)rh= L(o5tr 5= 37- Srn

Speed (m/s)lvadhtrSte=*xb*Vt

of kopertulns o*d i-r.{an6!e, .

i*5 x?

=Sn

Time (s)

(a) Work out an estimate forUse 4 strips of equal widthrl f ni.l O nQ.il Ul.rDE€. GaAPH by 0tvtg61-

INro Trar ft ,\xrLE}- F T2.A. PEzr urn S .

Drshornce = 5+ll-S *3?.5r?O : [30'n

r30

(b) Is your answer to (a) an underestimate or an overestimate of the actual distance thetrain travelled?Give a reason for your answer.

O-vo*sHrncrfa l>eca.** crrva Soas bnd* .d3 o-

Nnnfnnpt=L,./t+$it- lttt rto)

= 70 rtt

iii

(Tgtal f91QgS$io_q 18_.,1 _4,ryrk$_

1

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19 Prove algebraically that the straight line with equation x - 2y : lO is a tangent to the

@d

+

6\t?

circle with equation x2 + yz = 29

# <tuahon y-- zl = r o rs ^

't-6rngcnt

L^,d haro a Comnlorl Sotulz&a 4 }Se

L'*5t = 20 @

z--2S = ro e T=r.Reorcalge@ x Fro+2t.O

S.,b O,n @

(,o*"3f + S- = 2o

[oOo uO3 r 4y'* h"= ZO

vY*=gV : - t-t''

-=-_-

i

W@n #.y [o.r&Am uf, ha n€clts e(ua.l'Dns ..

Io

,2.{

= loO ++O3ttUyL

5\"+ r+o.{ + 8O = d t -,6ql"oNso

[o solveJ J ' -ott x =16

5 ( U'* 53 +'il6)= 6 't" $ = qro

s ( g+ LL l(t {- +) = d L'ro 2uadrdtl 6rn'o[a '

qJ

0nly 1Sotuhovt *orddI orlcl hna Susf taoch/irosJoi rn LpLace;i,,-I 9'rltwt be.AAN6EN I

/:

(Total for Question 19 is 5 marks)

rco \'zo3

@ S"U y=-S tntno @I-lO+Zx-+

= tD _g

= 2. /ffi, Grcta e^d fu^pqti:,nhssod ./\? \-^'\,rL ;t irrq"], _s

18

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20

A, B and C are points on the circumference of a circle, centre O.AOB is a diameter of the circle.

Prove that angle ACB is 90You must not use any circle theorems in your proof.

O Drvtde mhD { rsosce,les -{rianqLasd.

AOL = rgo_ ?r buat* hsa ondes of an mXekS hia

""d *t eb in

^"fNarrSle add lo LW'. *

o{QE

CoB=14.-2.1bot.-t9'ln&ntJ6s(ol"stnandeora-J ;; ;A;t-i''r a't""qL "dd t'r8'0". "

L+x*3"j=[gC2r+ 23 = t-?O"

e(L*j)= tfo" );

t*-J = 10' V

Ac-B=**j=1C"

barou:o -gt.t tn a hi odu add to lg0o

be qo '.

__ (Totd for Que!tion?0"is1gpf$)_

19

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2t

OAN, AMiB and,APB are straight lines.GMis the midpoint of OB.

OA=a OB:bfr : kfr whereft is a scalar quantity..

Giv,en that l/Pl/is a straight ling, find the value of ft.

s" m*a/\d tt^UNe ludtte-l'

-)AB =-4.+b=b-O,AP r h(&)=k(b-a)d =-fr+oVr*V

=' -ib +a + K (b-q), -+

^,t ; -\ffi +- oi

\ _-\ff nU aad np pretbl.ril mrsl^bo rnutl'rlO.s ol ,irch sftlar-rn l4z

of (6q-b).

ffi =-ib ra-+ k0-a)

=-Ib+a+kb-Ka'= (K-ilb + (t -kh-=(t- rc)a + Ctt-t) b

. 6 hytnes

l-Kt-K

l+ 5(5n

tonger rn o. duec-hl

= -(.(R-L) *=-6K+ 3. 2 o!rur=3

1 J- r

TOTAL FOR PA.PER IS 80 MARKS

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