Pu bl ic E x amin a tion G CSE Mat h ema t ic s Edexcel s t y l e M a y 20 1 7 H i gher Tier Paper 2H N ame ID: 595957
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Slide1
Pre
Pu
bl
ic
E
x
amin
a
tion
G
CSE
Mat
h
ema
t
ic
s
(Edexcel
s
t
y
l
e)
M
a
y
20
1
7
H
i
gher
Tier
Paper
2H
N
ame
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Cl
ass
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T
IM
E
A
L
L
O
WED
1 hour
30 minutesINSTRUCTIONS TO CANDIDATES Answer all the questions. Read each question carefully. Make sure you know what you have to do before starting your answer. You are permitted to use a calculator in this paper. Do all rough work in this book.INFORMATION FOR CANDIDATES The number of marks is given in brackets ( ) at the end of each question or part question on the Question Paper. You are reminded of the need for clear presentation in your answers. The total number of marks for this paper is 80.
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1
Question
Mark
Out of
1
2
2
4
3
5
4
2
5
2
6
4
7
4
8
4
9
5
10
4
11
5
12
4
13
3
14
4
15
4
16
4
17
4
18
4
19
6
20
6
T
otal
80Slide2
Ans
w
e
r
ALL questio
ns.
Wr
ite you
r an
swers in
the s
paces
provid
ed.
You
must w
rite d
own
all the
stages in
your
work
ing.
Q
uestion 1
.A c
ricke
t team p
laye
d ei
ght innin
gs.The
mean numb
er of ru
ns for the
eight
innings is
20The
crick
et tea
m play
ed one
more inni
ng.
The me
an number of
runs for a
ll nine
inning
s is 23
Work o
ut the
number of r
uns the tea
m made
in th
e ninth inn
ing.
.......................... poin
ts
(Total 2
mark
s)
Question
2.
The
width of a rec
tangu
lar spor
ts pitch is x
metres, wh
ere x
is an intege
r.
The
length of the
pitc
h is 20 m more
than its width.Given that the perimeter of the pitch must be less than 300 mFind the greatest possible width of the rectan
gular sports pitch.
…………………………………….. m(Total 4 marks)
2Slide3
Ans
w
e
r
ALL questio
ns.
Wr
ite you
r an
swers in
the spaces
provide
d.
You m
ust wr
ite do
wn a
ll the stag
es in yo
ur w
orki
ng.
Qu
estion 1.
A cri
cket
team pl
ayed
eig
ht inning
s.The
mean numbe
r of run
s for the e
ight i
nnings is 20
The c
ricke
t team p
laye
d one more
innin
g.
The mea
n number of ru
ns for all
nine innings is
23
Work out
the number
of runs the
team
made
in the
ninth inn
ing.
20 x 8 = 160 or
23 x 9 = 207 M1
207 – 160 = 47
47 A1
(Total 2
mark
s)
Que
stion 2.
The width of a
rectan
gula
r sports pi
tch is x
metres, wh
ere x
is an intege
r. The
leng
th of the pit
ch is 20 m
more than its wid
th.Given that the perimeter of the pitch must be less than 300 mFind the greatest possible width of the rectangular
sports pitch.
x + 202(x) + 2(x+20) = 4
x + 404
x + 40 < 3004x < 260x < 65
B1M1A164m B1(Total 4 marks)2Slide4
Q
u
e
stion
3.
B
ec
k
y
c
y
c
les ho
m
e
f
r
om
wo
r
k
e
a
c
h d
a
y
.
The
s
ca
t
t
e
r
gr
a
ph shows
i
nfo
r
mation about h
e
r jo
u
rn
e
y
t
i
mes.
40
35
T
i
m
e ta
k
en
(m
i
n
u
t
e
s
)
30
25
20
15
0
4
.
45
4.50 4.55 5.00 5.05 5.10 5.15 5.20 5.25
5.30Leaves work (pm)(a) The table shows one more set of journey times.Complete the scatter graph using the data from the table.(1)(b) Describe the correlation...................................................................(1)(c) Becky leaves work at 5.12 pmWhat time will Sara arrive home?..................................................................(3) (Total 5 marks)3Leaves work (pm)5.17Arrives home (pm)5.51Slide5
Q
u
e
stion
3.
B
ec
k
y
c
y
c
les ho
m
e
f
r
om
wo
r
k
e
a
c
h d
a
y
.
The
s
ca
t
t
e
r
gr
a
ph shows
i
nfo
r
mation
a
bout her
jo
u
rn
e
y
t
i
mes.
40
35
X
T
i
m
e ta
k
en
(m
i
n
u
t
e
s
)
30
25
20
15
04.45 4.50 4.55
5.00 5.05 5.10Leaves work (pm)5.15 5.20 5.25 5.30(a) The table shows one more set of journey times.Complete the scatter graph using the data from the table.B1(1)(b) Describe the correlation.Positive B1(1)(c) Becky leaves work at 5.12 pmWhat time will Sara arrive home.Correct line of best fit30 min – 34 minB1M15.42pm – 5.46pmA1(3)(Total 5 marks)3Leaves work (pm)5.17
Arrives home
(pm)
5.51Slide6
Q
u
e
stion
4.
Here
are four cumu
lati
ve frequ
ency
diag
rams.
F
or each box
plot wr
ite down the
number of the
approp
riate c
umulat
ive f
reque
ncy di
agra
m.
(Total 2
mark
s)
4Slide7
Q
u
e
stion
4.
He
re are four c
umulat
ive fre
quenc
y dia
grams.
F
or each box
plot w
rite
down the number
of the appro
priate
cumula
tive
frequ
ency
diagr
am.
A & 3
B &
4C &
2
D & 1
B2 f
or all
co
rrect
B1 for
tw
o co
rrect
(Tot
al 2 ma
rks)
4Slide8
Q
u
e
stion
5.
B
e
low is a
di
a
gr
a
m of
a
c
ir
c
le.
QR is the diam
e
ter
of the
c
ir
c
le and
C is the
centre
of the circ
le. F
ind the coordinat
es of point
R.
Q(1
,8)
C(
3.5,2
)
R
(………..….. , ………..…..)
(Tota
l 2 mar
ks)
5Slide9
Q
u
e
stion
5.
B
e
low is a
di
a
gr
a
m of
a
c
ir
c
le.
QR is the diam
e
ter
of the
c
ir
c
le and
C is the
centre
of the circ
le. F
ind the coordinat
es of point
R.
Q(1
,8)
C(
3.5,2
)
R
3.5 x 2 = 7
7 – 1 = 62 x 2 = 4
4 – 8 = -
4
M1
(6
,-4)
A1(Tot
al 2 ma
rks)
5Slide10
Q
u
e
stion
6
.
Here
is a tra
peziu
m.
Work o
ut the a
rea
of the
trape
zium.
Give y
our a
nswer
corre
ct to
3 signifi
cant fig
ures
.
..................................................................cm
2(Tot
al 4 ma
rks)
6Slide11
Q
u
e
stion
6
.
Here
is a tra
peziu
m.
Work o
ut the a
rea
of the
trape
zium.
Give y
our a
nswer
corr
ect to
3 signifi
cant fig
ures
.
51.7c
m2
A1
(Tot
al 4 ma
rks)
6Slide12
Q
u
e
stion
7.D
ave i
mports ca
rs from Austr
alia.
He
sell
s them in the UK. He h
as just bou
ght a
car in A
ustrali
a costi
ng $25 0
00. It cost him £900
to import the
car to the
UK.
The exc
hang
e ra
te is £1 =
$1.25
Dave
needs to make
a p
rofit of 15%
on his tota
l costs.Work out
the le
ast amount that Dave must
sell
the car
for in the
UK. Give
your a
nswer in po
unds.
£..................................................................
(Total 4
mark
s)
7Slide13
Q
u
e
stion
7.D
ave i
mports ca
rs from Austr
alia.
He
sell
s them in the UK.
He has just bou
ght a
car in
Australi
a costi
ng $25
000. I
t cost him £900 to im
port the car to the
UK.
The ex
chan
ge r
ate is £1 =
$1.25
Dave
nee
ds to make a
profit of 15
% on his tot
al costs.W
ork out the
least amount that Da
ve must se
ll the ca
r for in the
UK. Give
your
answe
r in pounds.
£24035
A1
(Tot
a
l 4 mar
ks)
7Slide14
Q
u
e
stion
8.
Ga
ry h
as a
70% cha
nce
of p
assing
his ma
ths test. J
osh has a
65% chan
ce o
f passi
ng his m
aths test.
(
a)
Compl
ete the pro
babili
ty tr
ee di
agra
m.
(2)
(b)
W
ork out the
probabi
lity
that G
ary
and Josh both p
ass th
eir maths
test.
.............................................
(2) (Tota
l 4 mar
ks)
8Slide15
Q
u
e
stion
8.
Ga
ry h
as a
70% ch
ance
of pa
ssing
his maths
test. Josh h
as a 65%
chan
ce of p
assing
his ma
ths test.
(
a)
Comple
te the probabil
ity
tree
diagr
am.
(2)
B2
for all
correc
t e
ntr
ies on
pro
bab
ili
ty tree
B1
for at le
ast 4 co
rrec
t e
ntr
ies on pr
oba
bil
ity tree
(b)
Work out t
he proba
bilit
y that
Gary
and J
osh both pass
their maths te
st.
0.7 x 0.65
M1
0.455 A1
(
2) (Total 4 m
arks)
8Slide16
Q
u
e
stion
9
.
The
di
a
g
r
a
m shows
a
plot
of l
a
nd.
20 m
A
fe
n
c
e
is bui
l
t on
t
he p
erimeter
of the land.
The
fence
costs £11.45
per m
etre.
W
ork out
the cost of
building
the fen
ce.
£..................................................................
(Total 5
mark
s)
9
50 m 60
oSlide17
Q
u
e
stion
9
.
The
di
a
g
r
a
m shows
a
plot
of l
a
nd.
20 m
A
fe
n
c
e
is bui
l
t on
t
he p
erimeter
of the land.
The
fence
costs £11.45
per m
etre.
W
ork out
the cost of bui
lding the f
ence.
50 x si
n(60)
= 43.3012701950 x
cos(60) = 25
Per
ime
ter
= 50 + 20 + 4
3.30.. + 20 + 25= 158.3012702
158.30… x 11.45 (
= 1812.549544)
P
1
M1M
1
M1
£1812.55
A1
(Tot
al 5
mark
s)
9
50 m 60
oSlide18
Q
u
e
stion
10.
The
line L
is drawn b
elow.
F
ind an equ
ation of
the line perp
endic
ular to l
ine L
that passes throug
h the point (1, 1).
..............................................
(Tot
al 4 ma
rks)
10Slide19
Q
u
e
stion
10.
The
l
i
ne L is dr
awn bel
ow.
Find an e
quat
ion of the line p
erpend
icular
to line
L that pa
sses through the
point (1, 1).
10Slide20
Q
u
e
stion
11.J
ulia a
nd Steve go to the
furni
ture stor
e.
Julia pur
chases 2 tabl
es and 3
chairs.
She
pays
a to
tal of £
2000.
Steve pur
chas
es 3 tables
and 2 c
hairs.
He pa
ys a to
tal of £2500.
Find t
he cost of eac
h table a
nd a ch
air.
Ta
ble .............................................
Ch
air .............................................
(Total 5
mark
s)
11Slide21
Q
u
e
stion
11.J
ulia a
nd Steve
go to the fur
niture
store.
Jul
ia purchases 2 tab
les a
nd 3 cha
irs. S
he pay
s a
total of
£2000.
Steve
purcha
ses 3 ta
bles and 2
chairs.
He p
ays a
total of £2500.
Find
the cost of
each table
and a c
hair.
2t + 3c
= 2000
3t + 2c = 2500
M
1 f
or at
tem
pt
to use va
riab
lesA1
for
both cor
rect
equations
4t + 6c
= 4000
9t + 6c
= 7500
M1
for c
orr
ect pro
cess
to el
imi
nate
5t = 3500
t = 700
2(700) + 3c
= 2000
3c = 600 c
= 200
M
1 for
sub
stituting
fo
und
valu
e i
nto e
ither
equation
Ta
ble £700 a
nd
Chair £200A1(Total 5 marks)11Slide22
Q
u
e
stion
12.
The mass of
a sp
here,
M,
is dire
ctly
propo
rtional t
o the cube
of r, w
here
r is the
radius of the
sphere in cm
W
hen
r = 10
cm, M
= 20
0 grams.
Work
out the
mass of a
sphere
, made
of the sa
me mat
erial, wi
th a radius of
15 cm
.
..............................................gr
ams
(Total 4 m
arks)
12Slide23
Q
u
e
stion
12.
The mass of
a sp
here,
M,
is dire
ctly
propo
rtional t
o the cube
of r, w
here
r is the
radius of the
sphere in cm
W
hen
r = 10
cm, M
= 20
0 grams.
Work
out the
mass of a
sphere
, made
of the sa
me mat
erial, wi
th a radius of
15 cm.
675g A1
(Tota
l 4 mar
ks)
12Slide24
Q
u
e
stion 1
3
.
Here
is a va
se in t
he shap
e of a
cyli
nder.
5
.6 cm
The
va
se ha
s a ra
dius of 5.6 c
m.
There
is 1250 c
m3 of
water in the
vas
e.
Work
out the
depth of the
water
in the v
ase.
Give y
our a
nswer
corr
ect
to 1 decima
l place.
..........................................
cm
(Total 3
mark
s)
13Slide25
Q
u
e
stion 1
3
.
Here
is a va
se in t
he shap
e of a
cyli
nder.
5
.6 cm
The
va
se ha
s a ra
dius of 5.6 c
m.
There
is 1250 c
m3 of
water in the
vas
e.
Work
out the
depth of the
water
in the
vase
.Give
your
answe
r cor
rect
to 1 decim
al place
.
12.7c
m A1
(Total 3
mark
s)
13Slide26
Q
u
e
stion
14.
The
diagr
am shows a
n L-sh
aped prism.
All
measur
ements are
in ce
ntimetre
s.Find an
expre
ssion, in t
erms of
x, for the volume,
in cm
3, of the prism.
You must show y
our wor
king.
Give yo
ur ans
wer in its si
mplest fo
rm.
..................................................................
(Total 4 m
arks)
14Slide27
Q
u
e
stion
14.
The
diagr
am shows a
n L-sh
aped prism.
All
measur
ements are
in ce
ntimetre
s.Find an
expre
ssion, in t
erms of
x, for the volume,
in cm
3, of the prism.
You must show y
our wor
king.
Give yo
ur ans
wer in its si
mplest fo
rm.
14Slide28
Q
u
e
stion
1
5
.M
ake a the subj
ect of the
formu
la
.............................................
(Total 4 m
arks)
Q
uestion
16.
Prove
that, for a
ll positi
ve va
lues of n,
.............................................
(Tota
l 4 mar
ks)
15Slide29
Q
u
e
stion
1
5
.M
ake a the subj
ect of the
formu
la
(Total 4
mark
s)
Que
stion 16
.P
rove that, f
or all posit
ive v
alues of n
,
M1
for e
ither
on
e
M1
M
1 for
ful
ly c
orrect
exp
ansion
C1
for
com
plet
e a
nd
corr
ect pr
oof
(Tota
l 4 mar
ks)
15Slide30
Q
u
e
stion
1
7.
The are
a of
recta
ngle A
is the same
as the area
of r
ectan
gle B
.
Find the
value of
x.
Give
you
r answ
er in the form
a√6
You must show all
your
working
.
.............................................(Tot
al 4 ma
rks)
16Slide31
Q
u
e
stion
1
7.
The are
a of
recta
ngle A
is the same
as the area
of r
ectan
gle B
.
Find the
value of
x.
Give
you
r answ
er in the form
a√6.
You must show a
ll your
workin
g.
(Total 4
mark
s)
16Slide32
Q
u
e
stion
18.
Emma drops a
ball
from
a h
eight of
d metres onto
the grou
nd.
The time,
t seconds, th
at the b
all tak
es to reac
h the ground
is g
iven by
2𝑑
t
= √
𝑔
wh
ere
g m/
��2
is the acce
lera
tion due
to gr
avity
.
d =
34.2 corr
ect to 3 si
gnifica
nt figure
s.g
= 7.6 c
orrect
to 2 sign
ificant fi
gure
s.
(a)
W
rite down the
upper bo
und of g.
..............................................
(1)
(b
)
Calcula
te the lowe
r bound of
t.You must show
all y
our wor
king.
..............................................
(3)
(Total 4 ma
rks)
17Slide33
Q
u
e
stion
18.
Emma drops a
ball
from
a h
eight of
d metres onto
the grou
nd.
The time,
t seconds, th
at the b
all tak
es to reac
h the ground
is g
iven by
2𝑑
t
= √
𝑔
wh
ere
g m/
��2
is the acce
ler
ation due
to gr
avity
.
d =
34.2 corr
ect to 3 si
gnifica
nt figure
s.g
= 7.6 c
orrect
to 2 sign
ificant fi
gure
s.
(a)
Write
down the uppe
r bound of g.
7.65
B1
(1)
(
b)
Calcula
te the lowe
r bound of
t.You must show
all y
our wor
king.
t
= 2.987…
A1
(3)
(Total 4 m
arks)
17Slide34
Q
u
e
stion
19.
This sk
e
tch shows p
art of
the gra
ph with equati
on =
��𝑥 , wh
ere
a and
b are
const
ants.
(1.7,
q)
(
1, 16
)
(0,
8)
The
points with coor
dinates (
0, 8), (1, 1
6) and (1
.7, q) lie
on the graph.
Ca
lculate the
values of
a, b a
nd q.
.............................................
(Tota
l 6 mar
ks)
18Slide35
Q
u
e
stion
19.
This sk
e
tch shows p
art of
the gra
ph with equati
on =
��𝑥 , wh
ere
a and
b are
const
ants.
(1.7,
q)
(
1, 16
)
(0,
8)
The
points
with coordina
tes (0, 8),
(1, 16)
and (1.
7, q) lie
on the graph.
Calcul
ate the va
lues of a,
b and
q.
q
= 25.99 or 26
A1
(Tot
al 6 m
arks)
18Slide36
Q
u
e
stion 20.
The
graph b
elow shows the first 10 s
econds of a
cycl
ists’ jou
rney
.
(a)
Calcul
ate a
n estimate
for the dist
ance
tra
vell
ed by
the c
yclist
in these 10
seconds.
Use
5 strips of equa
l widths.
..............................................
(4)
19Slide37
Q
u
e
stion
20.
The
gr
a
ph
b
e
low shows the
f
irst 10 s
ec
onds of
a
c
y
c
l
i
st
s
’ jou
r
ney
.
E
D
C
B
A
(
a
) Calcul
ate a
n esti
mate for
the distanc
e tr
avel
led by
the c
ycli
st in these
10 sec
onds.Use
5 strips of equa
l widths.
66 A1
(
4)
19Slide38
(
b
)
I
s this a
rea an ov
eres
tima
te or unde
restimate
for the
distan
ce tra
vell
ed?Give
a re
ason.
…………………………………………………………………………………………………………………..………………………………………………………………………………….
...............................................
..………………………………………………………………………………….
.................................................
(2) (Tot
al 6 ma
rks)
TOT
AL FOR PA
PER IS 80 MAR
KS
20Slide39
(b)
I
s th
i
s area a
n over
esti
mate or
undere
stimate f
or the dist
ance
tra
vell
ed?You must
explain
your a
nswer.
Un
derest
ima
te
B1
Curve
b
ends o
utw
ard
s
C1(
2)
(Total 6
mark
s)
TOTAL
FOR PAP
ER IS 80 MARK
S
20