1MA1-1H-Nov-2017-model-answers

Write your name here Other names

Surname

Centre Number Candidate Number

Pearson Edexcel

Level 1/Level 2 GCSE (9-t )

Mathematics $,^4

Paper 1 (Non-Calculator) ANSwre-P S

Thursday 2 November 2017 - Morning Higher Tier
Time: t hour 30 minutes
t.*r *t"""*

1MA1IlH

You must have: Ruler graduated in centimetres and millimetres,
protractor, pair of compasses, p€fl, HB pencil, eraser.
Tracing paper may be used.

lnstructions

o 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 Answer the questions in the spaces provided

- there may be more spacethan you need.

o You must show allyour working.
o Diagrams are NOT accurately drawn, unless otherwise indicated.
o Calculators may not be used.

lnformation

o The total mark for this paper is 80
r The marks for each question are shown in brackets

- use this as a guide as to how much time to spend on eoch question.

Advice

o 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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Pearson

Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.

I Write 36 as a product of its prime factors.

A\36

l\L": l@\// r,/s\:a

Cr @

2t*3'

(Total for Question I is 2 marks)

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2 Kiaria is 7 years older than Jay. *

Martha is twice as old as Kiaria.

The sum of their three ages is 77

r@,Find the *tio o@us.,"@illPl"

)c trx.t.J +2s -t-\+ '= l-1

t{.u. + >f :' -T -'tr

Lf;C a -7-I -2 (

L+x- = S(
5c : lt-f

Job ; !{uirre A'\ ar+l"..

r + ^. Ll L+2-

r+ -. z-l: +L
-Gp"f*Lkr"Qr"srtrgr-?4-nsrla.nrkls*s) -

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Iurn over N

ABCD is a parallelogram.
EDC is a straight line.
F is the point on AD so that BFE is a straight line.

Angle EFD:35"
Angle DCB:75"

Show that angle ABF:70"

Give a reason for each stage of your working.

Z nFS= 3-s-* ( t-r$cc-tl.-', oPP stt<-
a;e Z"E=o_]
FAK ? -IS*
C =Fpos it* e"gle s

tva pc;bll.-t:Sfu*t

<.q'.^ tr-l )

1S+ 3S- \\Cl*
CC ISC *l tc"l *TC

A( o,q\o-r \e,4. Atr(s

o.dd 6'.- lS.*J

3 is 4 marks

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4 The diagram shows a logo made from three circles.

Each circle has centre O.

IDaisy says that exactly of the logo is shaded,

J

Is Daisy correct?
You must show all your working.

ftrer. v*, hc,t<, c. "'..-[*- }\X [(3 "- l l(fc lT*

/{ ,e* t-t't e"- r "rclq @

A o* r.r',, *dd \x- (./-.l%Pt*- "J-f-r. +t = l(=r:.
@
-= t\X r+1 rl 3

frt** 3L"cdcc{ @ -@,

-< -->SLTf cn4

3-3Tr* r'-s* ^*t a-)6*.*tJ \ UJ fril c{ii-tr-

,lFI

3 .t

$c --l-l-)\ c.-. S -r uS \,{ fC13

--_.J

(Total for Question 4 is 4 marks)

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The table shows information about the weekly earnings of 20 people who work in a shop.

/r^Lq p&L -t{-'--rr:t-
5€*
Weekly earnings (f,x) Frequency

c150<x(250 I 2*a 2*a;

250<x(350 ll 3so 3 3*<e

350<x(450 5 +os 2C,(}t=

450<x(550 0 s*(] c, _g_

550<x(650 3 $** t &'c:c

2e *,1 30o

(a) Work out an estimate for the mean of the weekly earntngs'

fr.S+=*"**e* t'l^e-<;"\r ':: iK*d € -5t.:J.-^> / <rya

2 !l'-s'c

f S65

{3}

Nadiya says,
"The mean may not be the best average to use to represent this information."

(b) Do you agree with Nadiya?

You must justify your answer.

r'fes f,s * ,-{bL "e;- 5 L*-*Qcuv-l
. I--

CL\

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)('R

(Total for Question 5 is 4 marks)

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6 Here is a rectangle.

All measurements are in centimetres.

The area of the rectangle is 48 cm2.

Show thaty:3

2-. f 6 S:s-1
6 r- a €' S:c* 2x'

lS =- 3:.

C}C

22<16 t />< St- 6 4E l€

Arqce fe, ctengto :- rrR ,;

l6 x ;3-tG+3-E €\- S fqq ,-r^'r*A

(Total for Question 6 is 4 marks)

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Brogan needs to draw the graph of .y: x2 + I

Here is her graph.

Write down one thing that is wrong with Brogan's graph.

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Write these numbers in order of size.
Start with the smallest number.

0.246 0.246 0.246 0.246

O 'Zt+ 6 L'-{'*i- s "Ztt'&66e v.2+6?J-v6 O -a$60 c"'t:

cr.*+4 ) tt "2^ry G cr "at+-& t a.

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9 James and Peter cycled along the same 50km route'
2:James took 1 hours to cycle the 50km'

2

Peter started to cycle 5 minutes after James started to cycle"
Peter caught up with James when they had both cycled 15 km'

James and Peter both cycled at constant speeds'

Work out Peter's sPeed.

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2.9

lcr-nt-* {"*e- --r!-'(3- IS AI h^ \{

2* = $t"r,

q L*o4e-c& . l.t : \[C].l-*\-</ ,
-"--r c*l*I^frs fl*+*- rvr'-

.yrl-. Lv c; 4,\ .tl *te S t'*'
: J t\-'fz, c4
L.*

----\-rq-*-r.,t s--S -= "L- II'-\''-
K

-Cpa*cl - s- > ":<:)- &+-S-
?_-
--r t

s .z/-r -{1- J----z- "fltt^; { 'l

^

22-. kmi h

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l0 (a) Write down the value ol 1001 NG

z {$}

(b) Find the value of 1253

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2

{3}

11 3 teas and 2 coffees have a total cost of f7.80 :lrkcbtal for Question 10 is 3 marks)
5 teas and 4 coffees have a total cost of f14.20
2*>
Work out the cost of one tea and the cost of one coffee.
/s6 o

3t t 2* c- *7 k<- G) x?*

_:;-b + tr c- I L1a c) @

6b+ fc "€- \ 5'6 c 6, *a &-a

Ugb +* t+- c-- +l Lf-Q-q (+- LC

o@ t{- s

S.^t L,'\ O 36o

3>- l t#a -5 2c"- E :7 &(3
+"2* + 2c* 4a --? 8- C
2*c: 3((3 teaf r{l *4-6
|

C ta tQ<= coffeeg uI'b'(C'\

*-*(rotul fo-' -Qqg*,.q L11-t'-"tIta*q)-

10

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12 The table shows information aboutthe heights, in cm, of a group of Year l1 girls'

height (cm)

least height t54

median 165

lower quartile 161 Lr&. s I eq

interquartile range 7 ff1dh )d

range 20 .[ Stf +*L{r * \*t ?

(a) Draw a box plot for this information.

Year 1l

height (cm)

{s}

The box plot below shows information about the heights, in cm, of a group of Year 7 girls'

Year 7

130 140 150 160 170 luu

height (cm)

(b) Compare the distribution of heights of the Year 7 girls with the distribution of heights

of the Year 1 I girls. ii

-T-he nrta_C,"1.. F*- Y**- F- r-\-s*oirre" ***c1-.-

+L,,qan U^e- rrre-c),. -4.
fu[*:*'l ''.e- Y nhv- Q--.*"{ri * i2-o,13: Y*sr

-*-l i * €\ r€-q.foar-- #'".P. -Lj^'e-

xJ/ e-a* .r i " *Gs14 {er Qse""'Jieql?"n: {trkq)
r.

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A factory makes 450 pies every day. f*Sc; +' I iS- '3 3 c

The pies are chicken pies or steak pies.

fl1,tlA-e{) L
P:-Each day Milo takes a sample of 15 pies to check.
&^r*3.' . c;The proportion of the pies in his sample that are chicken is the same as the proffrtion of

the pies made that day that are chicken.

On Monday Milo calculated that he needed exactly 4 chicken pies in his sample.

(a) Work out the total number of chicken pies that were made on Monday.

4- ,ra J c-' -:* L €* cr

\2'-cf
{}}

On Tuesday, the number of steak pies Milo needs in his sample is 5 correct to the nearest

whole number.

Milo takes at random a pie from the 450 pies made on Tuesday.

(b) Work out the lower bound of the probability that the pie is a steak pie. -!=.6'._s*

p-e-,t-*'d -: t:o C e{-gc:

IuoLuf *{'e*eJ^L.bI ')={'t**^Ctl' I rt
\kJ
3-S^>.- 3c = i

13 is 4 marks

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0

t4 The ratio (y + x): (y - x) is equivalent to k: I

. x(k+l)
'Shorv that v k-l

5 t-x' : \1 *-)c-

b "I
.ll

>< 1?-

l: hz

J\z+-t .- { ( h*tl

al for Question 4 is 3 marks

15 x:0.436

u,'jProve algebraicall y thatx can be written
55

)c? G t*:-G
+lqoI
[c] to : +36" 36 @ q-8
CcCoC =
N FEE-

@-c 1{- 3 2- z+
cA3OG.
='c +3L =- trE'

a'1 (3 llo

(Total for Question 15 is 3 marks)

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l6 y is directly proportional to Vi

'v6:l I whenx:8

-

:Find the value ofy when x 64

"t?1-32( ".l
e"1 :

*J:

{,

j hax 2*

,'F:ff- 3

I &xz t2*

LJ

'Iur--

3 3^nt4" 33_:28€. *:1_
;5- 3t?-
\- e| "1<-*
btal for Ouestion 16 is 3 marks

17 nis an integer.

lA.Prove algebraically that the sum of ln@ + l) and \@ +2) is always a square number.

)C,'* o*]fu 5*?-

2L-"(nrl\ r-a n+Z \
_)
tL{ "., r

L2- (n\!+!) / Z(^i-t)

f/n' +ij ,'it t71;t!-!atCA q S c-twq5-s ci-

1

Sq L(@\ p\tJLrn.\:::)e-"r-

(Total for Question 17 is 2 marks)

14

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8 tt_-.----l*_---l
7
78
-6

5
4
-l

*2

I

-8 -7

2

--l
* A-

-a

-5
-6
-7
-8

Enlarge shape P by scale factor -] with centre of enlargement (0, 0).
2

Label your image Q.

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19 Qt", o')
\

NI,\\\\
ts,A-/*,/\
Y.- P,5)

// |- l{-E\

/12- /2*\
/\ \c t2,o)

/

ABCD is a rectangle.

4:A, E and B are points on the straight line L with equation x * 12

A and D arc points on the straight line M. Zy-;.*Jn, = lLL--€ccc-
?,-
AE: EB =

Find an equation for M.

K q-cFd,''^tdte-,s tz=(:e =) Jc. =

E ceetd'''^<e#et rc:C *+:j = (
63
\r1zr'a'nr"-b -o o-d.-t *fq5 (-lg

A o^e- ( -lzt t2-

c-tJ ftE= €-6

Gr.cie,-c- f-,''\ =

q"a( < n^. Ca.

t*J z (.c

= 2s-

uestion 19 is 4 marks

16

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y:20 The table shows some values of x and y that satisfy the equation acosx" * b

x 0 30 60 90 120 150 180

v 3 1+^6 2 1 0 t-\6 -l

:Find the value ofy when x 45 for* 'Z 4r'-L*" R'€l\4dt..#\s

C(iS CJF.V €- ig €-JL*'-_'* .5*l v $r-*r'r.-*- Lto'** l3

{3 S=Ct +*-bkS* -l=3- ! I
CCAYU c."T_, \L-- ;rt. F' (
i
/'*'
cc;J
a i - r) g.:{t*
q -t.- JQ'T q-1F ;t f I

.t! ltJE_

I a

*1

'L\j l.r *^ J( : '\L, {" g$ t*Ci' :

.,uf-a=?-Zx'Z c6-s' +-S *iz--1' 1

1- -l

(T-"-teL tp"r Q*sqtle"n ?-0" ifl -4 rcr"F-:)"-"-- ..,-

21 Show that Y6-f{Js Jican be written in the form a + b where a and 6 are integers.
42-l

*-\ c {n * "l-5--fie t 6

-tg
J€U]{{,, /)
Lf \r' 7--^- '' \)

-_? t- 4 t-^ Z_. +*

vl

+ q-'E

f": he'c- (a -5- L

fu.x ?

I for Question 2l is 3 marks)

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22 The two triangles in the diagram are similar. I

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7::,.'l

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There are two possible values of x. ur working. 3cm Is E.

Work out each of these values. x' lsv tz +
State any assumptions you make i
6'r:< SSt'.ru-q
tz
E' 6t)p:cQraJU
e
Cr..r, 'fr*r-
-sF
D C-

tr )<+{, = F t->c Lei&^od g or,.\

Ie & r-cc Aot Ae
AD( B r)^i [o-
trC-

f, Mo€t^*4 2-
A\s AAgbEe 4""4
&egr\-La/-'A+$\i1)leZc'"* /
s;^il
i
><! -s A e -* I S>o r '*S =2-Z'S
E)"i'5ir1?- rL-- LZ.s: E

.?e- : !9 's-

tion 22 is 5 marks

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23 Here is a rectangle and a right-angled triangle.

"\

All measurements are in centimetres.
The area of the rectangle is greater than the area of the triangle.

Find the set of possible values of x.

(-c*t)(T.*-z) z

*7 .:c

) --z*.g=-- t Z *7C)

/ \--A--

2_

,\\/tf"* n

\'l' \

(,:* * ii*"q

t :)q >2*

2- GpJe! t$ Q-uqrti-o-n -?-1 h -{ qlarkil .-

"Sc",\tetzte"r I o'-t*

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(**

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TOTAL FOR PAPER IS 80 MARKS

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