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Syllabus Snapshot
GCSE Mathematics
Exam Board: OCR
© OCR 2016
GCSE (9–1) in Mathematics4
2
2 Thespecificationoverview
2a. OCR’sGCSE(9–1)inMathematics(J560)ea ne s a e ente e eithe n ati n tie ( a e 1 a e an a e ) or i he tie ( a e a e an a e )
QualificationOverview AssessmentOverview
Foundationtier a es t 1• a e 1 ( n ati n tie )
1
• a e ( n ati n tie )
• a e ( n ati n tie )
i en a e1 ma s
1 h min tesCa c at e mi e
331–3
%
t ta
GCSE
i en a e1 ma s
1 h min tesCalculator not e mi e
331–3
%
t ta
GCSE
i en a e1 ma s
1 h min tesCa c at e mi e
331–3
%
t ta
GCSE
Highertier a es 9 t • a e ( i he tie )
• a e ( i he tie )
• a e ( i he tie )
i en a e1 ma s
1 h min tesCa c at e mi e
331–3
%
t ta
GCSE
i en a e1 ma s
1 h min tesCalculator not e mi e
331–3
%
t ta
GCSE
i en a e1 ma s
1 h min tesCa c at e mi e
331–3
%
t ta
GCSE
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2
2b. ContentofGCSE(9–1)inMathematics(J560)Thecontentofthisspecification.• his is a inea a i cati n he c ntent is
a an e t ic a ea an e em i es the e e eman i e ent tie s t cent es a e ee t teach the c ntent the a iate tie
in the e m st a iate t thei ea ne s nee s
• n t ic a ea ma e assesse n an c m nent as e e ant at that tie
• he c ntent this s eci cati n is esente in th ee c mns e esentin a essi n
ithin the c ntent st an s
• he c mns a e c m ati e s that the e ectati n a n ati n tie ea ne is e em i e the st t c mns an that a i he tie ea ne is the s m the statements in a th ee c mns
• Man hi he tie ea ne s i a ea e c n ent an c m etent ith the c ntent the st c mn hen the e in thei GCSE (9–1) c se t ma the e e n t e necessa t c e this c ntent e icit ith a ea ne s th h a ea ne s i e assesse n this c ntent at an a iate e e eman
• ea ne s sh i n a the c ntent m ea ie e sta es n e e the c ntent
e Sta es 1 an is the e e ass me t i n t e assesse i ect
he i isi n c ntent int th ee c mns is inten e t i e an in icati n the essi n in c nce t a an ce a i c t in each c ntent st an
his st ct e
• he s teache s t ta et teachin a iate
• m tes assessment ea nin esentin the c ntent as a essi n n t sim the en
int
• a s teache s t sta t this GCSE (9–1) c se at a e e hich is a iate t thei ea ne s
ith t ee in that the ha e t s en time n c ntent ith hich thei ea ne s a e ami ia
• a s easie m ement m n ati n tie t i he tie sh in h the e i e c ntent the me esses t the a e
e em a s c ntaine in the s eci cati n a e i st ati n n an n t c nstit te an e ha sti e ist
he e c ntent in ne c mn is n t the e em i e in the c mn(s) t its i ht that c ntent ma e assesse at a hi he e e eman than
i en as a iate ea ne s a ainin a hi he a e he e ectati n is that themes i e
e e e the an c nnecti ns e e e en hen n t e icit state
Formulaehe assessment this s eci cati n i n t inc e
a m a sheet m ae hich ea ne s a e e i e t n a e i en in the s eci cati n n e
the m ae e i e i e i en in the assessment
Unitsandmeasuresea ne s sh e ami ia ith an ca c ate ith
a iate nits h an 1 h c c sec n s (s) min tes (min) h s (h) a s m nths an ea s inc in the e ati n et een c nsec ti e
nits (1 ea a s) an ence an cents an cents e ees stan a nits mass en th
a ea me an ca acit an e ate c m n nits ea ne s sh e a e t c n e t et een nits e cient ea ne s sh e a e t se e s
an t act s t meas e the en ths ines an the si es an es
Calculators n e e ence is ma e in the s eci cati n t
ca c at se then ea ne s a e e ecte t e a e t se th ca c at an n n ca c at meth s c ntent ma e assesse n eithe the ca c at n n ca c at a e s
© OCR 2016
GCSE (9–1) in Mathematics
2
Sketchingandplottingcurveshis s eci cati n ma es a istincti n et een
s etchin an n c es
• sketch sh s the m st im tant eat es a c e t es n t ha e t e t sca e th h a es sh e a e e an the a h sh inte act ith the a es c ect s etch sh a ithin the c ect a ants an sh the
c ect n te m eha i s etch n nee s t e a e e ith inte ce ts inte ce ts t nin ints the eat es hen e este in the assessment s etch es n t e i e
a h s a e a e he assessment this s eci cati n i e ect a s etch t e a n
eehan
• plot is a n n s a e a h a e a i en an e a es ca c atin
the c inates ints n the c e an c nnectin them as a iate he e a ta e
a es is i en it i inc e s cient ints t ete mine the c e he e s ch a ta e is n t i en the n m e ints e i e is e t the isc eti n the ea ne
StatementReferencesn i i a e e ences the statements this
s eci cati n a e inc e in the c mn hea e GCSE (9–1) C ntent e C es n in statements m the
e a tment E cati n ( E) Mathematics – GCSE subject content and assessment objectives document
a e inc e in the c mn hea e E e
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OCR 1 NumberOperationsandIntegers
1.01 Calculationswithintegers
1 1a es se n n ca c at meth s t ca c ate the s m i e ence
ct an tient siti e an ne ati e h e
n m e s
1.02 Wholenumbertheory
1 a e niti ns an te ms n e stan an se the te ms e en ime act
( i is ) m ti e c mm n act ( i is ) c mm n
m ti e s a e c e tn e stan an se ace a e
1 ime n m e s enti ime n m e s ess than E ess a h e n m e as a
ct its ime act se.g. 24 2 2 2 3# # #=
n e stan that each n m e can e e esse as a ct
ime act s in n ne way.
enti ime n m e sse e n tati n in
e essin a h e n m e as a ct its ime act se.g. 600 2 3 53 2
# #=
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1 c i hest C mm n act ( C ) an est C mm n M ti e ( CM)
in the C an CM t h e n m e s istin
in the C an CM t h e n m e s m thei ime act isati ns
1.03 Combiningarithmeticoperations
1 a i it e ati ns n the c n enti na e e min ca c ati ns
in in ac ets es an e s ts an
eci ca s
1.04 Inverseoperations
1 a n e se e ati ns n that a iti n an s t acti n m ti icati n an
i isi n an e s an ts a e in e se e ati ns an
se this t sim i an chec ca c ati ns e am e in e e sin a ithmetic in m
thin in a n m e missin i it ems
e.g.
– 9 – 1 11 1
[see also Calculation and estimation of powers and roots, 3.01b]
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OCR 2 Fractions,DecimalsandPercentages
2.01 Fractions
1a E i a ent acti ns ec nise an se e i a ence et een sim e acti ns an
mi e n m e s
e.g. 62
31
=
221
25
=
1 Ca c ati ns ith acti ns s t act m ti an i i e sim e acti ns ( e
an im e ) inc in mi e n m e s an ne ati e
acti ns
e.g. 121
43+
65
103
#
3 54#-
Ca t m e c m e ca c ati ns inc in the se
im e acti ns
e.g. 52
65+
32
21
53#+
[see also Algebraic fractions, 6.01g]
1c acti ns a antit Ca c ate a acti n a antit
e.g. 52
E ess ne antit as a acti n an the
[see also Ratios and fractions, 5.01c]
Ca c ate ith acti ns greater than 1.
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2.02 Decimalfractions
a ecima s an acti ns E ess a sim e acti n as a te minatin ecima ice e sa ith t a ca c at
e 52
n e stan an se ace a e in ecima s
se i isi n t c n e t a sim e acti n t a ecima e.g. 6
1 1
C n e t a ec in ecima t an e act acti n ice e sae.g. .0 41 99
41=o o
1
iti n s t acti n an m ti icati n ecima s
s t act an m ti ecima s inc in ne ati e ecima s ith t a ca c at
c i isi n ecima s i i e a ecima a h e n m e inc in ne ati e
ecima s ith t a ca c ate.g. .0 24 6'
ith t a ca c at i i e a ecima a ecima
e.g. . .0 3 0 6'
2.03 Percentages
a e centa e c n e si ns C n e t et een acti ns ecima s an e centa es
e.g. . %41 0 25 25= =
%121 150=
9
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e centa e ca c ati ns n e stan e centa e is n m e a ts e h n e
Ca c ate a e centa e a antit an e ess ne antit as a e centa e
an the ith ith t a calculator.
9 1
c Percentage change nc ease ec ease a antit a sim e e centa e
inc in sim e ecima acti na m ti ie s
this t sim e i ina a e ems an sim e
inte este 1 t
eithe n in 1 an a in m ti in
1 1
100110
Ca c ate i ina ice an item c stin 1 a e a
isc nt
E ess e centa e chan e as a ecima acti na m ti ie this t
e centa e chan e ems (inc in i ina a e
ems)[see also Growth and decay, 5.03a]
9 1
2.04 Orderingfractions,decimalsandpercentages
a ina it e inte e s acti ns ecima s an e centa es
e.g. 54 4
3 – 9
1
9
S m s se 1 2 !G H = 1
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OCR 3 IndicesandSurds
3.01 Powersandroots
1a n e n tati n se siti e inte e in ices t ite e am e
2 2 2 2 24# # # =
se ne ati e inte e in ices t e esent eci ca s
se acti na in ices t e esent ts an c m inati ns e s an
ts
1 Ca c ati n an estimati n e s an ts
Ca c ate siti e inte e e s an e act ts
e.g.
2 1698
32
4
3
=
=
=
ec nise sim e e s an
e.g. 27 33=
[see also Inverse operations, 1.04a]
Ca c ate ith inte e e se.g. 2 8
13=
-
Ca c ate ith ts
Ca c ate acti na e s
e.g. 1616
181
4 343
= =-
_ iEstimate e s an ts e.g. 51 t the nea est h e n m e
1c a s in ices [see also Simplifying products and quotients, 6.01c]
n an a
a a aa a a
a a
m n m n
m n m n
m n mn
#
'
=
=
=
+
-
_ i[see also Calculations with numbers in standard form, 3.02b, Simplifying products and quotients, 6.01c]
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3.02 Standardform
a Stan a m nte et an e n m e s e esse in stan a m C n e t n m e s t an m stan a me.g. .1320 1 32 103#=
. .0 00943 9 43 10 3#=
-
9
Ca c ati ns ith n m e s in stan a m
se a ca c at t e m ca c ati ns ith n m e s in stan a m
s t act m ti an i i e n m e s in stan a
m ith t a ca c at[see also Laws of indices, 3.01c]
9
3.03 Exactcalculations
a E act ca c ati ns se acti ns in e act ca c ati ns ith t a calculator.
se m ti es π in exact
ca c ati ns ith t a calculator.
se s s in e act ca c ati ns without a calculator.
Mani atin s s Sim i e essi ns ith s s inc in ati na isin
en minat se.g. 12 2 3=
31
33
=
31
23
1
1–=
+
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OCR 4 ApproximationandEstimation
4.01 Approximationandestimation
1a n in n n m e s t the nea est h e n m e ten h n e
etc t a i en n m e si ni cant es (s )
ecima aces ( )
n ans e s t an a iate e e acc ac
1
1 Estimati n Estimate chec ith t a ca c at the es t a ca c ati n sin s ita e a imati nse Estimate t ne si ni cant e the c st
tat es at e
Estimate chec ith t a ca c at the es t m e c m e ca c ati ns inc in
ts
se the s m a iate
e.g. . ..
0 051 0 622 9 10#
.
1
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1c e an e n s se ine a it n tati n t ite n an e inte a a n m e meas ement
rounded or truncated to a
i en e ee acc ace x 1 n e t 1 then . .x2 05 2 151G .
x 1 t ncate t 1 then . .x2 1 2 21G .
an inte et imits accuracy.
Ca c ate the e an e n s a ca c ati n sin
n m e s n e t a n n e ee acc ac
e Ca c ate the a ea a rectangle with length and
i th i en t sn e stan the i e ence et een n s isc ete
an c ntin s antitiese ha e ca s t the nea est h n e then the n m e ca s n satis es n150 2501G and
n150 249G G .
1 1
OCR 5 Ratio,ProportionandRatesOfChange
5.01 Calculationswithratio
1a E i a ent ati s in the ati antities in the m a b an sim i
in the ati antities in the m 1 n.
e cm 1 m 1 1
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1 i isi n in a i en ati S it a antit int t a ts i en the ati the a ts
e in the ati E ess the i isi n a
antit int t a ts as a ati
Ca c ate ne antit m an the i en the ati the t antities
S it a antit int th ee m e a ts i en the ati the a ts
1c ati s an acti ns nte et a ati t a ts as a acti n a h ee 9 s it in the ati 1
i es a ts £32 9# and £3
1 9# .
[see also Fractions of a quantity, 2.01c]
11
1 S e ati an ti n ems S e sim e ati an ti n ems
e a t a eci e e en e stan the e ati nshi et een ati an inea ncti ns
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5.02 Directandinverseproportion
a i ect ti n S e sim e ems in in antities in i ect
ti n inc in a e aic ti ns
e sin e a it ati s
i y x? then yy
xx
2
1
2
1= or
xy
xy
1
1
2
2= .
C enc c n e si n ems
[see also Similar shapes, 9.04c]
S e m e ma ems in in antities in i ect
ti n (i e he e y x? ).
ec nise that i y kx he e k is a c nstant then y is
ti na t x.
m ate e ati ns an s e ems in in a antit
in i ect ti n t a e t an the antit
1 1
n e se ti n S e sim e ems in in antities in in e se
ti n sim e a e aic ti ns
e s ee –time c nte ts (i s ee is e time is ha e )
S e m e ma ems in in antities in in e se
ti n (i e he e y x1
? ).
ec nise that i y xk
= where k is a c nstant then y is in e se ti na t x.
m ate e ati ns an s e ems in in a
antit in in e se ti n t a e t an the
antit
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5.03 Discretegrowthanddecay
a Growth and decay Ca c ate sim e inte est inc in in nancia c nte ts
S e ems steste in in m ti ie s
e a i en inte a e am e c m n inte est
e eciati n etce ca th 1 ne
e eciatin an 1 es ecti e in th ee ea s
[see also Percentage change, 2.03c]
E ess e nentia th eca as a m a
e m nt A s ect t c m n inte est 1 a n 1 as
.A 100 1 1n#= .
S e an inte et ans e s in th an eca ems
[see also Exponential functions, 7.01d, Formulate algebraic expressions, 6.02a]
9 1
OCR 6 Algebra
6.01 Algebraicexpressions
1a e aic te min an s n e stan an se the c nce ts an ca a
e essi ns e ati ns m ae ine a ities te ms
an act s
ec nise the i e ence et een an e ati n an an
i entit an sh a e aic e essi ns a e e i a ente sh that
( )x x x1 2 2 32 2+ + = + +
se a e a t c nst ct a ments
se a e a t c nst ct s an a ments
e e that the s m th ee c nsec ti e
inte e s is a m ti e
1 C ectin i e te ms in s ms an i e ences te ms
Sim i a e aic e essi ns c ectin i e te ms
e.g. a a a2 3 5+ =
1
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1c Sim i in cts an tients Sim i a e aic cts an tientse.g.
a a a aa b aba a aa a a
2 3 6
3 3
3
2 3 5
3 2
# #
#
#
'
=
=
=
=
[see also Laws of indices, 3.01c]
Sim i a e aic cts an tients sin the a s
in icese.g.
2 2a a a2 23# =
-- 51
a b a b a b2 42 3 321 5 2
' =-
1
1 M ti in t ac ets Sim i a e aic e essi ns m ti in a sin e te m e a ac et
e.g. ( )( ) ( )a b a ba b a b a
2 3 2 62 3 3 2 5+ = +
+ + - =
E an cts t in mia s
e.g.
( ) ( )x x x x1 2 3 22- - = - +
( ) ( )a b a b a ab b2 22 2+ - = + -
E an cts m e than t in mia se.g.
( ) ( ) ( )x x x1 1 2 1+ - +
x x x2 2 13 2= + - -
1
1e act isin a e t c mm n act s e.g. ( )
( )a b a bx x x x3 9 3 32 3 2 32- = -
+ = +
act ise a atic e essi ns the m x bx c+ + .
e.g. ( ) ( )x x x x6 3 22- - = - +
( ) ( )x x x16 4 42- = - +
x x x3 3 32- = - +_ _i i
act ise a atic e essi ns the m ax bx c (where
a 1)e.g.
( ) ( )x x x x2 3 2 2 1 22+ - = - +
1
1 C m etin the s a e C m ete the s a e n a a atic e essi n
e.g.
( )x x x4 6 2 102 2+ - = + -
x x x2 5 1 2 45
8172 2
+ + = + -d n
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1 e aic acti ns Sim i an mani ate a e aic acti nse.g. Write
n nn
1
1
1-++
as a
sin e acti n
Sim i n n
n n
+ -
+.
1
6.02 Algebraicformulae
a m ate a e aic e essi ns m ate sim e m ae an e essi ns m ea
c nte tse C st ca hi e at e
a s 1 e mi e he e imete a
rectangle when the
en th is cm m e than the width.
[See, for example, Direct proportion, 5.02a, Inverse proportion, 5.02b, Growth and decay, 5.03a]
1 1
S stit te n me ica a es int m ae an e essi ns
S stit te siti e n m e s int sim e e essi ns an
m ae t n the a e the s ecte Gi en that v u at n
v when t 1 a an u
S stit te siti e ne ati e n m e s int m e c m e
m ae inc in e s ts an a e aic acti ns
e v u as= + with
. , . , .u s a2 1 0 18 9 8= = = - .
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c Chan e the s ect a m a ea an e m ae t chan e the s ect he e the s ect a ea s nce ne.g. Make d the s ect the
m a πc d= .
Make x the s ect the m a y x3 2= - .
ea an e m ae t chan e the s ect inc in cases
he e the s ect a ea s t ice he e a e
eci ca the s ect a ea se.g. Make t the s ect the
m ae
(i) s at21 2
=
(ii) v tx
=
(iii) ty t2 1= +
[Examples may include manipulation of algebraic fractions, 6.01g]
eca an se stan a m ae eca an seCi c m e ence a ci c e π πr d=
ea a ci c e πr
eca an setha as the em
a b c+ =
i n met m ae , ,sin cos tan
ho
ha
ao
i i i= = =
eca an sehe a atic m a
x ab b ac
242
!=
--
Sine rule
sin sin sinAa
Bb
Cc
= =
C sine e
cosa b c bc A22 2 2= + -
ea a t ian e
sinab C21
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e se inematics m ae sev u at= +
s ut at21 2
= +
v u as= +
where a is c nstant acce e ati n u is initia e cit v is na e cit
s is is acement m siti n when t an t is time ta en
6.03 Algebraicequations
a inea e ati ns in ne n n n S e inea e ati ns in ne n n n a e aica
e S e x3 1 5- =
Set an s e inea e ati ns in mathematica an n n mathematica c nte ts inc in th se ith the
n n n n th si es the e ati ne S e ( )x x5 1 4- = -
nte et s ti ns in c nte t
[Examples may include manipulation of algebraic fractions, 6.01g]
1
1
a atic e ati ns S e a atic e ati ns ith c e cient x e a t 1 act isin
e S e x x5 6 02- + = .
Find x an x cm (x ) cm ectan e area 40cm2
.
n the a atic m a ea an e an s e a atic
e ati ns act isin c m etin the s a e sin the a atic m a e.g. x x2 3 52
= +
x x2
12 1-+=
1
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c Sim tane s e ati ns Set an s e t inea sim tane s e ati ns in t a ia es a e aica
e S e sim tane s x y2 3 18+ = and
y x3 5= -
Set an s e t sim tane s e ati ns ( ne inea an ne a atic) in
t a ia es a e aicae S e sim tane s x y 502 2+ = and y x2 5= +
19 1
imate s ti ns sin a a h se a a h t n the a imate s ti n a inea e ati n
se a hs t n a imate ts
a atic e ati ns an the a imate s ti n t inea sim tane s e ati ns
n that the c inates the ints inte secti n a c e an a st ai ht
ine a e the s ti ns t the sim tane s e ati ns the ine an c e
11 1 1 19
e imate s ti ns ite ati n in a imate s ti ns t e ati ns sin s stematic si n chan e meth s ( e am e ecima sea ch inte a isecti n) hen the e is n sim e ana tica meth
s in them S eci c meth s i n t e e este in the assessment
1
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6.04 Algebraicinequalities
a ne a ities in ne a ia e n e stan an se the s m s 1 2G and H
S e inea ine a ities in ne a ia e e essin s ti ns n a n m e ine sin the
c n enti na n tati ne.g x2 1 7H+
3 4 5 6
x1 3 5 101 G-
2 3 4 5
S e a atic ine a ities in ne a ia e
e.g. x x2 321-
E ess s ti ns in set n tati ne.g. x x 3| H# -
x x2 5| 1 G# -[See also Polynomial and exponential functions, 7.01c]
1
ne a ities in t a ia es S e (se e a ) inea ine a ities in t a ia es e esentin the s ti n set n a a h
[See also Straight line graphs, 7.02a]
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6.05 Languageoffunctions
a ncti ns nte et he e a iate sim e e essi ns as
ncti ns ith in ts an t ts
e.g. y x as
x y×2 +3
nte et the e e se cess as the in e se ncti nnte et the s ccessi n
t ncti ns as a c m site ncti nn e e ncti n
n tati n i n t e e i e[see also Translations and reflections, 7.03a]
6.06 Sequences
a Gene ate te ms a se ence Gene ate a se ence s n a a e n sin a te m t te m e i en a e aica in se C ntin e the se ences 1 1 1 9 1
in a siti n t te m e sim e a ithmetic se ences a e aica in se n n
Gene ate a se ence m a m a the nth term.
e.g. nth te m n n+ i es 1
in a m a the nth term
an a ithmetic se encee 1 – n
se s sc i t n tati n siti n t te m an te m t
te m ese.g. x nn = +
x x2 3n 1 n= -+
in a m a the nth term
a a atic se encee 1 1 u n n2 3 1n
2= - +
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S ecia se ences ec nise se ences t ian a s a e an c e n m e s an sim e a ithmetic essi ns
ec nise i nacci an a atic se ences an
sim e e met ic essi ns (rn
where n is an inte e an r
is a ati na n m e )
Gene ate an n nth te ms the se ences
e.g. , , , ,1 2 2 2 2 …
, , ,21
32
43
…
OCR 7 GraphsofEquationsandFunctions
7.01 Graphsofequationsandfunctions
1a x- and y c inates Work with x- and y c inates in a a ants
1 G a hs e ati ns an ncti ns se a ta e a es t t a hs inea an a atic ncti ns
e.g. y xy x
2 32 12= +
= +
se a ta e a es t t the n mia a hs an eci ca s
e.g. y x x23= -
y x x1
= +
x y2 3 6+ =
se a ta e a es t t e nentia a hse.g. .y 3 1 1x#=
9 1
1c n mia an e nentia ncti ns ec nise an s etch the a hs sim e inea an a atic ncti ns
e.g. y x 1 y x y x=
ec nise an s etch a hs ,y x y x
13= = .
enti inte ce ts an sin s mmet the t nin int
a hs a atic ncti nsin the ts a a atic
e ati n a e aica
S etch a hs a atic ncti ns i enti in the
t nin int c m etin the s a e
11 1
1 E nentia ncti ns ec nise an s etch a hs e nentia ncti ns in the m y kx siti e k.
1
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1e i n met ic ncti ns ec nise an s etch the a hs siny x= cosy x=
and tany x= .
1
1 E ati ns ci c es ec nise an se the e ati n a ci c e ith cent e at the origin.
1
7.02 Straightlinegraphs
a St ai ht ine a hs in an inte et the a ient an inte ce t st ai ht ines a hica an sin y mx c= + .
se the m y mx c= + to
n an s etch e ati ns st ai ht ines
in the e ati n a ine th h t i en ints th h ne int ith a i en gradient.
enti the s ti n sets inea ine a ities in t
a ia es sin the c n enti n ashe an s i ines
9 1
a a e an e en ic a ines enti an n e ati ns a a e ines
enti an n e ati ns e en ic a ines
Ca c ate the e ati n a tan ent t a ci c e at a i en
int [See also Equations of circles, 7.01f]
9 1
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7.03 Transformationsofcurvesandtheirequations
a ans ati ns an e ecti ns enti an s etch t ans ati ns an e ecti ns a i en
a h ( the a h a i en e ati n)
n e e ncti n n tati n i n t e e i e[see also Functions, 6.05a]e S etch the a h siny x 2= +
( )y x 2 12= + -
y x=-
1
7.04 Interpretinggraphs
a G a hs ea c nte ts C nst ct an inte et a hs in ea c nte tse istance time m ne c n e si n tem e at e c n e si n[see also Direct proportion, 5.02a, Inverse proportion, 5.02b]
ec nise an inte et a hs that i st ate i ect an in e se ti n
1 1 1
9©
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G a ients n e stan the e ati nshi et een a ient an ati
nte et st ai ht ine a ients as ates chan ee G a ient a istance
time a h as a e cit
Ca c ate estimate a ients a hs an inte et in
c nte ts s ch as istance time a hs e cit time a hs
an nancia a hs the c nce ts a e a e
an instantane s ate chan e ( a ients ch s
tan ents) in n me ica a e aic an a hica c nte ts
1 1
11
c eas Ca c ate estimate a eas n e a hs an inte et in
c nte ts s ch as istance time a hs e cit time a hs
an nancia a hs
1
OCR 8 BasicGeometry
8.01 Conventions,notationandtermsea ne s i e e ecte t e ami ia ith the in e met ica s i s c n enti ns n tati n an te ms hich i e assesse in
esti ns at th tie s
1a an sha es se the te ms ints ines ine se ments e tices e es anes a a e ines e en ic a ines
G1
1 n es n the te ms ac te t se i ht an e e an es
se the stan a c n enti ns a e in an e e in t the si es an an es t ian es
e ABC+ an e C a is the si e site an e
G1
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1c ns n the te ms• e a n• sca ene is sce es an e i ate a t ian e• a i ate a s a e ectan e ite h m s a a e am t a e i m• enta n he a n cta n
G1
1 he a an the s i s ec nise the te ms ace s ace e e an e te c e c i ism c in e ami c ne an s he e
G1
1e ia ams a ia ams m i en esc i ti ns as e i e esti ns G1
1 Ge met ica inst ments se a e t c nst ct an meas e st ai ht inesse a t act t c nst ct an meas e an esse c m asses t c nst ct ci c es
GG1
1 x- and y c inates se x- and y c inates in ane e met ems inc in t ans mati ns sim e sha es GG11
8.02 Rulerandcompassconstructions
a e en ic a isect C nst ct the e en ic a isect an mi int a ine
se ment
G
n e isect C nst ct the isect an an e me m t ines
G
31
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c e en ic a m a int t a ine C nst ct the e en ic a m a int t a ine
C nst ct the e en ic a t a ine at a int
n that the e en ic a istance m a int t a ine
is the sh test istance t the line.
G
Loci e an c m ass c nst cti ns t c nst ct
es an i enti the ci ints t inc e ea
emsn e stan the te m
e i istant
G
8.03 Angles
a n es at a int n an se the s m the an es at a int is 360c.
these an e acts t n an es in ecti inea es an t sti es ts in sim e
s e he s m the inte i
an es a t ian e is 180c.
these an e e ties in m e ma s
e met ica es ts
G G
n es n a ine n that the s m the an es at a int n a ine is180c.
G G
c n es et een inte sectin an a a e ines
n an se
e tica site an es a e e a
a te nate an es n a a e ines a e e a
c es n in an es n a a e ines a e e a
G G
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n es in ns e i e an se the s m the inte i an es a t ian e is 180c.
e i e an se the s m the e te i an es a n is
036 c.in the s m the inte i
an es a nin the inte i an e a e a n
these an e acts t n an es in ecti inea es an t sti es ts in sim e
s e he s m the inte i
an es a t ian e is 180c.
these an e e ties in m e ma s
e met ica es ts
G G
8.04 Propertiesofpolygons
a e ties a t ian e n the asic e ties is sce es e i ate a an i htan e t ian esGi e e met ica eas ns t
sti these e ties
se these acts t n en ths an an es in ecti inea es an in sim e s
se these acts in m e ma s e met ica es ts
e am e ci c e the ems
G G
e ties a i ate a s n the asic e ties the s a e ectan e
a a e am t a e i m ite an h m sGi e e met ica eas ns t
sti these e ties
se these acts t n en ths an an es in ecti inea es an in sim e s
se these acts in m e ma s e met ica es ts
e am e ci c e the ems
G G
c Symmetry enti e ecti n an tati n s mmet ies t ian es
a i ate a s an the ns
G1G4
33
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8.05 Circles
a Circle nomenclature n e stan an se the te ms cent e a i s ch iamete an ci c m e ence
n e stan an se the te ms tan ent a c sect an se ment
G9
n es s ten e at cent e an ci c m e ence
an e
the an e s ten e an a c at the cent e is t ice the an e at the ci c m e ence
G1
c n e in a semici c e an e
the an e n the ci c m e ence s ten e a iamete is a right angle.
G1
n es in the same se ment an e
t an es in the same se ment a e e a
G1
e n e et een a i s an ch an e
a a i s iamete isects a ch i an n i it is
e en ic a t the ch
G1
n e et een a i s an tan ent an e
a int n the ci c m e ence the a i s
iamete th h is e en ic a t the tan ent
at P.
G1
34
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he a te nate se ment the em an e
a int n the ci c m e ence the an e
et een the tan ent an a ch th h e a s the an e s ten e the ch in the site se ment
G1
h C c ic a i ate a s an e
the site an es a c c ic a i ate a a e s ementa
G1
8.06 Three-dimensionalshapes
a imensi na s i s ec nise an n the e ties the c e c i
ism c in e ami c ne an s he e
G1
ans an e e ati ns nte et ans an e e ati ns sim e s i s
C nst ct ans an e e ati ns sim e s i s an
e esentati ns (e sin is met ic a e ) s i s m
ans an e e ati ns
G1 G13
OCR 9 CongruenceandSimilarity
9.01 Planeisometrictransformations
9 1a e ecti n e ect a sim e sha e in a i en mi ine an i enti
the mi ine m a sha e an its ima e
enti a mi ine x a y b or y x m a sim e sha e an its ima e n e e ecti n
G7
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9 1 tati n tate a sim e sha e c c ise anti c c ise th h a m ti e 90c a t a i en cent e tati n
enti the cent e an e an sense a tati n m a sim e sha e an its ima e
n e tati n
G7
9 1c ans ati n se a c mn ect t esc i e a t ans ati n a
sim e sha e an e m a s eci e t ans ati n
G G
9 1 C m inati ns t ans mati ns e m a se ence is met ic t ans mati ns ( e ecti ns tati ns t ans ati ns) n a sim e sha e esc i e the es tin t ans mati n an the chan es an in a iance achie e
G
9.02 Congruence
9 a C n ent t ian es enti c n ent t ian es e that t t ian es a e c n ent sin the cases
si es (SSS) an es 1 si e ( S ) si es inc e an e (S S) i ht an e h ten se si e
( S)
G G7
9 in c n ent t ian es c n ent t ian es in ca c ati ns an sim e se he ase an es an
is sce es t ian e a e e a
G G19
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9.03 Planevectorgeometry
9 a ect a ithmetic n e stan a iti n s t acti n an sca a m ti icati n ect s
se ect s in e met ic a ments an s
G
9 C mn ect s e esent a imensi na ect as a c mn ect
an a c mn ect s n a s a e c inate i
G
9.04 Similarity
9 a Simi a t ian es enti simi a t ian es e that t t ian es a e simi a
G G7
9 Enlargement En a e a sim e sha e m a i en cent e sin a h e n m e sca e act an i enti the sca e act an enlargement.
enti the cent e an sca e act (inc in
acti na sca e act s) an en a ement a sim e sha e an e m s ch an en a ement n a sim e sha e
e m an ec nise en a ements ith ne ati e sca e act s
1
G7
9 c Simi a sha es C m a e en ths a eas an mes sin ati n tati n
an sca e act s
simi a it t ca c ate n n n en ths in simi a
es[see also Direct proportion, 5.02a]
n e stan the e ati nshi et een en ths a eas an
mes simi a sha es[see also Direct proportion, 5.02a]
1 G19
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OCR 10 Mensuration
10.01 Unitsandmeasurement
1 1a nits meas ement se an c n e t stan a nits meas ement en th
a ea me ca acit mass time an m ne
se an c n e t stan a nits in a e aic c nte ts
1 1
G14
1 1 C m n nits se an c n e t sim e c m n nits (e s ee ates a nit
icin )n an a in sim e
cases s ee istance time
se an c n e t the c m n nits (e ensit
ess e)n an a ensit mass mese an c n e t c m n nits in a e aic c nte ts
1 1 11
G14
1 1c Ma s an sca e a in s se the sca e a ma an ith ea in s
C nst ct an inte et sca e a in s
G1
10.02 Perimetercalculations
1 a e imete ecti inea sha es Ca c ate the e imete ecti inea sha es
G17
1 Ci c m e ence a ci c e n an a the m a ci c m e ence π πr d= to
ca c ate the ci c m e ence a circle.
Ca c ate the a c en th a sect a ci c e i en its an e an a i s
G1 G1
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1 c e imete c m site sha es e imete m ae in ca c ati ns in in the
e imete c m site sha es
G1 G1
10.03 Areacalculations
1 a ea a t ian e n an a the m aa ea 2
1 ase hei htn an a the m a
a ea sinab C21
.
G1 G
1 ea a a a e am n an a the m aa ea ase hei ht
nc es a ea a ectan e
G1
1 c ea a t a e i m Ca c ate the a ea a t a e i m
G1
1 ea a ci c e n an a the m a a ea πr to calculate the
a ea a ci c e
Ca c ate the a ea a sect a ci c e i en its an e an
a i s
G1 G1
1 e ea c m site sha es a ea m ae in ca c ati ns in in the a ea
c m site sha es
G1 G1
10.04 Volumeandsurfaceareacalculations
1 a Polyhedra Ca c ate the s ace a ea an me c i s an
the i ht isms (inc in c in e s)
G1
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1 C nes an s he es Ca c ate the s ace a ea an me s he es c nes an sim e c m site s i s ( m ae i e i en)
G17
1 c ami s Ca c ate the s ace a ea an me a ami (the m a 3
1 a ea ase hei ht i e i en)
G17
10.05 Trianglemensuration
1 a tha as the em n e i e an a tha as the em
a b c+ = t n en ths in i ht an e t ian es in
es
tha as the em in m e c m e es inc in es
G G
1 i n met in i ht an e t ian es n an a the t i n met ic ati s sinicosi and tani an a them t n an es an en ths in i ht an e
t ian es in es[see also Similar shapes, 9.04c]
the t i n met i ht an e t ian es in m e
c m e es inc in es
1 G
1 c E act t i n met ic ati s n the e act a es sini
and cosi °0i = 30c 45c 60c and 90c.
n the e act a e tani
°0i = 30c 45c and 60c.
1 G 1
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DfE
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1 Sine rule n an a the sine e
sin sin sinAa
Bb
Cc
= = t n
en ths an an es
G
1 e C sine e n an a the c sine e cosa b c bc A22 2 2
= + - t n en ths an an es
G
OCR 11 Probability
11.01 Basicprobabilityandexperiments
11 1a he a i it sca e se the 1 a i it sca e as a meas e i e ih an m e ents e am e im ssi e ith e ens
ith ce tain ith 1
P3
11 1 e ati e e enc ec esc i e an ana se the e ati e e enc
tc mes e eate e e iments sin ta es an
e enc t ees
P1
11 1c e ati e e enc an a i it se e ati e e enc as an estimate a i it
n e stan that e ati e e encies a ach the
the etica a i it as the n m e t ia s inc eases
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GCSE (9–1)
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11 1 E a i e tc mes an a i it Ca c ate a i ities e esse as acti ns
ecima s in sim e e e iments ith e a i e
tc mes e am e i in c ins in ice etc
i eas an mness an ai ness in sim e e e iments Ca c ate a i ities sim e c m ine e ents e am e in t ice an
in at the t ta sse a i ities t ca c ate
the n m e e ecte tc mes in e eate
e e iments
11.02 Combinedeventsandprobabilitydiagrams
11 a Sam e s aces se ta es an i s t ist the tc mes sin e e ents an
sim e c m inati ns e ents an t ca c ate the etica
a i itiese i in t c ins
in in the n m e e s in hich the
e e s E an G can e i en
se sam e s aces m e c m e c m inati ns e entse ec in the tc mes
s m t ice ems ith t
s inne s
ec nise hen a sam e s ace is the m st a iate
m t se hen s in a c m e a i it em
se the m st a iate ia ams t s e nst ct e
esti ns he e the te t the s ti n is ess i s
P7
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GCSE (9–1)
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11 En me ati n se s stematic istin st ate ies
se the ct e c ntin n m e s tc mes
c m ine e ents
11 c enn ia ams an sets se a t ci c e enn ia am t en me ate sets an se this t ca c ate e ate
a i itiesse sim e set n tati n
t esc i e sim e sets n m e s ectse e en n m e s
mathematics ea ne s
C is sce es t ian es
C nst ct a enn ia am t c assi tc mes an ca c ate a i ities
se set n tati n t esc i e a set n m e s ectse x x1 3| 1 1# - E x x is a factor of 280|# -
C nst ct t ee ia ams ta ta es enn ia ams
t s e m e c m e a i it ems (inc in
c n iti na a i ities st ct e ia ams ma n t
e i en)
P9
11 ee ia ams se t ee ia ams t en me ate sets an t ec the a i ities s ccessi e e ents (t ee ames ma e
i en an in s me cases i e a t c m ete )
P9
11 e he a iti n a a i it se the a iti n a m t a e c si e e ents
se ( ) (not ) 1
e i e in ma n e stan an a the
m a ( or )
( ) ( ) – ( and B)
P4
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GCSE (9–1)
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11 he m ti icati n a a i it an c n iti na a i it
se t ee ia ams an the e esentati ns t ca c ate
the a i it in e en ent an e en ent c m ine e ents
n e stan the c nce t c n iti na a i it an ca c ate it m st inci es in n n c nte tse n a an m c t a ac
ca s ca c ate the a i it a in a
iam n i en a e ca is a n
e i e in ma n e stan an a the
m a ( and ) ( given ) ( )n that e ents an a e
in e en ent i an n i ( given ) ( )
9
OCR 12 Statistics
12.01 Sampling
1 1a ati ns an sam es e ne the ati n in a st an n e stan the
i e ence et een ati n an sam e n e e ties
ati ns ist i ti ns m a sam e
n e stan hat is meant sim e an m sam in an
ias in sam in
S1
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12.02 Interpretingandrepresentingdata
1 a Categorical and numerical data nte et an c nst ct cha ts a iate t the ata t e inc in e enc ta es
a cha ts ie cha ts an ict ams cate ica ata e tica ine cha ts n e isc ete n me ica
data.
nte et m ti e an c m site a cha ts
esi n ta es t c assi atante et an c nst ct ine
a hs time se ies ata an i enti t en s (e seas na a iati ns)
S
1 G e ata nte et an c nst ct ia ams e ata as
a iate i e c m ati e e enc a hs an
hist ams ( ith eithe e a ne a c ass inte a s)
S3
S4
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12.03 Analysingdata
1 a S mma statistics Ca c ate the mean m e me ian an an e
n e atain the m a c ass an
ca c ate estimates the an e mean an me ian
e ata an n e stan h the a e estimatesesc i e a ati n sin
statistics Ma e sim e c m a is nsC m a e ata sets sin i e
i e s mma a esn e stan the a anta es
an isa anta es s mma a es
Ca c ate estimates mean me ian m e an e a ti es an inte a ti e an e m
a hica e esentati n e ata
a an inte et ts se the me ian an
inte a ti e an e t c m a e ist i ti ns
SS
1 Mis e esentin ata ec nise a hica mis e esentati n th h inc ect sca es a e s etc
S4
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GCSE (9–1)
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1 c i a iate ata t an inte et sca e ia ams i a iate ataec nise c e ati n
nte et c e ati n ithin the c nte t the a ia es an a eciate the istincti n
et een c e ati n an ca sati n
a a ine est t e e an se it t ma e e icti nsnte ate an e t a ate
m ata an e a a e the imitati ns these
techni es
S
1 t ie s enti an t ie in sim e cases
eciate the e ma e e s in ata m a es ( t ie s) that n t t
ec nise t ie s n a sca e a h
S4
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GCSE (9–1) in Mathematics 47
2
2c. Priorknowledge,learningandprogression
ea ne s in En an h a e e innin a GCSE (9–1)c se a e i e t ha e e a e Sta e
amme st an sh ha e achie e a ene a e cati na e e e i a ent t ati na
C ic m e e
he e a e n i a i cati ns e i e in e ea ne s t ente a GCSE (9–1) in Mathematics n
is an i n e e n e stan in e i e ent nt this c se
GCSEs (9–1) a e a i cati ns that ena e ea ne s t ess t the a i cati ns eithe cati na
General.
he e a e a n m e mathematics s eci cati ns a ai a e m C
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