OCR GCSE (9-1) J560 Mathematics Specification · tta GCSE t i ©en a e 1 mas 1 h mintes Calculator...

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


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


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


331–3

%

t ta

GCSE

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GCSE (9–1) in Mathematics

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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

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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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content

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Initiallearningforthisqualificationwillenablelearnersto…

Foundationtierlearnersshouldalsobeableto…

Highertierlearnersshouldadditionallybeableto…

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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–=

+

14

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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#

.

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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

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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.

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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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R 2

01

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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

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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

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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

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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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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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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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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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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

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statistics Ma e sim e c m a is nsC m a e ata sets sin i e

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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

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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

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1 t ie s enti an t ie in sim e cases

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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

Find out more at www.ocr.org.uk.

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