Please check the examination details below before entering your candidate information

Candidate surname Other names

Centre Number Candidate Number

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

Monday 11 Novemberz0lg
Afternoon (Time: t hour 30 minutes) Paper Reference 1MAI /3H

Mathematics
Paper 3 (Calculator)
f'1Y Arr-i.Srru G-P*-y
Higher Tier

You must have: Ruler graduated in centimetres and millimetres,

protractor, pair of compasses, pen, HB pencil, eraser, calculator.
Tracing paper may be used.

lnstructions
o Useblack ink or ball-point pen.
o Fillin the boxes at the top of this page with your name,
centre number and candidate number.
a Answer all questions.
a Answer the questions in the spaces provided
- there may be more space than you need.
a You must show allyour working.
O Diagrams are NOT accurately drawn, unless otherwise indicated.
o Calculators may be used.
O lf your calculator does not have a z button, take the value of z to be 3.142 unless
the question instructs otherwise.

lnformation
o The total mark for this paper is 80
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
o Read each question carefully before you start to answer it.
o Keep an eye on the time.
o Try to answer every question.
o Check your answers if you have time at the end.
Turnover W

:,:"99,.1.9nA ilililI] il llilil]Iililililil ]ilil ililil ilil ilililflililr]

@
6/1/1/1/1/ P58876RA0124 Pearson
t_
 Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

I (a) Expand and simplify (x + 5)(x

- 9)

4
<-
JC.

'z-_
.3C - q-.)q =+s
{?}
(b) Factorise fully 9x2 + 6x

3 r. (3;r* +- 2 )

4&,
{r,}

(Total for Question I is 4 marks)

(a) Use your calculator to work out Y
J:s - t.q'
Write down all the figures on your ealculator display.

!s1 6 682-SS-
(b) Write your answer to part (a) correct to 4 significant figures.

I s*l'J
{e}

Total for Ouestion 2 is 3 marks

Illllriltil il] illt llillilll ]illl iltiltililtililt illtilltil]

P58876RA0224
The scatter graph shows information about the marks a group of students got in a Science
test and in a Maths test.

tr-'a't-\-l

...1.....1....j. ...,

- .:i

ll: \ t

Maths test mark

0 10 20 30 40

Science test mark

Jamie got a mark of 34 in the Science test.

Using the scatter graph, find an estimate for Jamie's mark in the Maths test.

(Total for Question 3 is 2 marks)

ililflil t] ]il llfl ililtilll lililil]il]tiltil iltil illil]ll ll]

P58876RA0324
4 The table gives information about the times taken, in seconds, by iB students to
run arace.
Sr cq
Time (t seconds) Frequency /r,.'<d f =:.
5</<10 I \< -1 .s _l"s
10</<15 2 x r2"rf 2s
15</<20 4
x r-l-s [ -- ' s
20<t<25 8 )c 22-.s I *c,
Work out an estimate for tire mean time" IB 3js
Give your answer correct to 3 significant figures.

EShr-of-ud l-\ ta-<r*.. 33S li F.6llt

rF

r>"6 seconds

4 is 3 marks

Ill]ll] il ]il ilt ilillltil illtil llltiltilil]Iil ilIilll] tilt

P58876RA0424
I

Write 37cm3 in mm3 fi_

il \-rlr.t tc
':.l(i b l (i(} (i f
]i c,"'" LC) >o! ,*"t

><t eC.e'

3--l ><- { (;-c' c

3r clc: cr mm3

(Total for Question 5 is 1 mark)

6 Nimer was driving to a hotel.

He looked at his Sat Nav at 13 30

Time 13 30

Distance to destination 65 miles

Nimer arrived at the hotel at 1448

Work out the average speed of the car from 13 30 to l4 48

You must show all your working.

&.t*t* :!ia t Ar* I E r"ln r-n .j

1 rD i l"rc*r-r^J
6(:'

A
Ai\- s=- 6s
r*
rsc
&13

Sfu' mph

(Total for Question 6 is 4 marks)

rllilillilt lil illtilililll ]ilfl r]riltililtriltilil Iil il] Turnover W

P58876RA0524
 I
I

(a) Write 32460000 in standard form.

.^--.4.4,,^\zt
3zq-6oooo

? .2,1-6>< l cf
{ r}
(b) Write 4.96 x 10-3 as an ordinary number.

o-,#)[).s6
cl "(3 o+-9 6
qaj

Asma was asked to compare the following two numbers.

A: 6.212 x 108 and B : 4.73 x l}e

She says,

"6.212 is bigger than 4.73 so I is bigger than B.',

(c) Is Asma correct?

You must give a reason for your answer.

No St-lra- t'S ir^C.r:|-;re et 9LS

roa I roq
{1t
\zj

uestionTis3marks

Iilil1]il illllliltililtlllll lilllllilt]tillllilll il]t]t ilt

P58876RA0624
8 The diagram shows a regular pentagon and a parallelogram.

&
Work out the size of the angle marked x.
You must show all your working.

/*<-$4 =- llJ* ( Wp*s-.+*.- ovr q}"a;

pqra\l l*-1o3''a-'.. *lArt \ l

c^ gle-.l ,'*-', pa.4. q\ '3 >r. t ?c -: S'hco

\tr4
f t-* 5*xiC (-)

, -^,. p cz^cn-t I *L* 3 -*** ..\ t* I tJ r-l I-l

2.-" ': 36C-t
23 + 2*3\* -= T6c
2g: l)ZG
Jc -r:3 * fc'&* *3=613 Ll*S o

trE: ra>*63 : +S' (Total for Question 8 is 4 marks)

Ilillll] il ilil ilt ililtilil lil]ll iltiltt]iltilll il]tlil il] Turnover W

P58876RA0724
 "4r
t-L*
t1
I t-
:_T \

Ll+

Enlarge triangle .d by scale factor 2.5 with centre (0, l)

"". ._ , _(fql4Jpreqqtjiqpgis*?**uru_

rililllllnlillll]]lliltilfl ililil l]tilililil illl-t-"i-'--

P 5 I 8 z 6 R A o-8 ilIil]t ilt
 Or *
l0 (a) Solve ' '-n = 1l - x
'
nr:F. = 1f ,, ---- \
e_rx .E ^7-l 7x_
7.- F --- : -?-7 '- ]
8.:* =- 6a
L- =. 68
-b
a

,r: t : iS-
r3I

(b)simprifl
H# ? ,*(:o3l

'.-(s*s)t'.3

(Total for Question 10 is 4 marks)

Iffiilil il ]]ltill l|ililllfl ]llffi ililt]tl]ll t]ll il]tll] lllt Turnover W

t_ P58876RA0924
 -t
ll The probability tree diagram shows the probabilities that Bismah
will be late for work on
two days next week.

Monday Tuesday

late

not late x
late -k

not late

not late

Calculate the probability that Bismah will be late on exactly one of the two davs.

O'O1 >< c> .<?8 t o- €13:<c: .t {

ci. ,-l cla

o- I*7Oc1

10

illilil il|ilil]lillilt illfi ]ilil il|il llilt il]ilil il]

5 8 8 7 6 RililAilil llilt
r
P O-r-'0-2-'4-'--
I
12 The stem and leaf diagram shows information about the heights, in cm, of 23 sunflowers.
t-c:'vt
7r4*.c{i* ry.-2*
E- l*
Key: 1713 represents l73cm

On the grid, draw a box plot for this information.

190 200 210 220

Height (cm)

(Total for Question 12 is 3 marks)

11

ilililil il lil] ilil llll lllll lllllll llll llll lllll llll lllll lllll llll llll Turnover W
P58876RA01124
13 Liquid A and liquid B are mixed together in the ratio 2:J3 by volume
to make liquid C.
Liquid A has densitv 1 "21 glcm3
Liquid B has density ll02glcm3

A cylindrical container is filled completely with liquici C.

The cylinder has radius 3 cm and height 25 cm.

Work out the mass of the liquid in the container.

Give your answer correct to 3 significant figures.
You must show all your working.

Vot'"t'-t* ': -TT- f L,xh -a. *iT-r Tt* Z-5-

2ZS rr c-l**3
2:2- 5 T-
ft:6 Z+-t3 - 1 S-. 2e-:s-rf -:- l -5^
2-:13 r3-- ! Sr;*
(x t"E;i* 'tr

3c'"i-r*:!*t{f-

ft'\* *., ft = 3c rr- p< t. z-t: 1-e] o:

la

A"'1ci
p 5 K = f 3S*fi.->s t -c>a- -*{ 13a" rl
IC,

"1=: !--- { {L ls_"

\ e' *u+l )t
s*
--7l4-'
-a. . . - 1G *Z-
*713"1g ( 3**
)

T3q"
(Total for Question 13 is 4 marks)
12

lllllll] ililil llilt llilt tilil ilililt iIlt ilt ilfi illt illll ilillllll ffi
P 5 8 I 7 6 R A o 1 2 2 4---
I
t4 A group of people went to a restaurant.
Each person chose one starter and one main course.

maln course

the number of people who chose soup:the number of people who chose prawns:2:3 L+3 S_
Of those who chose soup,
the number of people who chose lasagne :the number of people who chose curry:5 : 3 .:r $
5*+-3
Of those who chose prawns,
the number of people who chose lasagne :the number of people who chose curry: I :5 \+ ,*-{,
What fraction of the people chose curry?
You rffiiTffi how you get your answer. r.-l f *
S2<4s><b-=- 2*rF*

A S.sL-a'A"!rq.- Z+C, p*e-=p!*.-

.S. ,. P
e rf$ S:&*\
2-" 3
\x t#A l
.=t 6 '. iL-{l{-
q& r k-q-.
L-- : \-
Gttb +S '':*'+, -{"
L^: C- / tt*tt---:-6 i 2$-
,S; 3 lr
l-
' t<-

\x' * -eqr
/t' ,, \

t..f-..-r
|x }

LO :i36,
\*-/ Z-t-r 1(i ?_<r l

lt tl q ilcJS €' dLr-rru*\

1--f,*Ctt-o.r t*-rt--- \*J

.36 *l'a G v g-./ fl-?

lr+ , '-:. €- 5:
.J

2-L*'a 2-@ ?.o

l-?
,-J
iL-(-J

(Total for Question 14 is 4 marks)

t3
Ililllill lll llil lilt ilil ilil ]illl ilt t]t llt ilffi ffiil illlt ]llll] Turnover W
P58876RA01324
15 Prove algebraically that the sum of the squares of any two consecutive even numbers is
always a multiple of 4

( zn )** C 2rr4_e)
'1L-
t+-n *+* Ll*rt2*fr+- E rt t h*
4
f-\r
Kn+ tn'*',j-.
+ 2.
//
\
r':
/-_-1
a' ,]
t- -t.4-rr -r- I I
"r
g\ J iJ c\ fi*'+--
>r^ *,.*-s-b be-
l.lAc:L&.'pl<- c; fr\
"
(Tqt4-F:_Sss_*ig*"ll p l"" n
16 y is inversely proportional to the square of x.
.:
y: 8 when x:2.5
Find the negative value of x when;, : 8
o

,i -:::-- ? 5;*c.
:J h
)<-<' 3 -t-
CC'
t
._J R**f-
"a- '2*
::q .)'€
H
rs- fe-
2.S ' I s'€
{ *i
hl* * 8'*2'S?
I <-rcs
V2*-*- So \" !r\ Cl
qi

=. s:
-+-
t-'L

(Total for Question 16 is 3 marks)

I ll]tilt ili lilti

P58876RA01424
flll tilil iltil iltffi ffit ilt ilil ilIil illl illit ]ll lilt
17 Here is the graph of y : xz - 3

Use the graph to find estimates for the solutions to the equation x2 - 2x - 2: 0
You must show how you get your solutions.
?-
*'*.:c-f
':-
?.-
')(-- * L tu /
C)
{*€.r*t pi"**- .l=i'r-e- jS q'u'g:'-q'*

/' , \-a 'L

gi a- (.c*i: -i ^'l-
ti -:. ( -, , \,t-' 3

T*h.- s r 1 "tj-,* c1r-t-6:r. ,lq = :- ci 'J 'i, 2'-1. "

'
L^^3c\.-,"{L- ,}}r r+*Cf
.*,.,r " -"}{c-.*&-.\ -,:-
(Total for euestion , 4 marks)
,., is
^..^-,,^- 17
{}.'+_
---- L-LY\\'i- r*u,3'"''
r f *i* 2
.S-'-\.1*t .:6- -1.1, cr.rci. cY\ { *,r-. &
t5
l lllllllilililililr llilililililIril llll llll illll illl lllll lllil lil illl Turn over W
P58876RA01524 -
18 The diagram shows triangle ABC.

AB:3.4cm AC:6.2cm 3C: 6.1 cm

D is the point on BC such that
2
size of angle DAC: _X size of angle BCA
5
Calculate the length DC.
Give your answer correct to 3 significant figures.
You must show all your working.

F."rsb f,;.^d z- 3LA (s) g .:}*S r N}€

flLr'€-
2_
cs.s {.:: ) = 6- tlo- (''L-* 3'+
2x 6' ,l 'x €)' ?*
€(3 s(jl:- 6&r*.1
*7 s 6r*-

-.i (a+oz
% = c.."-s \{s<_r --ll .32 -(}& tr"1'{11

t- CIA c- 't- \2^"F19Lr8"]es*

{- ft i>c * ) Eiq:, * A f.l.s ft"-* /+t\l.S
-*' x ts*'(> &j -:k-3z- *

S r N€ lturc€
'-€-
6-2.
.\
i-\ (t a- 8 3e- r &-t6s- gn rl (l:t S"*' S*f 3l*'32
S: )

: 6.2 s r.,r (r, .832rF*:d*r] *.t"qS-oi't-

r'! . cll-q*-
Stn (tSS-e'8*13q-XZ) cm

(Total for Question 18 is 5 marks)

l llllllll il ilr ililt

P58876RA01624
tilil illllililil ilililfiil ililt ]ilt ilIil il] lllt
19 The graph shows information about part of a cyclist's journey.

Distance travelled
(metres)

0246
3.2-
Time (seconds)

Work out an estimate of the speed, in m/s, of the cyclist at time 6 seconds.

lc>
.= 3. f 2*5*
3.2

3'l zs-
(Total for Question 19 is 3 marks)

I il]fft ilt ilt ilt ilil lllil Iillil ilt ilt lffi ilililll il]r ilr ril
P58876RA01724
20 Here are the first five ternls ol a sequence.

-l
r3s1
Find an expression, in temrs of n. forttrre rirh tennr of ihis sequence.

r
(Tt
\*-z'/

fl ll
.-2
3 L#
l*
K-
-a
n &*. a I & 2-s*
t
$

{^
-I*er"n -t O 3

D;f,F -+ *6 *r
-2- -a

G
/\ * Z--YI

*-(3eq!"s_r_9s*iDr_eg !' ? rqq rt$)

21 When a biasecl coin is throu,n ri. times, the probabilitir of gening 4 heads is 1! ={I ?t\+
8i ?J
work out the prohability of getting 4 tails when the coin is thrown 4 times.

I
Fi
!:':

Ss"*-l i"s:-p= $ qr$* n "2-l*iq ? {'rn T,Bq)

llilllllilil lil] illt tilililil iltilil t!illilililtiiliil tf;tiF fi$ilEiFiilnt

Ps8B76RAo182i
 22 Show that simplifies to ax where a is an integer.
x2 +4x-12 xt -36x

\
-t (-. -4 >< .:c(ci-3 6)
( *'* l+--x
- t?) (-*&)
1;$l
/*,. -r(ZA)<s<- C>41 ,>r-4
. qi{
"&('
..ri.)i..
l

)( (2
i:l."\
....\,;.1,
.Yl )i'
,>!:../.
< .>:,:.
..\-,/,7.\
'T x-
=7-tl
a'::11
' ./l':\,

Y'w,)
'wa.
.\;r*.
':$q,,
'"{n}
..9.
K)
,W
'&z
r"$Ar
.Mi
ffi>.
,'b44,
.ffi;
.,W
w;;
'"rci)
dN1
x<")
)1.i.,,\
..V,
w/"".
.nt*
..//\
"4*"::)?

(Total for Question 22 is 4 marks)

19

ililIilIil] |ilIil]lililililil lillilillil

P58876RA01924
illl lllll lllll lil llll llll llll Turnover W
-
 The diagram shows a sector OACB of a circle with centre O.
The point f- is the midpoint of the arc AB.
Volume of cone : ! 1 orr7,,
-)
The diagram also shows a hollow cone with vertex O.
The cone is formed by joining O,4 and OB. Curved surface area of cone: Trl
.

i/ \,r
t///\-- \
{/--.._Al

The cone has volurne 56.8cm3 and height 3.6cm.

Calculate the size of angle ,4AB of sector OACB. -I

?t
Give your answer correct to 3 significanf figures. 3
-rT* r* L-1

You must show all your working. LI

TT* r t-\
2*
{*
"-ir* L*
t'F
/ :r,
t€
J TiLt
t* 3>og€'E s.b a Rc} S=1:
7T-x 3'&
i-.^
'r.--J
tL cl.ca.=rR I
'-2

CJc- = | .5'e)
U "-
-z' t r
c* 3d- .-r Q *1 * {> c"**r

ilililIlil] llil il1ilIililIllllililil ilil tilHilililil l]il ilIil ilt lllt

P58876RA02024
': .)X
.7.. \
,^. -/

' ./t'
C.'f <ur..{"-*.*-
I =t i:<e.se
3 " & I t se€ S :t cl x2*
t:1' 'i
,4
\.h5l
Tr-><
.w:
:+ .= L+'*3R863otq c,sn
.Id
'.w.
,.%i:

T >< 7>. g.. 2't +c>21 qc 6 :2t{-'3

-'.)M )
P,
,Eg' 9-- ><
!'W"!
,Mt
w
a6o
1&t.
,..w
\&.'
'. .'7X::. e=
Tr-< 2:< S " 23t{-o2*[ r a 6
f1l:')1
iX
i.
l'::,
:X;,i

:. -r<.
':'Y.!'. >
1.:.::,/
:t1'/\')'
/1.',>Z

{,q;
,/,/...
E:T:?A;T'
I&/
,w
:w
i*/i\
. :sta:
.
&\, *>aZ
\4,@ \
"w&1.

.'&>
,/,x
/w<,/,/
,&
w
ffi,
'ffi(:,:
,\z
..:i.Xd'i
x)) 26*
va\
:,,/\ (Total for Question 23 is 5 marks)
.1r'\
//r:,1
^//
/f.,^.'
6
\w
)€
..w4,
)\&."
H(
€>
."d\
'W12.
:;#.\
'M,
\i6;..>
4-W?
',K;.
W
irli$
,x\*..2
\,/^-
.x/./ ) )
7.:r\|t
.'.',4."4N'
>\"1
\x/.
''

21

Iillllltil ]il il] tilililil lil]il illlilltllill ltiltilil lllillil il]

P58876RA02124 Turnover W
24 OXYZ is a paralleiogram.

t^
:q
b H

OX:a
ts- -F-q
--)
oY:b *-=")
a F -: ;{-ar
*\ t
P is the point on OX such t:hat {}P:PX=- 1:Z
-- ' *J --'a- |
trx -?* =-q
1-
R is the point on OIsuch that OR:lRf : I :3
+

8/
J
O{<-:---b &r** <
+Er
Work out, in its simplesi forrn, the ratio Zp:ZR
) - *--
You must show all yoi:r rvorla-ing.
*€ *sa *-*=>
r--> -?
\-, {'-- -= Lj Y +- YZ =k) *q
**? *+
x-r -; a(3 C'P -= "\ ,/''l t)-q P\
\
1
+- Fq
J '-\
!. I
Y) : Lt (^U\ i r\
-r*- q Lt-;*i
3^& j \-^

*+ **) **n
2.1<* - ZO -t- C)R* :

-'--==\
-e-p f'

: z-p*
3l
::-/a.
3 \t -I-fr
4r
.
-*(+-
L,\ _ --:-- 2
'
-ll
ry_ ril
3
k 3 11
: .-s
a

-* _ _ *__._ ggtal--&r_asee!ee^?1*'!_g_rryFU--*

TSTAL FOR PAPER IS 80 MARKS

Ililillt fl ilil ilil ilfitifiil !ililililllltitilil ililt iltil ililtllltlll

P58876RAQ2224