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Cambridge IGCSE®

MATHEMATICS 0580/02Paper 2 (Extended) For examination from 2020MARK SCHEME

Maximum Mark: 70

Specimen

0580/02 Cambridge IGCSE – Mark Scheme For examination SPECIMEN from 2020

Page 2 of 10© UCLES 2017

Gen

eric

Mar

king

Pri

ncip

les

Thes

e ge

nera

l mar

king

prin

cipl

es m

ust b

e ap

plie

d by

all

exam

iner

s whe

n m

arki

ng c

andi

date

ans

wer

s. Th

ey sh

ould

be

appl

ied

alon

gsid

e th

e sp

ecifi

c co

nten

t of t

he

mar

k sc

hem

e or

gen

eric

leve

l des

crip

tors

for a

que

stio

n. E

ach

ques

tion

pape

r and

mar

k sc

hem

e w

ill a

lso

com

ply

with

thes

e m

arki

ng p

rinci

ples

.

GEN

ERIC

MA

RK

ING

PR

INC

IPLE

1:

Mar

ks m

ust b

e aw

arde

d in

line

with

:

•th

e sp

ecifi

c co

nten

t of t

he m

ark

sche

me

or th

e ge

neric

leve

l des

crip

tors

for t

he q

uest

ion

•th

e sp

ecifi

c sk

ills d

efin

ed in

the

mar

k sc

hem

e or

in th

e ge

neric

leve

l des

crip

tors

for t

he q

uest

ion

•th

e st

anda

rd o

f res

pons

e re

quire

d by

a c

andi

date

as e

xem

plifi

ed b

y th

e st

anda

rdis

atio

n sc

ripts

.

GEN

ERIC

MA

RK

ING

PR

INC

IPLE

2:

Mar

ks a

war

ded

are

alw

ays w

hole

mar

ks (n

ot h

alf m

arks

, or o

ther

frac

tions

).

GEN

ERIC

MA

RK

ING

PR

INC

IPLE

3:

Mar

ks m

ust b

e aw

arde

d po

sitiv

ely:

•m

arks

are

aw

arde

d fo

r cor

rect

/val

id a

nsw

ers,

as d

efin

ed in

the

mar

k sc

hem

e. H

owev

er, c

redi

t is g

iven

for v

alid

ans

wer

s whi

ch g

o be

yond

the

scop

e of

the

sylla

bus a

nd m

ark

sche

me,

refe

rrin

g to

you

r Tea

m L

eade

r as a

ppro

pria

te •

mar

ks a

re a

war

ded

whe

n ca

ndid

ates

cle

arly

dem

onst

rate

wha

t the

y kn

ow a

nd c

an d

o •

mar

ks a

re n

ot d

educ

ted

for e

rror

s •

mar

ks a

re n

ot d

educ

ted

for o

mis

sion

s •

answ

ers s

houl

d on

ly b

e ju

dged

on

the

qual

ity o

f spe

lling

, pun

ctua

tion

and

gram

mar

whe

n th

ese

feat

ures

are

spec

ifica

lly a

sses

sed

by th

e qu

estio

n as

indi

cate

d by

the

mar

k sc

hem

e. T

he m

eani

ng, h

owev

er, s

houl

d be

una

mbi

guou

s.

GEN

ERIC

MA

RK

ING

PR

INC

IPLE

4:

Rul

es m

ust b

e ap

plie

d co

nsis

tent

ly e

.g. i

n si

tuat

ions

whe

re c

andi

date

s hav

e no

t fol

low

ed in

stru

ctio

ns o

r in

the

appl

icat

ion

of g

ener

ic le

vel d

escr

ipto

rs.

GEN

ERIC

MA

RK

ING

PR

INC

IPLE

5:

Mar

ks sh

ould

be

awar

ded

usin

g th

e fu

ll ra

nge

of m

arks

def

ined

in th

e m

ark

sche

me

for t

he q

uest

ion

(how

ever

; the

use

of t

he fu

ll m

ark

rang

e m

ay b

e lim

ited

acco

rdin

g to

the

qual

ity o

f the

can

dida

te re

spon

ses s

een)

.



GEN

ERIC

MA

RK

ING

PR

INC

IPLE

6:

Mar

ks a

war

ded

are

base

d so

lely

on

the

requ

irem

ents

as d

efin

ed in

the

mar

k sc

hem

e. M

arks

shou

ld n

ot b

e aw

arde

d w

ith g

rade

thre

shol

ds o

r gra

de d

escr

ipto

rs in

m

ind.

MA

RK

SC

HE

ME

NO

TE

S

The

follo

win

g no

tes a

re in

tend

ed to

aid

inte

rpre

tatio

n of

mar

k sc

hem

es in

gen

eral

, but

indi

vidu

al m

ark

sche

mes

may

incl

ude

mar

ks a

war

ded

for s

peci

fic re

ason

s ou

tsid

e th

e sc

ope

of th

ese

note

s.

Type

s of m

ark

M

Met

hod

mar

k, a

war

ded

for a

val

id m

etho

d ap

plie

d to

the

prob

lem

. A

A

ccur

acy

mar

k, g

iven

for a

cor

rect

ans

wer

or i

nter

med

iate

step

cor

rect

ly o

btai

ned.

For

acc

urac

y m

arks

to b

e gi

ven,

the

asso

ciat

ed M

etho

d m

ark

mus

t be

earn

ed

or im

plie

d.B

M

ark

for a

cor

rect

resu

lt or

stat

emen

t ind

epen

dent

of M

etho

d m

arks

.

Whe

n a

part

of a

que

stio

n ha

s tw

o or

mor

e ‘m

etho

d’ st

eps,

the

M m

arks

are

in p

rinci

ple

inde

pend

ent u

nles

s the

sche

me

spec

ifica

lly sa

ys o

ther

wis

e; a

nd si

mila

rly

whe

re th

ere

are

seve

ral B

mar

ks a

lloca

ted.

The

not

atio

n ‘d

ep’ i

s use

d to

indi

cate

that

a p

artic

ular

M o

r B m

ark

is d

epen

dent

on

an e

arlie

r mar

k in

the

sche

me.

Abb

revi

atio

ns

cao

co

rrec

t ans

wer

onl

yde

p

depe

nden

tFT

follo

w th

roug

h af

ter e

rror

isw

igno

re su

bseq

uent

wor

king

nfw

w

not f

rom

wro

ng w

orki

ngoe

or e

quiv

alen

tSC

spec

ial c

ase

soi

se

en o

r im

plie

d



Que

stio

nA

nsw

erM

arks

Part

ial M

arks

18(

h) 5

2 (m

in)

1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

23.

75 o

r 343

1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

331

1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

4Id

entif

ies e

rror

cor

rect

ly (R

efer

s to

100 m

m2 =

1 cm

2 oe

)1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

511

2M

1 fo

r –2 ×

–7 –

3

soi

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

610

7 4 6

8

0 4

7

9

0 2

11 12 13

2B

1 fo

r 8 o

r 9 c

orre

ct n

umbe

rs o

rder

edor

for 1

0 co

rrec

t num

bers

not

ord

ered

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

7Tr

iang

le d

raw

n ac

cura

tely

with

a ru

ler a

nd a

pai

r of a

rcs

2B

1 fo

r tw

o si

des o

f the

cor

rect

leng

th d

raw

n as

pa

rt of

a tr

iang

le



Que

stio

nA

nsw

erM

arks

Part

ial M

arks

8(a

=) 7

0(b

=) 4

02

B1

for e

ach

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

9w

=

y 53

7−

oe

2M

1 fo

r 5w

+ 7

= 3

y or

5w

– 3

y =

–7

or 5

w =

3y

– 7

or w

–

y 53 +

57 =

0

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

10C

anno

t be

writ

ten

as a

frac

tion

oe

1A

ccep

t 3 is

a p

rime

num

ber

Acc

ept d

ecim

al g

oing

on

fore

ver w

ith n

o pa

ttern

oe

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

1142

8.5

1Fi

rst v

alue

429.

51

Seco

nd v

alue

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

129.

1 o

e2

M1

for .

..PQ52

217

124

=

oe

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

13n

> 3.

752

M1

for 7

+ 8

< 5

n –

n o

eal

low

3¾



Que

stio

nA

nsw

erM

arks

Part

ial M

arks

14C

omm

on d

enom

inat

or 6

0B

1A

ccep

t k ×

60

()

or 6035

956039+

M1

Acc

ept

()

or kk

kkk

6035

956039+

60134 o

r 16074

or 2 6014

and

2307

A1

Acc

ept

kk60134

or

kk1 6074

or

kk2 6014

and

2307

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

15(a

)–3

1

15(b

)9

– 2n

oe

2B

1 fo

r – 2

n +

k or

dn

+ 9

whe

re d

≠ 0

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

1614

53

M2

for (

6 –

2) ×

180

– 5

× 1

15

oeor

M1

for (

6 –

2) ×

180

oe

Alte

rnat

ive

met

hod

M2

for 1

80 –

(360

– 5

× (1

80 –

115

))or

M1

for 3

60 –

5 ×

(180

– 1

15)

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

1769

.3 o

r 69.

28...

4M

2 fo

r hei

ght 8

42

2−

oe

or M

1 fo

r 42 +

h2 =

82

oe

and

M1

for 21

(8 +

12)

× th

eir p

erp

heig

ht

oe



Que

stio

nA

nsw

erM

arks

Part

ial M

arks

18(a

)

AB

1

18(b

)D

E

F

1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

191.

37 o

r 1.3

74…

1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

2010

0x =

32.

22…

oe

M1

9029

oe fr

actio

nB

1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

21A

C

D

3B

1 fo

r eac

h



Que

stio

nA

nsw

erM

arks

Part

ial M

arks

221210

oe

3M

2 fo

r 13241#

- o

r for

3143

3141

3243

##

#+

+

or

M1

for 3241#

or f

or 31

413243

##

+

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

2327

3M

2 fo

r 2

96##rr

× π

× 9

2 oe

or M

1 fo

r 2

96##rr

oe

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

24M

edia

n is

gre

ater

for E

lect

ro c

ompa

ny so

Tom

is w

rong

bec

ause

Spa

rk is

che

aper

oe

2M

1 fo

r Spa

rk m

edia

n =

46 a

nd

Elec

tro m

edia

n =

52

IQR

is g

reat

er fo

r Spa

rk c

ompa

ny so

Tom

is ri

ght S

park

is m

ore

varie

d o

e2

M1

for S

park

IQR

= 2

6 an

d El

ectro

IQR

= 1

8

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

25(x

+ 2

)2 or x

2 + 2

ax +

a2 −

bM

1

–3 –

(the

ir 2

)2 or a

2 − b

= −

3 or

2a

= 4

M1

(x +

2)2 –

7 o

r a =

2 a

nd b

= 7

M1

(−2,

−7)

B1

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

26(a

)55

1

Alte

rnat

e se

gmen

t1

26(b

)11

51

Cyc

lic q

uadr

ilate

ral

1



Que

stio

nA

nsw

erM

arks

Part

ial M

arks

27(a

)3x

22

B1

for 3

xk or k

x2 (k ≠

0 )

27(b

)32

3M

2 fo

r 8x2 a

nd x4 2

or B1

for

8x2 o

r x4 2

Que

stio

nA

nsw

erM

arks

Part

ial M

arks

285x

2 + 4

x –

19 =

4x

+ 1

M1

For s

ubtra

ctin

g th

e tw

o eq

uatio

ns

5x2 –

20

= 0

M1

Alte

rnat

ive

met

hod

5x2 =

20

[5] (

x –

2)(x

+ 2

) [=

0]M

1x2 =

4

x =

2 an

d –2

B1

y =

9 an

d –7

B1



BL

AN

K P

AG

E