edexcel level 1/level 2 certificate in mathematics (kma0) · edexcel level 1/level 2 certificate in...
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Scheme of work: Bridging to GCE
Edexcel Level 1/Level 2 Certificate in Mathematics (KMA0)First examination 2012
Teaching the Level 1/Level 2 Certificate in Mathematics alongside Core Mathematics 1
Edexcel, a Pearson company, is the UK’s largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, IGCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Higher National Diplomas, recognised by employers and higher education institutions worldwide.
We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.
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 development.
References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)
Authorised by Martin Stretton Prepared by Sharon Wood
Publications Code UG027243
All the material in this publication is copyright © Pearson Education Limited 2011
Introduction
The Edexcel Level 1/Level 2 Certificate in Mathematics 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 Level 1/Level 2 Certificate in Mathematics 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 Certificate 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 Certificate:
Sequences and series
Integration.
Contents
Mapping of Certificate in Mathematics Higher tier content to GCE Core Mathematics 1 unit content 1
Higher tier Mathematics Certificate/GCE Core Mathematics 1 unit content summary 33
Higher tier Mathematics Certificate/GCE Core Mathematics 1 unit scheme of work 35
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
1
Map
pin
g of
Cer
tifi
cate
in M
athem
atic
s H
igher
tie
r co
nte
nt
to G
CE
Cor
e M
athem
atic
s 1 u
nit
con
tent
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
1
Nu
mb
ers
an
d t
he
nu
mb
er
syst
em
S
tud
en
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts n
eed
to
learn
N
ote
s
1.1
In
teg
ers
See
Foundat
ion T
ier
1.2
Fra
ctio
ns
See
Foundat
ion T
ier
1.3
Deci
mals
co
nve
rt r
ecurr
ing
dec
imal
s in
to f
ract
ions
3.0
= 31
,
0.23
33…
= 9021
1.4
Po
wers
an
d
roo
ts
under
stan
d t
he
mea
nin
g o
f su
rds
m
anip
ula
te s
urd
s,
incl
udin
g r
atio
nal
isin
g
the
den
om
inat
or
wher
e th
e den
om
inat
or
is a
pure
surd
Exp
ress
in t
he
form
a2:
82
, 18
+ 32
Exp
ress
in t
he
form
a
+ b2
: (
3 +
52
)2
Exte
nsi
on
to
pic
Use
an
d
man
ipu
lati
on
of
surd
s
Stu
den
ts s
ho
uld
be
ab
le t
o r
ati
on
alise
d
en
om
inato
rs
use
index
law
s to
si
mplif
y an
d e
valu
ate
num
eric
al e
xpre
ssio
ns
invo
lvin
g inte
ger
, fr
actional
and n
egat
ive
pow
ers
Eva
luat
e:
3 82 ,
21
625
,
23
251
Exte
nsi
on
to
pic
Law
s o
f in
dic
es
for
all r
ati
on
al
exp
on
en
ts
Th
e e
qu
ivale
nce
of
nm a a
nd
nm a
sh
ou
ld
be k
no
wn
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
2
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
1
Nu
mb
ers
an
d t
he
nu
mb
er
syst
em
S
tud
en
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts n
eed
to
learn
N
ote
s
1.4
P
ow
ers
an
d
roo
ts c
on
tin
ued
ev
aluat
e H
ighes
t Com
mon F
acto
rs (
HCF)
an
d L
ow
est
Com
mon
Multip
les
(LCM
)
1.5
Set
lan
gu
ag
e
an
d n
ota
tio
n
under
stan
d s
ets
def
ined
in a
lgeb
raic
te
rms
under
stan
d a
nd u
se
subse
ts
under
stan
d a
nd u
se
the
com
ple
men
t of
a se
t
If A
is a
subse
t of
B,
then
A
B
Use
the
nota
tion A
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
3
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
1
Nu
mb
ers
an
d t
he
nu
mb
er
syst
em
S
tud
en
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
1.5
Set
lan
gu
ag
e a
nd
n
ota
tio
n
con
tin
ued
use
Ven
n d
iagra
ms
to
repre
sent
sets
and t
he
num
ber
of
elem
ents
in
sets
use
the
nota
tion n
(A)
for
the
num
ber
of
elem
ents
in t
he
set
A
use
set
s in
pra
ctic
al
situ
atio
ns
1.6
Perc
en
tag
es
use
rev
erse
per
centa
ges
repea
ted p
erce
nta
ge
chan
ge
In a
sal
e, p
rice
s w
ere
reduce
d b
y 30%
. The
sale
pri
ce o
f an
ite
m
was
£17.5
0.
Cal
cula
te
the
ori
gin
al p
rice
of
the
item
Cal
cula
te t
he
tota
l per
centa
ge
incr
ease
w
hen
an incr
ease
of
30%
is
follo
wed
by
a dec
rease
of
20%
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
4
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
1
Nu
mb
ers
an
d t
he
nu
mb
er
syst
em
S
tud
en
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
1.6
Perc
en
tag
es
con
tin
ued
so
lve
com
pound
inte
rest
pro
ble
ms
To incl
ude
dep
reci
atio
n
1.7
Rati
o a
nd
p
rop
ort
ion
See
Foundat
ion T
ier.
1.8
D
eg
ree o
f acc
ura
cy
solv
e pro
ble
ms
usi
ng
upper
and low
er
bounds
wher
e va
lues
ar
e giv
en t
o a
deg
ree
of
accu
racy
The
dim
ensi
ons
of
a re
ctan
gle
are
12cm
an
d 8
cm t
o t
he
nea
rest
cm
. Cal
cula
te,
to 3
sig
nific
ant
figure
s,
the
smal
lest
poss
ible
ar
ea a
s a
per
centa
ge
of
the
larg
est
poss
ible
ar
ea
1.9
Sta
nd
ard
fo
rm
expre
ss n
um
ber
s in
the
form
a
10n w
her
e n
is
an inte
ger
and
1 ≤
a <
10
solv
e pro
ble
ms
invo
lvin
g s
tandar
d
form
150
000
000
=
1.5
1
08
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
5
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
1 N
um
bers
an
d t
he
nu
mb
er
syst
em
S
tud
en
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
1.1
0 A
pp
lyin
g
nu
mb
er
See
Foundat
ion T
ier
1.1
1 Ele
ctro
nic
ca
lcu
lato
rs
See
Foundat
ion T
ier
2 E
qu
ati
on
s,
form
ula
e a
nd
id
en
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
:
No
tes
1
Alg
eb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts
need
to
learn
N
ote
s
2.1
Use
of
sym
bo
ls
use
index
nota
tion
invo
lvin
g f
ract
ional
, neg
ativ
e an
d z
ero
pow
ers
Sim
plif
y:
32
364
t,
31
4321
aa
a
Exte
nsi
on
to
pic
law
s o
f in
dic
es
for
all r
ati
on
al
exp
on
en
ts
Th
e e
qu
ivale
nce
of
nm a a
nd
nm a
sh
ou
ld
be k
no
wn
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
6
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
2 E
qu
ati
on
s,
form
ula
e a
nd
id
en
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts
need
to
learn
N
ote
s
2.2
Alg
eb
raic
m
an
ipu
lati
on
ex
pan
d t
he
pro
duct
of
two lin
ear
expre
ssio
ns
under
stan
d t
he
conce
pt
of
a quad
ratic
expre
ssio
n a
nd b
e ab
le
to f
acto
rise
such
ex
pre
ssio
ns
man
ipula
te a
lgeb
raic
fr
actions
wher
e th
e num
erat
or
and/o
r th
e den
om
inat
or
can b
e num
eric
, lin
ear
or
quad
ratic
(2x
+ 3
)(3x
– 1
)
(2x
– y)
(3x
+ y
)
Fact
ori
se:
x2 + 1
2x –
45
6 x2 –
5x
– 4
Exp
ress
as
a si
ngle
fr
action: 4
3
3
1
xx
3
)35(2
2
)14(3
x
x
xx
34
23
, x
x
1
2
1
3
12
21
xx
xx
Exte
nsi
on
to
pic
Alg
eb
raic
m
an
ipu
lati
on
of
po
lyn
om
ials
, in
clu
din
g
exp
an
din
g
bra
ckets
an
d
coll
ect
ing
lik
e
term
s,
fact
ori
sati
on
Stu
den
ts s
ho
uld
be
ab
le t
o u
se b
rack
ets
.
Fact
ori
sati
on
of
po
lyn
om
ials
of
deg
ree n
, n
≤ 3
, eg
xx
x3
42
3
.
Th
e
no
tati
on
f(x
). (
Use
of
the f
act
or
theo
rem
is
no
t re
qu
ired
)
Fact
ori
se a
nd s
implif
y:
12
42
2
x
xx
x
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
7
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
2 E
qu
ati
on
s,
form
ula
e a
nd
id
en
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
2.3
Exp
ress
ion
s an
d
form
ula
e
under
stan
d t
he
pro
cess
of
man
ipula
ting
form
ula
e to
chan
ge
the
subje
ct,
to incl
ude
case
s w
her
e th
e su
bje
ct m
ay a
ppea
r tw
ice,
or
a pow
er o
f th
e su
bje
ct o
ccurs
v2 = u
2 + 2
gs;
m
ake
s th
e su
bje
ct
m =
atat
11
;
mak
e t t
he
subje
ct
V =
34πr
3 ;
mak
e r
the
subje
ct
glT
2
;
mak
e l t
he
subje
ct
2.4
Lin
ear
eq
uati
on
s See
Foundat
ion T
ier.
4
17x
=
2 –
x,
25
3
)2(
6
)32(
xx
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
8
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
2 E
qu
ati
on
s,
form
ula
e a
nd
id
en
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
2.5
Pro
po
rtio
n
set
up p
roble
ms
invo
lvin
g d
irec
t or
inve
rse
pro
port
ion a
nd
rela
te a
lgeb
raic
so
lution
s to
gra
phic
al
repre
senta
tion o
f th
e eq
uat
ions
To incl
ude
only
the
follo
win
g:
y
x,
y
x1,
y
x2 ,
y
21 x
,
y
x3 ,
y
x
2.6
Sim
ult
an
eo
us
lin
ear
eq
uati
on
s ca
lcula
te t
he
exac
t so
lution
of
two
sim
ultan
eous
equat
ions
in t
wo
unkn
owns
inte
rpre
t th
e eq
uat
ions
as lin
es a
nd t
he
com
mon s
olu
tion a
s th
e poin
t of
inte
rsec
tion
3x –
4y
= 7
2x
– y
= 8
2x +
3y
= 1
7 3x
– 5
y =
35
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
9
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
2 E
qu
ati
on
s,
form
ula
e a
nd
id
en
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts n
eed
to
learn
N
ote
s
2.7
Qu
ad
rati
c eq
uati
on
s so
lve
quad
ratic
equat
ions
by
fact
ori
sation
solv
e quad
ratic
equat
ions
by
usi
ng t
he
quad
ratic
form
ula
form
and s
olv
e quad
ratic
equat
ions
from
dat
a giv
en in a
co
nte
xt
2x2 –
3x
+ 1
= 0
,
x(3x
– 2
) =
5
New
to
pic
Co
mp
leti
ng
th
e
squ
are
. S
olv
e
qu
ad
rati
c eq
uati
on
s
So
lve q
uad
rati
c eq
uati
on
s b
y
com
ple
tin
g t
he
squ
are
so
lve
sim
ultan
eous
equat
ions
in t
wo
unkn
ow
ns,
one
equat
ion b
eing lin
ear
and t
he
oth
er b
eing
quad
ratic
y =
2x
– 11
and
x2 +
y2 =
25
y =
11x
– 2
and
y =
5x2
New
to
pic
Sim
ult
an
eo
us
eq
uati
on
s: a
naly
tica
l so
luti
on
by
sub
stit
uti
on
Fo
r exam
ple
, w
here
o
ne e
qu
ati
on
is
lin
ear
an
d o
ne
eq
uati
on
is
qu
ad
rati
c
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
10
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
2 E
qu
ati
on
s,
form
ula
e a
nd
id
en
titi
es
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts n
eed
to
learn
N
ote
s
2.8
In
eq
ualiti
es
solv
e quad
ratic
ineq
ual
itie
s in
one
unkn
ow
n a
nd r
epre
sent
the
solu
tion s
et o
n a
num
ber
lin
e
iden
tify
har
der
ex
ample
s of re
gio
ns
def
ined
by
linea
r in
equal
itie
s
For
exam
ple
, b
ax
>d
cx
,
x2 ≤ 2
5, 4
x2 > 2
5
Shad
e th
e re
gio
n
def
ined
by
the
ineq
ual
itie
s x
≤ 4
,
y ≤
2x
+ 1
,
5x +
2y
≤ 2
0
New
to
pic
So
luti
on
of
lin
ear
an
d q
uad
rati
c in
eq
ualiti
es
Fo
r exam
ple
,
ax +
b, c
x +
d,
02
r
qxpx
,
bax
rqx
px
2
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
11
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Seq
uen
ces
an
d s
eri
es
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 3
S
eq
uen
ces
an
d s
eri
es
Wh
at
stu
den
ts n
eed
to
le
arn
N
ote
s
3.1
Seq
uen
ces
use
lin
ear
expre
ssio
ns
to d
escr
ibe
the
nth
term
of
an a
rith
met
ic
sequen
ce
1,
3,
5,
7,
9,
…
nth t
erm
= 2
n –
1
New
to
pic
New
to
pic
Seq
uen
ces,
in
clu
din
g
tho
se g
iven
by a
fo
rmu
la
for
the n
th t
erm
an
d t
ho
se
gen
era
ted
by a
sim
ple
re
lati
on
of
the f
orm
1nx =
f(
nx)
Ari
thm
eti
c se
ries,
in
clu
din
g t
he f
orm
ula
fo
r th
e s
um
of
the f
irst
n
natu
ral n
um
bers
Th
e g
en
era
l te
rm
an
d t
he s
um
of
n te
rms
of
the s
eri
es
are
req
uir
ed
. Th
e
pro
of
of
the s
um
fo
rmu
la s
ho
uld
be
kn
ow
n
Un
ders
tan
din
g o
f
no
tati
on
wil
l b
e
exp
ect
ed
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
12
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts n
eed
to
le
arn
N
ote
s
3.2
Fu
nct
ion
n
ota
tio
n
under
stan
d t
he
conce
pt
that
a f
unct
ion is
a m
appin
g b
etw
een
elem
ents
of
two s
ets
use
funct
ion n
ota
tions
of
the
form
f(
x) =
… a
nd
f :
x
…
under
stan
d t
he
term
s dom
ain a
nd r
ange
and
whic
h v
alues
may
nee
d
to b
e ex
cluded
fro
m t
he
dom
ain
under
stan
d a
nd f
ind t
he
com
posi
te f
unct
ion f
g an
d t
he
inve
rse
funct
ion
f 1
f (x)
=
x1,
excl
ude
x = 0
f(x)
=
3x
,
excl
ude
x <
–3
‘ fg’ w
ill m
ean ‘do
g
firs
t, t
hen
f’
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
13
C
ert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
3.3
Gra
ph
s plo
t an
d d
raw
gra
phs
with e
quat
ion:
y =
Ax3 +
Bx2 +
Cx
+ D
in
whic
h:
(i)
the
const
ants
are
in
teger
s an
d s
om
e co
uld
be
zero
(ii)
the
lett
ers
x an
d y
can b
e re
pla
ced
with a
ny
oth
er t
wo
lett
ers
y =
x3 ,
y =
3x3 –
2x2 +
5x
– 4,
y =
2x3 –
6x
+ 2
,
V =
60w
(60
– w
)
New
to
pic
Qu
ad
rati
c fu
nct
ion
s an
d
their
gra
ph
s
Th
e d
iscr
imin
an
t o
f a
qu
ad
rati
c fu
nct
ion
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
14
C
ert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
3.3
G
rap
hs
con
tin
ued
or:
y =
Ax3 +
Bx2 +
Cx
+ D
+
E/x
+ F
/x2
in w
hic
h:
(i)
the
const
ants
are
num
eric
al a
nd a
t le
ast
thre
e of
them
are
zer
o
(ii)
the
lett
ers
x an
d y
ca
n b
e re
pla
ced
with a
ny
oth
er t
wo
lett
ers
find t
he
gra
die
nts
of
non-l
inea
r gra
phs
y =
x1
, x
0,
y =
2x2 +
3x
+ 1
/x,
x
0,
y =
x1
(3x2 –
5),
x
0,
W =
25 d
, d
0
By
dra
win
g a
tan
gen
t
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
15
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 1
A
lgeb
ra a
nd
fu
nct
ion
s W
hat
stu
den
ts n
eed
to
le
arn
N
ote
s
3.3
Gra
ph
s co
nti
nu
ed
find t
he
inte
rsec
tion
poin
ts o
f tw
o gra
phs,
one
linea
r ( y
1) a
nd o
ne
non-l
inea
r (y
2),
and
reco
gnis
e th
at t
he
solu
tion
s co
rres
pond
to t
he
solu
tion
s of
y 2 –
y1
= 0
The
x-va
lues
of
the
inte
rsec
tion o
f th
e tw
o
gra
phs:
y =
2x
+ 1
y =
x2 +
3x
– 2
are
the
solu
tions
of:
x2 + x
– 3
= 0
Exte
nsi
on
to
pic
Gra
ph
s o
f fu
nct
ion
s;
sketc
hin
g c
urv
es
defi
ned
b
y s
imp
le e
qu
ati
on
s.
Geo
metr
ical
inte
rpre
tati
on
of
alg
eb
raic
so
luti
on
of
eq
uati
on
s. U
se
inte
rsect
ion
po
ints
of
gra
ph
s o
f fu
nct
ion
s to
so
lve e
qu
ati
on
s
Fu
nct
ion
s to
in
clu
de
sim
ple
cu
bic
fu
nct
ion
s an
d t
he
reci
pro
cal fu
nct
ion
xky
, w
ith
0
x
Kn
ow
led
ge o
f th
e
term
asy
mp
tote
is
exp
ect
ed
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
16
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
3.3
G
rap
hs
con
tin
ued
calc
ula
te t
he
gra
die
nt
of
a st
raig
ht
line
giv
en
the
Car
tesi
an
coord
inat
es o
f tw
o
poin
ts
Sim
ilarly,
the
x-va
lues
of
the
inte
rsec
tion o
f th
e tw
o g
raphs:
y =
5
y =
x3 –
3x2 +
7
are
the
solu
tions
of:
x3 – 3
x2 + 2
= 0
re
cognis
e th
at
equat
ions
of th
e fo
rm
y =
mx
+ c
are
str
aight
line
gra
phs
with
gra
die
nt
m a
nd
inte
rcep
t on t
he
y axi
s at
the
poin
t ( 0
, c)
find t
he
equat
ion o
f a
stra
ight
line
par
alle
l to
a
giv
en lin
e
Find t
he
equat
ion o
f th
e st
raig
ht
line
thro
ugh
(1,
7)
and (
2,
9)
Exte
nsi
on
to
pic
Eq
uati
on
s o
f a s
traig
ht
lin
e,
incl
ud
ing
th
e
form
s)
(2
12
1x
xm
yy
an
d
0
cby
ax
To
in
clu
de:
1)
the e
qu
ati
on
of
a
lin
e t
hro
ug
h t
wo
g
iven
po
ints
2
) th
e e
qu
ati
on
of
a
lin
e p
ara
llel (o
r p
erp
en
dic
ula
r) t
o a
g
iven
lin
e t
hro
ug
h
a g
iven
po
int.
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
17
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Co
ord
inate
geo
metr
y in
th
e (
x, y
)
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 2
C
oo
rdin
ate
g
eo
metr
y in
th
e (
x, y
)
Wh
at
stu
den
ts n
eed
to
le
arn
N
ote
s
Exte
nsi
on
to
pic
Co
nd
itio
ns
for
two
st
raig
ht
lin
es
to b
e
para
llel o
r p
erp
en
dic
ula
r to
each
oth
er
Fo
r exam
ple
, th
e
lin
e p
erp
en
dic
ula
r to
th
e lin
e
184
3
y
x,
thro
ug
h t
he p
oin
t ,2(
)3,
has
the
eq
uati
on
)2(
343
x
y
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
18
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Co
ord
inate
geo
metr
y in
th
e (
x, y
)
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 2
C
oo
rdin
ate
g
eo
metr
y in
th
e (
x, y
)
Wh
at
stu
den
ts n
eed
to
le
arn
N
ote
s
3.3
Gra
ph
s co
nti
nu
ed
Exte
nsi
on
to
pic
Kn
ow
led
ge o
f th
e e
ffect
o
f si
mp
le t
ran
sfo
rmati
on
s o
n t
he g
rap
h o
f y
= f
(x)
as
rep
rese
nte
d b
y y
= a
f(x)
,
y =
f (
x) +
a,
y =
f (
x +
a),
y
= f
(ax
)
Stu
den
ts s
ho
uld
b
e a
ble
to
ap
ply
o
ne o
f th
ese
tr
an
sfo
rmati
on
s
to a
ny f
un
ctio
n
(qu
ad
rati
cs,
cub
ics,
re
cip
roca
l) a
nd
sk
etc
h t
he r
esu
ltin
g
gra
ph
.
Giv
en
th
e g
rap
h o
f
an
y f
un
ctio
n y
= f
(x)
stu
den
ts s
ho
uld
be
ab
le t
o s
ketc
h t
he
gra
ph
resu
ltin
g
fro
m o
ne o
f th
ese
tran
sfo
rmati
on
s.
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
19
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Dif
fere
nti
ati
on
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 4
D
iffe
ren
tiati
on
W
hat
stu
den
ts n
eed
to
le
arn
No
tes
3.4
Calc
ulu
s D
iffe
ren
tiati
on
under
stan
d t
he
conce
pt
of
a va
riab
le
rate
of
chan
ge
diffe
rentiat
e in
teger
pow
ers
of x
det
erm
ine
gra
die
nts
, ra
tes
of
chan
ge,
tu
rnin
g p
oin
ts
(max
ima
and m
inim
a)
by
diffe
rentiat
ion a
nd
rela
te t
hes
e to
gra
phs
dis
tinguis
h b
etw
een
max
ima
and m
inim
a by
consi
der
ing t
he
gen
eral
shap
e of
the
gra
ph
y =
x +
x9
Find t
he
Car
tesi
an
coord
inat
es o
f th
e m
axim
um
and
min
imum
poi
nts
Exte
nsi
on
to
pic
Th
e d
eri
vati
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
gra
die
nt
of
the t
an
gen
t as
a lim
it;
inte
rpre
tati
on
as
a
rate
of
chan
ge;
seco
nd
o
rder
deri
vati
ves
Fo
r exam
ple
,
kn
ow
led
ge t
hat
dxdy
is t
he r
ate
of
chan
ge
of
y wit
h r
esp
ect
to
x
UG
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evel
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ath
ematics
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de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
20
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Dif
fere
nti
ati
on
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 4
D
iffe
ren
tiati
on
co
nti
nu
ed
W
hat
stu
den
ts n
eed
to
le
arn
No
tes
3.4
Calc
ulu
s D
iffe
ren
tiati
on
co
nti
nu
ed
apply
cal
culu
s to
lin
ear
kinem
atic
s an
d
to o
ther
sim
ple
pra
ctic
al p
roble
ms
The
dis
pla
cem
ent,
s
met
res,
of
a par
ticl
e fr
om
a f
ixed
poin
t 0
afte
r t s
econds
is g
iven
by:
s = 2
4t2 –
t3 ,
0 ≤
t ≤
20
Find e
xpre
ssio
ns
for
the
velo
city
and t
he
acce
lera
tion
Exte
nsi
on
to
pic
K
no
wle
dg
e o
f th
e
chain
ru
le i
s n
ot
req
uir
ed
Th
e n
ota
tio
n f
/ (x)
may b
e u
sed
Fo
r exam
ple
, fo
r 1
n
, th
e a
bilit
y t
o
dif
fere
nti
ate
exp
ress
ion
s su
ch a
s )1
)(52(
xx
an
d
21
2
3
35 xx
x
is
exp
ect
ed
UG
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eme
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evel
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ertifica
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ematics
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de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
21
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Dif
fere
nti
ati
on
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 4
D
iffe
ren
tiati
on
co
nti
nu
ed
W
hat
stu
den
ts n
eed
to
le
arn
No
tes
New
co
nce
pts
Ap
plica
tio
ns
of
dif
fere
nti
ati
on
to
g
rad
ien
ts,
tan
gen
ts a
nd
n
orm
als
Use
of
dif
fere
nti
ati
on
to
fi
nd
eq
uati
on
s o
f ta
ng
en
ts a
nd
n
orm
als
at
speci
fic
po
ints
on
a c
urv
e
Inte
gra
tio
n
5
Inte
gra
tio
n
Wh
at
stu
den
ts n
eed
to
le
arn
N
ote
s
3.4
Calc
ulu
s D
iffe
ren
tiati
on
co
nti
nu
ed
New
to
pic
Ind
efi
nit
e in
teg
rati
on
as
the r
evers
e o
f d
iffe
ren
tiati
on
inte
gra
tio
n o
f n x
Stu
den
ts s
ho
uld
kn
ow
th
at
a
con
stan
t o
f in
teg
rati
on
is
req
uir
ed
.
UG
027243 –
Sch
eme
of
Work
: Tea
chin
g L
evel
1/L
evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
22
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
1 N
um
ber
an
d a
lgeb
ra
Dif
fere
nti
ati
on
3 S
eq
uen
ces,
fu
nct
ion
s an
d
gra
ph
s
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s 5
In
teg
rati
on
co
nti
nu
ed
W
hat
stu
den
ts n
eed
to
le
arn
No
tes
3.4
Calc
ulu
s D
iffe
ren
tiati
on
co
nti
nu
ed
N
ew
to
pic
Fo
r exam
ple
, th
e
ab
ilit
y t
o in
teg
rate
exp
ress
ion
s su
ch
as:
21
23
21
x
x a
nd
21
2 )2(
x
x
is
exp
ect
ed
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evel
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ertifica
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ematics
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de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
23
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
4.1
Lin
es
an
d
tria
ng
les
See
Foundat
ion T
ier.
4.2
Po
lyg
on
s See
Foundat
ion T
ier.
4.3
Sym
metr
y
See
Foundat
ion T
ier.
4.4
Measu
res
See
Foundat
ion T
ier.
4.5
Co
nst
ruct
ion
See
Foundat
ion T
ier.
UG
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eme
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evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
24
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
4.6
Cir
cle
pro
pert
ies
under
stan
d a
nd u
se
the
inte
rnal
and
exte
rnal
inte
rsec
ting
chord
pro
per
ties
re
cognis
e th
e te
rm
cycl
ic q
uad
rila
tera
l under
stan
d a
nd u
se
angle
pro
per
ties
of
the
circ
le incl
udin
g:
an
gle
subte
nded
by
an a
rc a
t th
e ce
ntr
e of
a ci
rcle
is
twic
e th
e an
gle
su
bte
nded
at
any
poin
t on t
he
rem
ainin
g p
art
of
the
circ
um
fere
nce
an
gle
subte
nded
at
the
circ
um
fere
nce
by
a dia
met
er is
a ri
ght
angle
Form
al p
roof of
thes
e th
eore
ms
is n
ot
requir
ed
UG
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eme
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evel
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ertifica
te in M
ath
ematics
alo
ngsi
de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
25
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
4.6
Cir
cle
pro
pert
ies
con
tin
ued
an
gle
s in
the
sam
e se
gm
ent
are
equal
th
e su
m o
f th
e opposi
te a
ngle
s of
a cy
clic
quad
rila
tera
l is
180
th
e al
tern
ate
segm
ent
theo
rem
4.7
Geo
metr
ical
reaso
nin
g
pro
vide
reas
ons,
usi
ng
stan
dar
d g
eom
etri
cal
stat
emen
ts,
to s
upport
num
eric
al v
alues
for
angle
s obta
ined
in a
ny
geo
met
rica
l co
nte
xt
invo
lvin
g lin
es,
poly
gons
and c
ircl
es
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evel
2 C
ertifica
te in M
ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
26
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
4.8
Tri
go
no
metr
y
an
d P
yth
ag
ora
s’
Th
eo
rem
under
stan
d a
nd u
se
sine,
cosi
ne
and
tangen
t of
obtu
se
angle
s
under
stan
d a
nd u
se
angle
s of
elev
atio
n
and d
epre
ssio
n
under
stan
d a
nd u
se
the
sine
and c
osi
ne
rule
s fo
r an
y tr
iangle
use
Pyt
hag
ora
s’
Theo
rem
in 3
dim
ensi
ons
under
stan
d a
nd u
se
the
form
ula
½
abs
in C
for
the
area
of
a tr
iangle
apply
tri
gonom
etri
cal
met
hods
to s
olv
e pro
ble
ms
in 3
dim
ensi
ons,
incl
udin
g
findin
g t
he
angle
bet
wee
n a
lin
e an
d a
pla
ne
The
angle
bet
wee
n
two p
lanes
will
not
be
requir
ed
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eme
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evel
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ertifica
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ematics
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de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
27
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
Alg
eb
ra a
nd
fu
nct
ion
s
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
4.9
M
en
sura
tio
n
find p
erim
eter
s an
d
area
s of
sect
ors
of
circ
les
Rad
ian m
easu
re is
excl
uded
4.1
0 3
-D s
hap
es
an
d v
olu
me
find t
he
surf
ace
area
an
d v
olu
me
of
a sp
her
e an
d a
rig
ht
circ
ula
r co
ne
usi
ng
rele
vant
form
ula
e
conve
rt b
etw
een
volu
me
mea
sure
s m
3 →
cm
3 a
nd v
ice
vers
a
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evel
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ematics
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de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
28
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
4 G
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
4.1
1 S
imil
ari
ty
under
stan
d t
hat
are
as
of
sim
ilar
figure
s ar
e in
the
ratio o
f th
e sq
uar
e of
corr
espondin
g s
ides
under
stan
d t
hat
vo
lum
es o
f si
mila
r figure
s ar
e in
the
ratio
of
the
cube
of
corr
espondin
g s
ides
use
are
as a
nd
volu
mes
of
sim
ilar
figure
s in
solv
ing
pro
ble
ms
UG
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eme
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chin
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evel
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ertifica
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ath
ematics
alo
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de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
29
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 N
um
ber
an
d a
lgeb
ra
5 V
ect
ors
an
d
tran
sfo
rmati
on
g
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
5.1
Vect
ors
under
stan
d t
hat
a
vect
or
has
both
m
agnitude
and
dir
ection
under
stan
d a
nd u
se
vect
or
nota
tion
multip
ly v
ecto
rs b
y sc
alar
quan
tities
add a
nd s
ubtr
act
vect
ors
calc
ula
te t
he
modulu
s (m
agnitude)
of
a ve
ctor
find t
he
resu
ltan
t of
two o
r m
ore
vec
tors
apply
vec
tor
met
hods
for
sim
ple
geo
met
rica
l pro
ofs
The
nota
tions ΟΑ
and
a w
ill b
e use
d
ΟΑ
= 3
a, A
B=
2b,
BC=
c
so:
OC
= 3
a +
2b
+ c
CA
=
c –
2b
UG
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evel
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ertifica
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ath
ematics
alongsi
de
Core
Mat
hem
atic
s 1 –
Iss
ue
1 –
July
2011
© P
ears
on E
duca
tion L
imited
2011
30
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
2 S
hap
e,
space
an
d m
easu
res
5 V
ect
ors
an
d
tran
sfo
rmati
on
g
eo
metr
y
Stu
den
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
5.2
Tra
nsf
orm
ati
on
g
eo
metr
y
See
Foundat
ion T
ier.
Colu
mn v
ecto
rs m
ay
be
use
d t
o d
efin
e
tran
slat
ions
6 S
tati
stic
s S
tud
en
ts s
ho
uld
be
tau
gh
t to
: N
ote
s
6.1
Gra
ph
ical
rep
rese
nta
tio
n
of
data
const
ruct
and
inte
rpre
t his
togra
ms
const
ruct
cum
ula
tive
fr
equen
cy d
iagra
ms
from
tab
ula
ted d
ata
use
cum
ula
tive
fr
equen
cy d
iagra
ms
For
continuou
s va
riab
les
with u
neq
ual
cl
ass
inte
rval
s
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evel
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ertifica
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ematics
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de
Core
Math
ematics
1 –
Iss
ue
1 –
July
2011 ©
Pea
rson E
duca
tion L
imited
2011
31
Cert
ific
ate
in
Math
em
ati
cs (
Hig
her
tier)
G
CE C
ore
Math
em
ati
cs 1
un
it
AO
3 H
an
dli
ng
data
6.2
Sta
tist
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UG027243 – Scheme of Work: Teaching Level 1/Level 2 Certificate in Mathematics alongside
Core Mathematics 1 – Issue 1 – July 2011 © Pearson Education Limited 2011
33
Higher tier Mathematics Certificate/GCE Core Mathematics 1 unit content summary The table below is a summary of the Mathematics Certificate 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 Mathematics Certificate Teacher’s Guide. The module numbers in the table below refer to the module numbers in the course planner within the Mathematics Certificate 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.
UG027243 – Scheme of Work: Teaching Level 1/Level 2 Certificate in Mathematics
alongside Core Mathematics 1 – Issue 1 – July 2011 © Pearson Education Limited 2011
34
The table below is a summary of the Mathematics Certificate 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 Mathematics Certificate Teacher’s Guide. The module numbers in the table below refer to the module numbers in the course planner within the Mathematics Certificate 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.
UG027243 – Scheme of Work: Teaching Level 1/Level 2 Certificate in Mathematics alongside
Core Mathematics 1 – Issue 1 – July 2011 © Pearson Education Limited 2011
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Higher tier Mathematics Certificate/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 Mathematics Certificate. It should be used alongside the Mathematics Certificate 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
UG027243 – Scheme of Work: Teaching Level 1/Level 2 Certificate in Mathematics
alongside Core Mathematics 1 – Issue 1 – July 2011 © Pearson Education Limited 2011
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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
Unit 1: Graphs 1 page 19 – 27
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GCE Core Mathematics 1
Content Textbook reference
Write the equation of a straight line in the form of y = mx + c or ax + by + c = 0 5.1
Work out the gradient m of the line joining the point with coordinates (x 1 , y 1 ) to the point with the coordinates (x 2 , y 2 )
by using the formula
m = 12
12
xxyy
5.2
Find the equation of a line with gradient m that passes through the point with coordinates (x 1 , y 1 ) by using the formula
)( 11 xxmyy 5.3
Find the equation of the line that passes through the points with the coordinates (x 1 , y 1 ) and (x 2 , y 2 ) by using the formula
12
1
12
1
xxxx
yyyy
5.4
Work out the gradient of a line that is perpendicular to the line y = mx + c 5.5
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 74 – 90
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Module 6 – Integer sequences [Year 1] Time: 4 – 6 hours
Target grades: B/C/D
Content Area of specification
Using term-to-term and position-to-term definitions to generate the terms of a sequence 3.1
Finding and using linear expressions to describe the nth term of an arithmetic sequence 3.1
Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 1
Unit 5: Sequences 5 page 254 – 264
GCE Core Mathematics 1
Content Textbook reference
A series of numbers following a set rule is called a sequence 6.1
Know a formula for the nth term of a sequence (eg 13 nU n )
to find any term in the sequence 6.2
Know the rule to get from one term to the next, and use this information to produce a recurrence relationship (or recurrence formula) 6.3
A sequence that increases by a constant amount each time is called an arithmetic sequence 6.4
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 92 – 100
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Module 7 – Quadratic equations [Year 2] Time: 9 – 11 hours
Target grade: A*/A/B/C
Content Area of specification
Solving quadratic equations by factorisation 2.7
Solving quadratic equations by using the quadratic formula 2.7
Setting up and solving quadratic equations from data given in a context 2.7
Solving exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear in each unknown and the other is linear in one unknown and quadratic in the other 2.7
Solving exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear in each unknown and the other is linear in one unknown and the other is of the form x2 + y2 = r2 2.7
Prior knowledge
Algebra: Modules 1 and 3
Notes
Remind students that they should factorise a quadratic before using the formula
A/A* notes/tips
Remind students that it is important to always factorise completely before resorting to using the quadratic formula
When applying the quadratic formula, students must substitute the correct values into the formula. They should be reminded that rounding or truncating during the process leads to inaccurate solutions
Often solving equations with algebraic fractions is a challenge for most students, however they should be encouraged to show their working out through using a few lines of correct algebra. Remind students of the value of retaining the structure of the equation throughout their working, rather than merely treating the algebra as an expression to be simplified
Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 1
Unit 5: Algebra 5 page 248 – 251
Edexcel IGCSE Mathematics A Student Book 2
Unit 2: Algebra 2 page 71 – 80 Unit 3: Algebra 3 page 176 – 182
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GCE Core Mathematics 1
Content Textbook reference
Plot graphs of quadratic equations 2.1
Solve quadratic equations using factorising 2.2
Write quadratic expressions in another form by completing the square 2.3
Solve quadratic equations by completing the square 2.4
Solve quadratic equations by using the formula 2.5
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 17 – 23
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Module 8 – Inequalities [Year 1] Time: 5 – 7 hours
Target grades: A/B/C
Content Area of specification
Understanding and using the symbols >, <, ≥ and ≤ 2.8
Understanding and using the convention for open and closed intervals on a number line 2.8
Solving simple linear inequalities in one variable, including ‘double-ended’ inequalities 2.8
Representing on a number line the solution set of simple linear inequalities 2.8
Finding the integer solutions of simple linear inequalities 2.8
Using regions to represent simple linear inequalities in one variable 2.8
Using regions to represent the solution set to several linear inequalities in one or two variables 2.8
Solving quadratic inequalities in one unknown and representing the solution set on a number line 2.8
Prior knowledge
Algebra: Modules 3, 5 and 7
Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 1
Unit 2: Algebra 2 page 74 – 78, 81 – 86
Edexcel IGCSE Mathematics A Student Book 2
Unit 2: Algebra 2 page 81 – 84 Unit 5: Algebra 5 page 356
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GCE Core Mathematics 1
Content Textbook reference
Solve linear inequalities using similar methods to those for solvinglinear equations 3.4
Solve quadratic inequalities 3.5
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 31 – 39
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Module 9 – Indices [Year 1] Time: 4 – 6 hours
Target grades: A/B/C/D
Content Area of specification
Using index notation for positive integer powers 2.1
Substituting positive and negative numbers into expressions and formulae with quadratic and/or cubic terms 2.1
Completing tables of values and drawing graphs of quadratic functions 3.3
Using index notation with positive, negative and fractional powers to simplify expressions 2.1
Prior knowledge
Algebra: Modules 2 and 4
Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 1
Unit 2: Number 2 page 60, 73 – 74 Unit 4: Graphs 4 page 185 – 190
Edexcel IGCSE Mathematics A Student Book 2
Unit 2: Number 2 page 66 – 70
GCE Core Mathematics 1
Content Textbook reference
Simplify expressions and functions by using rules of indices (powers) 1.2
Extend rules of indices to all rational exponents 1.6
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 3,4 and 8,9
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Module 11 – Function notation [Year 2] Time: 9 – 11 hours
Target grades: A*/A/B
Content Area of specification
Understanding the concept that a function is a mapping between elements of two sets 3.2
Using function notation of the form f(x) = … and f x: 3.2
Understanding the terms domain and range 3.2
Understanding which parts of the domain may need to be excluded 3.2
Understanding and using composite function fg and inverse function f –1 3.2
Prior knowledge
Algebra: Modules 1, 2 and 3
A/A* notes/tips
This tends to be demanding topic for students and in order to deepen their understanding of how to apply their knowledge of functions in different types of questions, they should be given plenty of practice
Students may need to be reminded that f(x) = y
When solving f(x) = g(x), given the graphs of both functions, remind students that they should give their answers as solutions of x
Remind students that when one function is followed by another, the result is a composite function, eg fg(x) means do f first followed by g, where the domain of f is the range of g
Students need to understand, and be able to, use the concepts of domain and range, as this will enable them to develop an appropriate working knowledge of functions. In particular, students must be familiar with the concept that division by zero is undefined,
eg for g(x) = 2
1
x, 02 x , which means
x = 2 must be excluded from the domain of g
For inverse functions, remind students that the inverse of f(x) is the function
that ‘undoes’ whatever f(x) has done, and that the notation f 1 (x) is used
It is helpful to remind students that if the inverse function is not obvious then:
– Step 1: write the function as y =…
– Step 2: change any x to y, and any y to x
– Step 3: make y the subject, giving the inverse function
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Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 2
Unit 3: Algebra 3 page 183 – 197
GCE Core Mathematics 1
Content Textbook reference
Transform the curve of a function f(x) by simple translations 4.5
Transform the curve of a function f(x) by simple stretches 4.6
Perform simple transformations on a given sketch of a function 4.7
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 55 – 65
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Module 12 – Harder graphs [Year 2] Time: 9 – 11 hours
Target grades: A*/A/B
Content Area of specification
Plotting and drawing graphs with equation y = Ax3 + Bx2 + Cx + D in which
(i) the constants are integers and some could be zero
(ii) the letters x and y can be replaced with any other two letters 3.3
Plotting and drawing graphs with equation
y = Ax3 + Bx2 + Cx + D + xE
+ 2x
F
in which
(i) the constants are integers and at least three of them are zero
(ii) the letters x and y can be replaced with any other two letters 3.3
Finding the gradients of non-linear graphs by drawing a tangent 3.3
Finding the intersection points of two graphs, one linear (y1) and one non-linear (y2) and recognising that the solutions correspond to y2 – y1 = 0 3.3
Prior knowledge
Algebra: Modules 1, 2, 3, 5 and 9
Notes
Students should be made aware that they should not use rulers to join plotted points on non-linear graphs
When plotting points or reading off values from a graph, the scales on the axes should be checked carefully
A/A* notes/tips
Remind students that when finding an estimate for the gradient of a graph y = f(x) at given point, a tangent drawn at this point is helpful, although a related, correct division, to find the gradient, is required to gain top marks in a question
Students should recognise that cubic graphs have distinctive shapes that depend on the coefficient of 3x
Students should recognise that reciprocal graphs have x as the denominator, and that they produce a type of curve called a hyperbola. An awareness of the concept of the smallest (minimum) value of y, and the value of x where this happens on the graph, is helpful
Students should appreciate that an accurately drawn graph can be used to solve equations that may prove difficult to solve by other methods. They should also appreciate that most graphs of real-life situations are curves rather than straight lines. Information on rates of change can still be found by drawing a tangent to a curve, and using this to estimate the gradient of the curve at this point
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Students should recognise that the algebraic method is more accurate than the graphical method of solving simultaneous equations, in particular when one equation is linear and the other equation is nonlinear
Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 2
Unit 1: Graphs 1 page 19 – 27 Unit 3: Graphs 3 page 198 – 209
GCE Core Mathematics 1
Content Textbook reference
Sketch graphs of quadratic equations and solve problems using the discriminant 2.6
Sketch cubic curve of the form y = Ax3 + Bx2 + Cx + D 4.1
Sketch and interpret graphs of the cubic form y = x3 4.2
Sketch the reciprocal function xky , where k is a constant 4.3
Sketch curves of functions to show points of intersection and solutions to equations 4.4
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 23 – 25, 42 – 55
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Module 13 – Calculus [Year 2] Time: 14 – 16 hours
Target grades: A*/A/B
Content Area of specification
Understanding the concept of a variable rate of change 3.4
Differentiating integer powers of x 3.4
Determining gradients, rates of change, maxima and minima by differentiation and relating these to graphs 3.4
Applying calculus to linear kinematics and to other simple practical problems 3.4
Prior knowledge
Algebra; Modules 1, 2, 5, 9 and 12
Notes
When applying calculus to linear kinematics, the reverse of differentiation will not be required
A/A* notes/tips
Student should understand that the process of finding the gradient of a curve is called differentiation, where the result is the derivative or the gradient
function, and that the gradient of a curve can also be represented by dxdy
Students should be encouraged to set their work out appropriately, maintaining the structure of their solution, as this will aid their understanding, and revision, of the topic, particularly as it increases in complexity
Students need to understand the turning points are points on the curve where the gradient is zero. They should also be able to distinguish between a minimum turning point and a maximum turning point
Students need to be able to apply their knowledge of differentiation to the motion of a particle in a straight line, including speed and acceleration
Resources
Textbook References
Edexcel IGCSE Mathematics A Student Book 2
Unit 4: Graphs 4 page 268 – 287
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GCE Core Mathematics 1
Differentiation
Content Textbook reference
Estimate the gradient of the tangent 7.1
Find the formula for the gradient of the function f(x) = nx 7.2
Find the gradient formula for a function such as f(x) = 384 2 xx 7.3
Find the gradient formula for a function such as f(x) = 2
123 xxx 7.4
Expand or simplify polynomial functions so they are easier to differentiate 7.5
Repeat the process of differentiation to give a second derivative 7.6
Find the rate of change of a function f at a particular points using f /(x) and substituting in the value of x 7.7
Use differentiation to find the gradient of a tangent to a curve and
then find the equation of the tangent and the normal to the curve at a specified point 7.8
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 113 – 131
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C1 topic
Module 1 – Sequences and Series [Year 2] Time: 9 – 11 hours
GCE Core Mathematics 1
Content Textbook reference
Arithmetic series are formed by adding together the terms of an arithmetic sequence 6.5
Find the sum of an arithmetic series 6.6
Use to signify ‘the sum of’ 6.7
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 100 – 110
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C1 topic
Module 2 – Integration [Year 2] Time: 14 – 16 hours
GCE unit Core Mathematics 1
Content Textbook reference
Integrate functions of the form f(x) = nax where n ℝ and a is a constant 8.1
Apply the principle of integration separately to each term of dxdy
8.2
Use the integral sign 8.3
Simplify an expression into separate terms of the form nx 8.4
Find the constant of integration, c, when given any point (x, y) that the curve of the function passes through 8.5
Resources
Textbook References
Edexcel AS and A Level Modular Mathematics Core Mathematics 1
page 134 – 142
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