-
IGCSE
Mathematics
Teaching the IGCSE in Mathematics (Specification A) alongside
Core Mathematics 1
Scheme of work: Bridging to GCE
Edexcel IGCSE in Mathematics (Specification A) (4MA0)First
examination 2012
-
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Acknowledgements
This document has been produced by Edexcel on the basis of
consultation with
teachers, examiners, consultants and other interested parties.
Edexcel would like to
thank all those who contributed their time and expertise to its
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Authorised by Martin Stretton
Prepared by Sharon Wood
Publications Code UG029447
All the material in this publication is copyright
© Pearson Education Limited 2011
-
Introduction
The Edexcel IGCSE in Mathematics (Specification A) is designed
for use in schools
and colleges. It is part of a suite of qualifications offered by
Edexcel.
About this scheme of work
It provides opportunities for you to extend and enrich the
mathematical learning of
your Higher Tier students. It is assumed that Higher Tier
students have knowledge
of all Foundation Tier content. This scheme of work should be
used together with
the higher tier course planner in the IGCSE in Mathematics
(Specification A)
Teacher’s Guide.
Through teaching the Edexcel GCE Core Mathematics 1 unit
alongside the Higher
Tier content, you will be able to prepare your Higher Tier
students for the transition
from Level 2 Mathematics to AS Mathematics, and beyond. It also
enables you to
extend several topic areas of the Mathematics IGCSE Higher Tier
content.
This scheme of work introduces the following topics from Edexcel
GCE Unit Core
Mathematics 1 in the first year of course:
Algebra and functions
Coordinate Geometry
The remaining topics from Edexcel GCE Unit Core Mathematics 1
could be taught
during the second year of the course:
Sequences and series
Differentiation
Integration.
This means that the scheme of work extends the following topic
areas:
1.4 Powers and roots
2.2 Algebraic manipulation
2.7 Quadratic equations
2.8 Inequalities
3.3 Graphs.
It introduces new concepts within the following topic area:
3.4 Calculus – Differentiation.
It also introduces the following topic areas not included in the
IGCSE:
Sequences and series
Integration.
-
Contents
Mapping of IGCSE Mathematics Higher tier content to GCE Core
Mathematics 1 unit content 1
Higher tier IGCSE Mathematics/GCE Core Mathematics 1 unit
content summary 33
Higher tier IGCSE Mathematics/GCE Core Mathematics 1 unit scheme
of work 35
-
Mappin
g o
f IG
CSE M
ath
em
ati
cs
Hig
her
tier
conte
nt
to G
CE C
ore
Math
em
ati
cs
1 u
nit
conte
nt
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
1
Nu
mb
ers a
nd
th
e
nu
mb
er s
yste
m
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts n
eed
to learn
No
tes
1.1
In
teg
ers
See F
oundation T
ier
1.2
Fracti
on
s
See F
oundation T
ier
1.3
D
ecim
als
convert
recurr
ing
decim
als
into
fra
ctions
3.0
=
31,
0.2
33
3…
=
9021
1.4
P
ow
ers a
nd
ro
ots
unders
tand t
he
meanin
g o
f surd
s
m
anip
ula
te s
urd
s,
inclu
din
g r
ationalisin
g
the d
enom
inato
r w
here
the d
enom
inato
r is
a
pure
surd
Expre
ss in t
he f
orm
a2
: 82
, 1
8 +
32
Expre
ss in t
he f
orm
a +
b2
: (
3 +
52
)2
Exte
nsio
n t
op
ic
Use a
nd
man
ipu
lati
on
of
su
rd
s
Stu
den
ts s
ho
uld
be
ab
le t
o r
ati
on
alise
den
om
inato
rs
use index law
s t
o
sim
plify
and e
valu
ate
num
eri
cal expre
ssio
ns
involv
ing inte
ger,
fractional and n
egative
pow
ers
Evalu
ate
:
38
2,
21
62
5
,
232
51
Exte
nsio
n t
op
ic
Law
s o
f in
dic
es f
or
all r
ati
on
al
exp
on
en
ts
Th
e e
qu
ivale
nce o
f
nm
a a
nd
n
ma
sh
ou
ld
be k
no
wn
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
1
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
1
Nu
mb
ers a
nd
th
e
nu
mb
er s
yste
m
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts n
eed
to learn
No
tes
1.4
P
ow
ers a
nd
ro
ots
co
nti
nu
ed
evalu
ate
Hig
hest
Com
mon F
acto
rs (
HCF)
and L
ow
est
Com
mon
Multip
les (
LCM
)
1.5
S
et
lan
gu
ag
e
an
d n
ota
tio
n
unders
tand s
ets
defined in a
lgebra
ic
term
s
unders
tand a
nd u
se
subsets
unders
tand a
nd u
se
the c
om
ple
ment
of
a
set
If A
is a
subset
of
B,
then
A
B
Use t
he n
ota
tion A
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
2
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
1
Nu
mb
ers a
nd
th
e
nu
mb
er s
yste
m
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1.5
Set
lan
gu
ag
e a
nd
no
tati
on
co
nti
nu
ed
use V
enn d
iagra
ms t
o
repre
sent
sets
and t
he
num
ber
of
ele
ments
in
sets
use t
he n
ota
tion n
(A)
for
the n
um
ber
of
ele
ments
in t
he s
et
A
use s
ets
in p
ractical
situations
1.6
Percen
tag
es
use r
evers
e
perc
enta
ges
repeate
d p
erc
enta
ge
change
In a
sale
, prices w
ere
reduced b
y 3
0%
. The
sale
pri
ce o
f an ite
m
was £
17.5
0.
Calc
ula
te
the o
rigin
al pri
ce o
f th
e
item
Calc
ula
te t
he t
ota
l
perc
enta
ge incre
ase
when a
n incre
ase o
f
30%
is f
ollow
ed b
y a
decre
ase o
f 20%
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
3
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
1
Nu
mb
ers a
nd
th
e
nu
mb
er s
yste
m
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1.6
P
ercen
tag
es
co
nti
nu
ed
solv
e c
om
pound
inte
rest
pro
ble
ms
To inclu
de d
epre
cia
tion
1.7
R
ati
o a
nd
pro
po
rti
on
See F
oundation T
ier.
1.8
D
eg
ree o
f
accu
racy
solv
e p
roble
ms u
sin
g
upper
and low
er
bounds w
here
valu
es
are
giv
en t
o a
degre
e
of
accura
cy
The d
imensio
ns o
f a
recta
ngle
are
12cm
and 8
cm
to t
he
neare
st
cm
. Calc
ula
te,
to 3
sig
nific
ant
figure
s,
the s
mallest
possib
le
are
a a
s a
perc
enta
ge o
f
the larg
est
possib
le
are
a
1.9
Sta
nd
ard
fo
rm
expre
ss n
um
bers
in t
he
form
a
10
n w
here
n is
an inte
ger
and
1 ≤
a <
10
solv
e p
roble
ms
involv
ing s
tandard
form
15
0 0
00
00
0
= 1
.5
10
8
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
4
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
1 N
um
bers a
nd
th
e
nu
mb
er s
yste
m
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1.1
0 A
pp
lyin
g
nu
mb
er
See F
oundation T
ier
1.1
1 Ele
ctr
on
ic
calc
ula
tors
See F
oundation T
ier
2 E
qu
ati
on
s,
form
ula
e a
nd
iden
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts
need
to
learn
No
tes
2.1
U
se o
f sym
bo
ls
use index n
ota
tion
involv
ing f
ractional,
negative a
nd z
ero
pow
ers
Sim
plify
:
32
36
4t
, 31
4321
a
aa
Exte
nsio
n t
op
ic
law
s o
f in
dic
es f
or
all r
ati
on
al
exp
on
en
ts
Th
e e
qu
ivale
nce o
f
nm
a a
nd
n
ma
sh
ou
ld
be k
no
wn
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
5
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
2 Eq
uati
on
s,
form
ula
e a
nd
iden
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts
need
to
learn
No
tes
2.2
A
lgeb
raic
man
ipu
lati
on
expand t
he p
roduct
of
two lin
ear
expre
ssio
ns
unders
tand t
he c
oncept
of
a q
uadra
tic
expre
ssio
n a
nd b
e a
ble
to f
acto
rise s
uch
expre
ssio
ns
manip
ula
te a
lgebra
ic
fractions w
here
the
num
era
tor
and/o
r th
e
denom
inato
r can b
e
num
eri
c,
linear
or
quadra
tic
(2x
+ 3
)(3
x –
1)
(2x
– y
)(3
x +
y)
Facto
rise:
x2 +
12
x –
45
6x2
– 5
x –
4
Expre
ss a
s a
sin
gle
fraction: 4
3
3
1
xx
3
)3
5(2
2
)14(
3
xx
xx
34
23
, x
x
1
2
1
3
12
21
xx
xx
Exte
nsio
n t
op
ic
Alg
eb
raic
man
ipu
lati
on
of
po
lyn
om
ials
,
inclu
din
g
exp
an
din
g
brackets
an
d
co
llecti
ng
lik
e
term
s,
facto
ris
ati
on
Stu
den
ts s
ho
uld
be
ab
le t
o u
se b
rackets
.
Facto
ris
ati
on
of
po
lyn
om
ials
of
deg
ree n
, n
≤
3,
eg
. Th
e
no
tati
on
f(x
). (
Use o
f
the f
acto
r t
heo
rem
is
no
t req
uir
ed
)
xx
x3
42
3
Facto
rise a
nd s
implify
:
12
42
2
x
x
xx
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
6
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
2 E
qu
ati
on
s,
form
ula
e a
nd
iden
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
2.3
Exp
ressio
ns a
nd
form
ula
e
unders
tand t
he p
rocess
of
manip
ula
ting
form
ula
e t
o c
hange t
he
subje
ct,
to inclu
de
cases w
here
the
subje
ct
may a
ppear
twic
e,
or
a p
ow
er
of
the s
ubje
ct
occurs
v2 =
u2 +
2g
s;
make s
the s
ubje
ct
m =
at
at
11
;
make t t
he s
ubje
ct
V =
34πr
3;
make r
the s
ubje
ct
glT
2
;
make
l the s
ubje
ct
2.4
Lin
ear e
qu
ati
on
s
See F
oundation T
ier.
4
17
x
= 2
– x
,
25
3
)2
(
6
)3
2(
x
x
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
7
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
2 E
qu
ati
on
s,
form
ula
e a
nd
iden
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
2.5
P
ro
po
rti
on
set
up p
roble
ms
involv
ing d
irect
or
invers
e p
roport
ion a
nd
rela
te a
lgebra
ic
solu
tions t
o g
raphic
al
repre
senta
tion o
f th
e
equations
To inclu
de o
nly
the
follow
ing:
y
x,
y
x1
,
y
x2,
y
21 x
,
y
x3,
y
x
2.6
S
imu
ltan
eo
us
lin
ear e
qu
ati
on
s
calc
ula
te t
he e
xact
solu
tion o
f tw
o
sim
ultaneous e
quations
in t
wo u
nknow
ns
inte
rpre
t th
e e
quations
as lin
es a
nd t
he
com
mon s
olu
tion a
s
the p
oin
t of
inte
rsection
3x
– 4
y =
7
2x
– y
= 8
2x
+ 3
y =
17
3x
– 5
y =
35
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
8
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
2 E
qu
ati
on
s,
form
ula
e a
nd
iden
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts n
eed
to learn
No
tes
2.7
Q
uad
rati
c
eq
uati
on
s
solv
e q
uadra
tic
equations b
y
facto
risation
solv
e q
uadra
tic
equations b
y u
sin
g t
he
quadra
tic f
orm
ula
form
and s
olv
e
quadra
tic e
quations
from
data
giv
en in a
conte
xt
2x2
– 3
x +
1 =
0,
x(3
x – 2
) =
5
New
to
pic
Co
mp
leti
ng
th
e
sq
uare.
So
lve
qu
ad
rati
c e
qu
ati
on
s
So
lve q
uad
rati
c
eq
uati
on
s b
y
co
mp
leti
ng
th
e
sq
uare
solv
e s
imultaneous
equations in t
wo
unknow
ns,
one
equation b
ein
g lin
ear
and t
he o
ther
bein
g
quadra
tic
y =
2x
– 1
1 a
nd
x2 +
y2 =
25
y =
11
x –
2 a
nd
y =
5x2
New
to
pic
Sim
ult
an
eo
us
eq
uati
on
s:
an
aly
tical
so
luti
on
by
su
bsti
tuti
on
Fo
r e
xam
ple
, w
here
on
e e
qu
ati
on
is
lin
ear a
nd
on
e
eq
uati
on
is q
uad
rati
c
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
9
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
2 E
qu
ati
on
s,
form
ula
e a
nd
iden
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts n
eed
to learn
No
tes
2.8
In
eq
ualiti
es
solv
e q
uadra
tic
inequalities in o
ne
unknow
n a
nd r
epre
sent
the s
olu
tion s
et
on a
num
ber
line
identify
hard
er
exam
ple
s o
f re
gio
ns
defined b
y lin
ear
inequalities
For
exam
ple
,
ba
x
>d
cx
,
x2 ≤
25,
4x2
> 2
5
Shade t
he r
egio
n
defined b
y t
he
inequalities
x ≤
4,
y ≤
2x
+ 1
,
5x
+ 2
y ≤
20
New
to
pic
So
luti
on
of
lin
ear
an
d q
uad
rati
c
ineq
ualiti
es
Fo
r e
xam
ple
,
ax
+ b
, cx
+ d
,
,
02
r
qx
px
ax
rqx
px
2
b
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
10
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Seq
uen
ces a
nd
serie
s
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
3
Seq
uen
ces
an
d s
erie
s
Wh
at
stu
den
ts n
eed
to
learn
No
tes
3.1
S
eq
uen
ces
use lin
ear
expre
ssio
ns
to d
escri
be t
he n
th
term
of
an a
rith
metic
sequence
1,
3,
5,
7,
9,
…
nth
term
= 2
n –
1
New
to
pic
New
to
pic
Seq
uen
ces,
inclu
din
g
tho
se g
iven
by a
fo
rm
ula
for t
he n
th t
erm
an
d t
ho
se
gen
erate
d b
y a
sim
ple
rela
tio
n o
f th
e f
orm
1n
x =
f(
) n
x
Arit
hm
eti
c s
erie
s,
inclu
din
g t
he f
orm
ula
fo
r
the s
um
of
the f
irst
n
natu
ral n
um
bers
Th
e g
en
eral te
rm
an
d t
he s
um
of
n
term
s o
f th
e s
erie
s
are r
eq
uir
ed
. Th
e
pro
of
of
the s
um
form
ula
sh
ou
ld b
e
kn
ow
n
Un
dersta
nd
ing
of
no
tati
on
wil
l b
e
exp
ecte
d
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
11
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts n
eed
to
learn
No
tes
3.2
Fu
ncti
on
no
tati
on
unders
tand t
he c
oncept
that
a f
unction is a
mappin
g b
etw
een
ele
ments
of
two s
ets
use f
unction n
ota
tions
of
the f
orm
f(x)
= …
and
f :
x
…
unders
tand t
he t
erm
s
dom
ain
and r
ange a
nd
whic
h v
alu
es m
ay n
eed
to b
e e
xclu
ded f
rom
the
dom
ain
unders
tand a
nd f
ind t
he
com
posite f
unction f
g
and t
he invers
e f
unction
f 1
f(x)
=
x1,
exclu
de x
= 0
f(x)
=
3
x,
exclu
de x
< –
3
‘ fg’ w
ill m
ean ‘do
g
firs
t, t
hen
f’
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
12
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
3.3
G
rap
hs
plo
t and d
raw
gra
phs
with e
quation:
y =
Ax3
+ B
x2 +
Cx
+ D
in w
hic
h:
(i)
the c
onsta
nts
are
inte
gers
and s
om
e
could
be z
ero
(ii)
th
e lett
ers
x a
nd y
can b
e r
epla
ced
with a
ny o
ther
two
lett
ers
y =
x3,
y =
3x3
– 2
x2 +
5x
– 4
,
y =
2x3
– 6
x +
2,
V =
60
w(6
0 –
w)
New
to
pic
Qu
ad
rati
c f
un
cti
on
s a
nd
their
grap
hs
Th
e d
iscrim
inan
t o
f a
qu
ad
rati
c f
un
cti
on
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
13
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
3.3
G
rap
hs
co
nti
nu
ed
or:
y =
Ax3
+ B
x2 +
Cx
+ D
+ E
/x +
F/x
2
in w
hic
h:
(i)
the c
onsta
nts
are
num
eri
cal and a
t
least
thre
e o
f
them
are
zero
(ii)
th
e lett
ers
x a
nd y
can b
e r
epla
ced
with a
ny o
ther
two
lett
ers
find t
he g
radie
nts
of
non-l
inear
gra
phs
y =
x1
, x
0,
y =
2x2
+ 3
x +
1/x
,
x
0,
y =
x1
(3x2
– 5
),
x
0,
W =
25 d
, d
0
By d
raw
ing a
tangent
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
14
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fun
cti
on
s
Wh
at
stu
den
ts n
eed
to
learn
No
tes
3.3
Grap
hs
co
nti
nu
ed
find t
he inte
rsection
poin
ts o
f tw
o g
raphs,
one lin
ear
(y1)
and o
ne
non-l
inear
(y2),
and
recognis
e t
hat
the
solu
tions c
orr
espond
to t
he s
olu
tions o
f
y 2 –
y1 =
0
The
x-v
alu
es o
f th
e
inte
rsection o
f th
e t
wo
gra
phs:
y =
2x
+ 1
y =
x2 +
3x
– 2
are
the s
olu
tions o
f:
x2 +
x –
3 =
0
Exte
nsio
n t
op
ic
Grap
hs o
f fu
ncti
on
s;
sketc
hin
g c
urves d
efi
ned
by s
imp
le e
qu
ati
on
s.
Geo
metr
ical
inte
rp
reta
tio
n o
f alg
eb
raic
so
luti
on
of
eq
uati
on
s.
Use
inte
rsecti
on
po
ints
of
grap
hs o
f fu
ncti
on
s t
o
so
lve e
qu
ati
on
s
Fu
ncti
on
s t
o in
clu
de
sim
ple
cu
bic
fun
cti
on
s a
nd
th
e
recip
ro
cal fu
ncti
on
xky
, w
ith
0
x
Kn
ow
led
ge o
f th
e
term
asym
pto
te is
exp
ecte
d
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
15
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
3.3
G
rap
hs
co
nti
nu
ed
calc
ula
te t
he g
radie
nt
of
a s
traig
ht
line g
iven
the C
art
esia
n
coord
inate
s o
f tw
o
poin
ts
Sim
ilarly,
the x
-valu
es
of
the inte
rsection o
f
the t
wo g
raphs:
y =
5
y =
x3 –
3x2
+ 7
are
the s
olu
tions o
f:
x3 –
3x2
+ 2
= 0
re
cognis
e t
hat
equations o
f th
e f
orm
y =
mx
+ c
are
str
aig
ht
line g
raphs w
ith
gra
die
nt
m a
nd
inte
rcept
on t
he
y a
xis
at
the p
oin
t ( 0
, c)
find t
he e
quation o
f a
str
aig
ht
line p
ara
llel to
a g
iven lin
e
Fin
d t
he e
quation o
f
the s
traig
ht
line
thro
ugh
(1,
7)
and (
2,
9)
Exte
nsio
n t
op
ic
Eq
uati
on
s o
f a s
traig
ht
lin
e,
inclu
din
g t
he
form
s)
(2
12
1x
xm
yy
an
d
0
cby
ax
To
in
clu
de:
1) t
he e
qu
ati
on
of
a
lin
e t
hro
ug
h t
wo
g
iven
po
ints
2) t
he e
qu
ati
on
of
a
lin
e p
arall
el (o
r
perp
en
dic
ula
r) t
o a
g
iven
lin
e t
hro
ug
h
a g
iven
po
int.
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
16
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Co
ord
inate
geo
metr
y in
th
e (
x, y
)
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
2
Co
ord
inate
geo
metr
y in
the (
x, y
)
Wh
at
stu
den
ts n
eed
to
learn
No
tes
Exte
nsio
n t
op
ic
Co
nd
itio
ns f
or t
wo
str
aig
ht
lin
es t
o b
e
parall
el o
r p
erp
en
dic
ula
r
to e
ach
oth
er
Fo
r e
xam
ple
, th
e
lin
e p
erp
en
dic
ula
r
to t
he lin
e
18
43
yx
,
thro
ug
h t
he p
oin
t
,2(
)3
, h
as t
he
eq
uati
on
)2
(34
3
xy
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
17
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Co
ord
inate
geo
metr
y in
th
e (
x, y
)
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
2
Co
ord
inate
geo
metr
y in
the (
x, y
)
Wh
at
stu
den
ts n
eed
to
learn
No
tes
3.3
Grap
hs
co
nti
nu
ed
Exte
nsio
n t
op
ic
Kn
ow
led
ge o
f th
e e
ffect
of
sim
ple
tran
sfo
rm
ati
on
s
on
th
e g
rap
h o
f y
= f
(x)
as
rep
resen
ted
by y
= a
f(x)
,
y =
f (
x) +
a,
y =
f (
x +
a),
y =
f (
ax)
Stu
den
ts s
ho
uld
be a
ble
to
ap
ply
on
e o
f th
ese
tran
sfo
rm
ati
on
s
to a
ny f
un
cti
on
(q
uad
rati
cs,
cu
bic
s,
recip
ro
cal)
an
d
sketc
h t
he r
esu
ltin
g
grap
h.
Giv
en
th
e g
rap
h o
f
an
y f
un
cti
on
y =
f(x
)
stu
den
ts s
ho
uld
be
ab
le t
o s
ketc
h t
he
grap
h r
esu
ltin
g
fro
m o
ne o
f th
ese
tran
sfo
rm
ati
on
s.
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
18
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Dif
feren
tiati
on
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4
Dif
feren
tiati
on
W
hat
stu
den
ts n
eed
to
learn
No
tes
3.4
C
alc
ulu
s
Dif
feren
tiati
on
unders
tand t
he
concept
of
a v
ari
able
rate
of
change
diffe
rentiate
inte
ger
pow
ers
of x
dete
rmin
e g
radie
nts
,
rate
s o
f change,
turn
ing p
oin
ts
(maxim
a a
nd m
inim
a)
by d
iffe
rentiation a
nd
rela
te t
hese t
o g
raphs
dis
tinguis
h b
etw
een
maxim
a a
nd m
inim
a
by c
onsid
eri
ng t
he
genera
l shape o
f th
e
gra
ph
y =
x +
x9
Fin
d t
he C
art
esia
n
coord
inate
s o
f th
e
maxim
um
and
min
imum
poin
ts
Exte
nsio
n t
op
ic
Th
e d
eriv
ati
ve o
f f(
x) a
s
the g
rad
ien
t o
f th
e
tan
gen
t to
th
e g
rap
h o
f
y =
f(x
) at
a p
oin
t; t
he
grad
ien
t o
f th
e t
an
gen
t as
a lim
it;
inte
rp
reta
tio
n a
s a
rate
of
ch
an
ge;
seco
nd
ord
er d
eriv
ati
ves
Fo
r e
xam
ple
,
kn
ow
led
ge t
hat
dx
dy
is t
he r
ate
of
ch
an
ge
of
y w
ith
resp
ect
to
x
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
19
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Dif
feren
tiati
on
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4
Dif
feren
tiati
on
co
nti
nu
ed
Wh
at
stu
den
ts n
eed
to
learn
No
tes
3.4
C
alc
ulu
s
Dif
feren
tiati
on
co
nti
nu
ed
apply
calc
ulu
s t
o
linear
kin
em
atics a
nd
to o
ther
sim
ple
pra
ctical pro
ble
ms
The d
ispla
cem
ent,
s
metr
es,
of
a p
art
icle
from
a f
ixed p
oin
t 0
aft
er
t seconds is g
iven
by:
s =
24
t2 –
t3,
0 ≤
t ≤
20
Fin
d e
xpre
ssio
ns f
or
the v
elo
city a
nd t
he
accele
ration
Exte
nsio
n t
op
ic
K
no
wle
dg
e o
f th
e
ch
ain
ru
le i
s n
ot
req
uir
ed
Th
e n
ota
tio
n f
/ (x)
may b
e u
sed
Fo
r e
xam
ple
, fo
r
1
n,
the a
bilit
y t
o
dif
feren
tiate
exp
ressio
ns s
uch
as
)1)(
52(
xx
an
d
21
2
3
5 x
xx
3
is
exp
ecte
d
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
20
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Dif
feren
tiati
on
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4
Dif
feren
tiati
on
co
nti
nu
ed
Wh
at
stu
den
ts n
eed
to
learn
No
tes
New
co
ncep
ts
Ap
plicati
on
s o
f
dif
feren
tiati
on
to
grad
ien
ts,
tan
gen
ts a
nd
no
rm
als
Use o
f
dif
feren
tiati
on
to
fin
d e
qu
ati
on
s o
f
tan
gen
ts a
nd
no
rm
als
at
sp
ecif
ic
po
ints
on
a c
urve
In
teg
rati
on
5
In
teg
rati
on
W
hat
stu
den
ts n
eed
to
learn
No
tes
3.4
C
alc
ulu
s
Dif
feren
tiati
on
co
nti
nu
ed
New
to
pic
In
defi
nit
e in
teg
rati
on
as
the r
everse o
f
dif
feren
tiati
on
inte
grati
on
of
n
x
Stu
den
ts s
ho
uld
kn
ow
th
at
a
co
nsta
nt
of
inte
grati
on
is
req
uir
ed
.
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
21
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
1 N
um
ber a
nd
alg
eb
ra
Dif
feren
tiati
on
3 S
eq
uen
ces,
fun
cti
on
s a
nd
grap
hs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
5
In
teg
rati
on
co
nti
nu
ed
Wh
at
stu
den
ts n
eed
to
learn
No
tes
3.4
Calc
ulu
s
Dif
feren
tiati
on
co
nti
nu
ed
New
to
pic
Fo
r e
xam
ple
, th
e
ab
ilit
y t
o in
teg
rate
exp
ressio
ns s
uch
as:
21
23
21
x
x a
nd
21
2 )2
(
x
x
is e
xp
ecte
d
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
22
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4.1
Lin
es a
nd
tria
ng
les
See F
oundation T
ier.
4.2
P
oly
go
ns
See F
oundation T
ier.
4.3
S
ym
metr
y
See F
oundation T
ier.
4.4
M
easu
res
See F
oundation T
ier.
4.5
C
on
str
ucti
on
See F
oundation T
ier.
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
23
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4.6
C
ircle
pro
perti
es
unders
tand a
nd u
se
the inte
rnal and
exte
rnal in
ters
ecting
chord
pro
pert
ies
recognis
e t
he t
erm
cyclic q
uadrila
tera
l
unders
tand a
nd u
se
angle
pro
pert
ies o
f th
e
cir
cle
inclu
din
g:
angle
subte
nded
by a
n a
rc a
t th
e
centr
e o
f a c
ircle
is
twic
e t
he a
ngle
subte
nded a
t any
poin
t on t
he
rem
ain
ing p
art
of
the c
ircum
fere
nce
angle
subte
nded
at
the
cir
cum
fere
nce b
y
a d
iam
ete
r is
a
right
angle
Form
al pro
of of
these
theore
ms is n
ot
requir
ed
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
24
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4.6
C
ircle
pro
perti
es
co
nti
nu
ed
angle
s in t
he s
am
e
segm
ent
are
equal
th
e s
um
of
the
opposite a
ngle
s o
f
a c
yclic
quadri
late
ral is
180
th
e a
ltern
ate
segm
ent
theore
m
4.7
G
eo
metr
ical
reaso
nin
g
pro
vid
e r
easons,
usin
g
sta
ndard
geom
etr
ical
sta
tem
ents
, to
support
num
eri
cal valu
es f
or
angle
s o
bta
ined in a
ny
geom
etr
ical conte
xt
involv
ing lin
es,
poly
gons a
nd c
ircle
s
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
25
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4.8
Trig
on
om
etr
y
an
d P
yth
ag
oras’
Th
eo
rem
unders
tand a
nd u
se
sin
e,
cosin
e a
nd
tangent
of
obtu
se
angle
s
unders
tand a
nd u
se
angle
s o
f ele
vation
and d
epre
ssio
n
unders
tand a
nd u
se
the s
ine a
nd c
osin
e
rule
s f
or
any t
riangle
use P
yth
agora
s’
Theore
m in 3
dim
ensio
ns
unders
tand a
nd u
se
the f
orm
ula
½ a
bsin
C for
the a
rea
of
a t
riangle
apply
tri
gonom
etr
ical
meth
ods t
o s
olv
e
pro
ble
ms in 3
dim
ensio
ns,
inclu
din
g
findin
g t
he a
ngle
betw
een a
lin
e a
nd a
pla
ne
The a
ngle
betw
een
two p
lanes w
ill not
be
requir
ed
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
26
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
Alg
eb
ra a
nd
fu
ncti
on
s
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4.9
M
en
su
rati
on
find p
eri
mete
rs a
nd
are
as o
f secto
rs o
f
cir
cle
s
Radia
n m
easure
is
exclu
ded
4.1
0 3
-D s
hap
es
an
d v
olu
me
find t
he s
urf
ace a
rea
and v
olu
me o
f a
sphere
and a
rig
ht
cir
cula
r cone u
sin
g
rele
vant
form
ula
e
convert
betw
een
volu
me m
easure
s
m3 →
cm
3 a
nd v
ice
vers
a
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
27
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
4.1
1 S
imil
arit
y
unders
tand t
hat
are
as
of
sim
ilar
figure
s a
re
in t
he r
atio o
f th
e
square
of
corr
espondin
g s
ides
unders
tand t
hat
volu
mes o
f sim
ilar
figure
s a
re in t
he r
atio
of
the c
ube o
f
corr
espondin
g s
ides
use a
reas a
nd
volu
mes o
f sim
ilar
figure
s in s
olv
ing
pro
ble
ms
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
28
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 N
um
ber a
nd
alg
eb
ra
5 V
ecto
rs a
nd
tran
sfo
rm
ati
on
geo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
5.1
V
ecto
rs
unders
tand t
hat
a
vecto
r has b
oth
magnitude a
nd
dir
ection
unders
tand a
nd u
se
vecto
r nota
tion
multip
ly v
ecto
rs b
y
scala
r quantities
add a
nd s
ubtr
act
vecto
rs
calc
ula
te t
he m
odulu
s
(magnitude)
of
a
vecto
r
find t
he r
esultant
of
two o
r m
ore
vecto
rs
apply
vecto
r m
eth
ods
for
sim
ple
geom
etr
ical
pro
ofs
The n
ota
tions ΟΑ
and
a w
ill be u
sed
ΟΑ
= 3
a,
AB
= 2
b,
BC
= c
so:
OC
= 3
a +
2b
+ c
CA
=
c –
2b
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
29
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
2 S
hap
e,
sp
ace a
nd
measu
res
5 V
ecto
rs a
nd
tran
sfo
rm
ati
on
geo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
5.2
Tran
sfo
rm
ati
on
geo
metr
y
See F
oundation T
ier.
Colu
mn v
ecto
rs m
ay
be u
sed t
o d
efine
transla
tions
6 S
tati
sti
cs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
6.1
G
rap
hic
al
rep
resen
tati
on
of
data
constr
uct
and
inte
rpre
t his
togra
ms
constr
uct
cum
ula
tive
frequency d
iagra
ms
from
tabula
ted d
ata
use c
um
ula
tive
frequency d
iagra
ms
For
continuous
vari
able
s w
ith u
nequal
cla
ss inte
rvals
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
30
-
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
3 H
an
dli
ng
data
6.2
S
tati
sti
cal
measu
res
estim
ate
the m
edia
n
from
a c
um
ula
tive
frequency d
iagra
m
unders
tand t
he
concept
of
a m
easure
of
spre
ad
find t
he inte
rquart
ile
range f
rom
a d
iscre
te
data
set
The t
erm
s ‘upper
quart
ile’ and ‘lo
wer
quart
ile’ m
ay b
e u
sed
estim
ate
the
inte
rquart
ile r
ange
from
a c
um
ula
tive
frequency d
iagra
m
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
31
-
UG
029447 –
Schem
e o
f W
ork
: Teachin
g I
GC
SE M
ath
em
atics a
longsid
e
Core
Math
em
atics 1
– I
ssue 1
– J
uly
2011 ©
Pears
on E
ducation L
imited 2
011
32
IG
CS
E M
ath
em
ati
cs (
Hig
her t
ier)
GC
E C
ore M
ath
em
ati
cs 1
un
it
AO
3 H
an
dli
ng
data
6 S
tati
sti
cs
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
6.3
P
ro
bab
ilit
y
dra
w a
nd u
se t
ree
dia
gra
ms
dete
rmin
e t
he
pro
bability t
hat
two o
r
more
independent
events
will both
occur
use s
imple
conditio
nal
pro
bability w
hen
com
bin
ing e
vents
Pic
kin
g t
wo b
alls o
ut
of
a b
ag,
one a
fter
the
oth
er,
without
repla
cem
ent
apply
pro
bability t
o
sim
ple
pro
ble
ms
-
Higher tier IGCSE Mathematics/GCE Core Mathematics 1 unit
content summary
The table below is a summary of the IGCSE Mathematics Higher
tier content and
GCE Core Mathematics 1 unit content that could be
delivered/taught alongside each
other, in the first year of the course. This scheme of work
should be used together
with the Higher tier course planner in the IGCSE Mathematics
Teacher’s Guide.
The module numbers in the table below refer to the module
numbers in the course
planner within the IGCSE Mathematics Teacher’s Guide. References
to topic areas in
GCE Core Mathematics 1 unit are in bold.
Year 1 content summary
Module number Module Title
*Estimated
teaching
hours
Number 2 Powers and roots
C1: Use and manipulation of surds 5
1
Algebraic manipulation
C1:Algebraic manipulation of polynomials, including
expanding brackets and collecting like terms,
factorisation
5
3
Linear equations and simultaneous linear equations
C1: Simultaneous equations: analytical solution by
substitution
7
5
Linear graphs
C1: Equation of a straight line, including the forms
)( 11 xxmyy and 0 cbyax . Conditions for two straight lines to
be parallel or perpendicular to
each other
7
6
Integer sequences
C1: Sequences, including those given by a formula for
the nth term and those generated by a simple relation
of the form 1nx f( ) nx
This could be done in the first year as an extension of
integer sequences
5
8 Inequalities
C1: Solution of linear and quadratic inequalities 6
Algebra
9 Indices
C1: Laws of indices for all rational exponents. 5
*Teachers should be aware that the estimated teaching hours are
approximate and
should only be used as a guideline.
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The table below is a summary of the IGCSE Mathematics Higher
tier content and
GCE Core Mathematics 1 unit content that could be
delivered/taught alongside each
other, in the second year of the course. This scheme of work
should be used
together with the Higher tier course planner in the IGCSE
Mathematics Teacher’s
Guide. The module numbers in the table below refer to the module
numbers in the
course planner within the IGCSE Mathematics Teacher’s Guide.
References to topic
areas in GCE Core Mathematics 1 unit are in bold.
Year 2 content summary
Module number Module Title
*Estimated
teaching
hours
7
Quadratic equations
C1: Completing the square. Solution of quadratic
graphs
10
11
Function notation
C1: Quadratic functions and their graphs. The
discriminant of the quadratic function.
10
12
Harder graphs
C1: Graphs of functions; sketching curves defined by
simple equations. Geometrical interpretation of
algebraic solution of equations. Use intersection points
of graphs of functions to solve equations. Knowledge
of the effect of simple transformations on the graphs
of y = f(x) as represented by y = af(x), y = f(x) + a,
y = f(x + a), y = f(ax)
10 Algebra
13
Calculus – Differentiation
C1: The derivative of f(x) as the gradient of the tangent to the
graph of f(x) at a point; the gradient of the
tangent as a limit; interpretation as a rate of change;
second order derivatives. Applications of
differentiation to gradients, tangents and normals
15
C1 topic 1
C1: Sequences and Series
Sequences could either be covered in Year 10 as an
extension of IGCSE/Certificate in Mathematics topic:
Integer sequence, or together with Arithmetic series in
the second year.
Arithmetic series, including the formula for the sum of
the first n natural numbers
10
C1 topic 2
C1: Calculus – Integration
Indefinite integration as the reverse of differentiation
integration of nx
15
*Teachers should be aware that the estimated teaching hours are
approximate and should
only be used as a guideline.
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Higher tier IGCSE Mathematics/GCE Core Mathematics 1 unit scheme
of work
This scheme of work only contains the modules that could be
extended through
teaching the Edexcel GCE Core Mathematics 1 unit alongside the
IGCSE
Mathematics. It should be used alongside the IGCSE Mathematics
course planner in
the Teacher’s Guide.
Number
Module 2 – Powers and roots [Year 1] Time: 4 – 6 hours
Target grades: A*/A/B/C
Content Area of specification
Squares and square roots 1.4
Cubes and cube roots 1.4
Using a calculator effectively to evaluate powers and roots
1.1
Powers of numbers – using index notation 1.4
Order of operations including powers (BIDMAS*) 1.1
Expressing a number as the product of powers of its prime
factors 1.4
Using prime factors to evaluate Highest Common Factors (HCF)
and
Lowest Common Multiples (LCM) 1.4
Understanding and using powers which are zero, negative or
fractions 1.4
Recognising the relationship between fractional powers and roots
1.4
Using laws of indices to simplify and evaluate numerical
expressions
involving integer, fractional and negative powers 1.4
Understanding the meaning of surds 1.4
Manipulating surds, including rationalising the denominator
1.4
*BIDMAS = Brackets, Indices, Division, Multiplication, Addition,
Subtraction
A/A* notes/tips
In order for students to aspire to the top grades, it is
essential that they are able to use algebraic manipulation and
index notation confidently
Remind students that when writing fractions, it is not usual to
write surds in the denominator, because without a calculator, it is
not always easy to work out the
value of the fraction, eg 2
1 , but ‘rationalising’ the denominator will help clear
the surds from the denominator
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Resources
Textbook References
Edexcel IGCSE
Mathematics A Student
Book 1
Unit 3: Number 3 page 117
Unit 3: Number 3 page 114 – 116
Edexcel IGCSE
Mathematics A Student
Book 2
Unit 2: Number 2 page 66 – 70
GCE Core Mathematics 1
Content Textbook reference
Write a number exactly as a surd 1.7
Rationalise the denominator of a fraction when it is a surd
1.8
Resources
Textbook References
Edexcel AS and A Level
Modular Mathematics Core
Mathematics 1
page 10 – 13
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ALGEBRA
Module 1 – Algebraic manipulation [Year 1] Time: 4 – 6 hours
Target grades: A*/A/B/C/D
Content Area of specification
Multiplying a single term over a bracket 2.2
Factorising by taking out a single common factor 2.2
Finding and simplifying the product of two linear
expressions,
eg (2x + 3)(3x – 1), (3x – 2y)(5x + 3y) 2.2
Factorising quadratic expressions, including the difference
of two squares 2.2
Adding and subtracting algebraic fractions, including
simplifying
algebraic fractions by cancelling common factors 2.2
Numerator and/or the denominator may be numeric, linear or
quadratic 2.2
Notes
Emphasise importance of using the correct symbolic notation, for
example 3a rather
than 3 a or a3. Students should be aware that there may be a
need to remove the numerical HCF of a quadratic expression before
factorising it in order to make
factorisation more obvious
A/A* notes/tips for Higher tier
Students need to be reminded that they should always factorise
algebraic expressions completely, setting their work out
clearly
In order for students to work towards to the top grades, it is
essential that they are confidently able to manipulate algebraic
expressions in a variety of
situations
When simplifying algebraic fractions, students should be
encouraged to fully factorise both the numerator and the
denominator, where possible
A typical common error is for students to ‘cancel out’ the terms
in x
Simplifying algebraic fractions is usually a challenging topic
for many students. A key point is that algebraic fractions are
actually generalised arithmetic, and
that the same rules apply
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Resources
Textbook References
Edexcel IGCSE
Mathematics A Student
Book 1
Unit 1: Algebra 1 page 11 – 12
Unit 2: Algebra 2 page 65 – 67
Unit 3: Algebra 3 page 121 – 123
Edexcel IGCSE
Mathematics A Student Book 2
Unit 5: Algebra 5 (Revision)
page 346 – 347
GCE Core Mathematics 1
Content Textbook reference
Simplify expressions by collecting like terms 1.1
Expand an expression by multiplying each term inside the
bracket by the term outside 1.3
Resources
Textbook References
Edexcel AS and A Level
Modular Mathematics Core
Mathematics 1
page 2, 4 – 6
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Module 3 – Linear equations and simultaneous linear equations
[Year 1]
Time: 6 – 8 hours
Target grades: B/C/D
Content Area of specification
Inverse operations 2.4
Understanding and use of ‘balancing’ methods 2.4
Solving simple linear equations 2.4
Solving linear equations:
with two or more operations 2.4
with the unknown on both sides 2.4
with brackets 2.4
with negative or fractional coefficients 2.4
with combinations of these 2.4
Setting up and solving simple linear equations to solve
problems, including
finding the value of a variable which is not the subject of the
formula 2.4
Solving simple simultaneous linear equations, including
cases
where one or both of the equations must be multiplied 2.6
Interpreting the equations as lines and their common
solution
as the point of intersection 2.6
Prior knowledge
Algebra: Modules 1 and 2
The idea that some operations are ‘opposite’ to each other
Notes
Students need to realise that not all linear equations can be
solved easily by either
observation or trial and improvement; a formal method is often
needed
Students should leave their answers in fractional form where
appropriate
Resources
Textbook References
Edexcel IGCSE
Mathematics A Student
Book 1
Unit 1: Algebra 1 page 12 – 17
Unit 2: Graphs 2 page 79 – 80
Unit 3: Algebra 3 page 126 – 130
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GCE Core Mathematics 1
Content Textbook reference
Solve simultaneous linear equations by elimination 3.1
Solve simultaneous linear equations by substitution 3.2
Use the substitution method to solve simultaneous equations
whereone equation is linear and the other is quadratic 3.3
Resources
Textbook References
Edexcel AS and A Level
Modular Mathematics Core Mathematics 1
page 28 – 31
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Module 5 – Linear graphs [Year 1] Time: 6 – 8 hours
Target grades: A/B/C/D
Content Area of specification
Recognising that equations of the form x = a and y = b
correspond to
straight line graphs parallel to the y-axis and to the x-axis
respectively 3.3
Completing tables of values and drawing graphs with equations of
the
form y = mx + c where the values of m and c are given and m may
be an
integer or a fraction 3.3
Drawing straight line graphs with equations in which y is given
implicitly in
terms of x, for example x + y = 7 3.3
Calculating the gradient of a straight line given its equation
of the
coordinates of two points on the line 3.3
Recognising that graphs with equations of the form y = mx +
c
are straight line graphs with gradient m and intercept (0, c) on
the y-axis 3.3
Finding the equation of a straight line given the coordinates of
two points
on the line 3.3
Finding the equation of a straight line parallel to a given line
3.3
Prior knowledge
Algebra: Modules 1, 2, 3 and 4
Notes
Axes should be labelled on graphs and a ruler should be used to
draw linear graphs
Science experiments/work could provide results which give linear
graphs
Resources
Textbook References
Edexcel IGCSE
Mathematics A Student Book 1
