Edexcel Award in Algebrafortpitt.medway.sch.uk/.../2012/11/Edexcel-Awards... · Introduction The...

Edexcel Award in

Algebra

Level 2 and Level 3

Algebra

Edexcel Level 2 Award in Algebra (AAL20)

Edexcel Level 3 Award in Algebra (AAL30)

Specification

Awards in Algebra For first teaching from October 2012

Pearson Education Ltd is one of the UK’s largest awarding organisations, offering academic and vocational qualifications and testing to schools, colleges, employers and other places of learning, both in the UK and internationally. Qualifications offered include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications, ranging from Entry Level to BTEC Higher National Diplomas. Pearson Education Ltd administers general qualifications.

Through initiatives such as onscreen marking and administration, Pearson is leading the way in using technology to modernise educational assessment, and to support teachers and learners.

Acknowledgements

This specification 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 specification are made in good faith. We do 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 UG031210

All the material in this publication is copyright © Pearson Education Limited 2012

Introduction

The Edexcel Level 2 and Level 3 Awards in Algebra are designed for use in schools and colleges. They are part of a suite of mathematics qualifications offered by Edexcel.

Qualification objectives

The Edexcel Level 2 and Level 3 Awards in Algebra enable students to:

develop a thorough knowledge and understanding of concepts in algebra and a sound foundation of mathematical techniques

acquire confidence in their mathematical skills to move into further study in the subject or related areas

enjoy using mathematics and become confident when using mathematics

develop proficiency in algebra to support progression in their studies, in the workplace and for training.

The qualifications support progression to other level 2 and level 3 qualifications, such as GCSE and GCE. The awards indicate clear progression from level 2 and level 3.

Contents

Specification at a glance 1 External assessment 2

Qualification content 3

National Qualifications framework (NQF) 3

Knowledge, skills and understanding 3

Assessment overview 4

Edexcel Level 2 Award in Algebra 5

Overview 5

Edexcel Level 3 Award in Algebra 9

Overview 9

Assessment 13

Assessment summary 13

Assessment objectives and weightings 14

Relationship of assessment objectives to papers 15

Entering your students for assessment 15

Student entry 15

Access arrangements and special considerations 15

Assessing your students 16

Awarding and reporting 16

Language of assessment 16

Malpractice and plagiarism 16

Student recruitment 17

Prior learning 17

Guided learning hours 17

Progression 18

Level descriptors 19

Support and training 20

Edexcel support services 20

Training 20

Appendices 21

Appendix 1: Wider curriculum 23

Appendix 2: Codes 25

Appendix 3: Mapping to GCSE Mathematics content 27

Appendix 4: Mapping to International GCSE and Level 1/ Level 2 Certificate in Mathematics qualifications 39

Appendix 5: Mapping of GCE AS Level Core Mathematics 1 (C1) 43

UG031210 – Specification – Edexcel Level 2 and Level 3 Award in Algebra –

Issue 1 – September 2012 © Pearson Education Limited 2012

1

Specification at a glance

These Level 2 and Level 3 Awards consist of a single assessment at each level.

Students are entered at either Level 2 or Level 3.

Each qualification is awarded as pass or unclassified.

Level 2 Paper code: AAL20

Externally assessed

Availability: January and June series

First assessment: June 2013

100% of the Award

Overview of content

Algebraic manipulation and solution of equations

Inequalities and number sequences

Linear and curved graphs, distance and time graphs, speed and time graphs

Overview of assessment

The award is assessed through a 1 hour and 30 minutes examination set and marked by Edexcel.

The total number of marks for the paper is 80.

The qualification is awarded as pass or unclassified.

Calculators are not allowed.

Level 3

Paper code: AAL30

Externally assessed

Availability: January and June series


100% of the Award

Overview of content

Algebraic manipulation and solution of equations

Inequalities and number sequences

Linear and curved graphs, distance and time graphs, speed and time graphs

Overview of assessment

The award is assessed through a 2 hour examination set and marked by Edexcel.


The qualification is awarded as pass or unclassified.

Calculators are not allowed



2

External assessment

In all examination papers:

diagrams will not necessarily be drawn to scale and measurements should not be taken from diagrams unless instructions to this effect are given

each student may be required to use mathematical instruments, eg ruler.



3

Qualification content

National Qualifications framework (NQF)

These qualifications comply with the requirements of the statutory regulation of qualifications in England, Wales and Northern Ireland which are prescribed by the regulatory authorities.

Knowledge, skills and understanding

The Edexcel Level 2 and Level 3 Awards in Algebra require students to demonstrate application and understanding of the following.

Level 2 content contains:

1 Roles of symbols

2 Algebraic manipulation

3 Formulae

4 Linear equations

5 Graph sketching

6 Linear inequalities

7 Number sequences

8 Gradients of straight line graphs

9 Straight line graphs

10 Graphs for real life situations

11 Simple quadratic functions

12 Distance-time and speed-time graphs



4

Knowledge, skills and understanding (continued)

Level 3 content contains:

1 Roles of symbols


3 Formulae

4 Simultaneous equations

5 Quadratic equations

6 Roots of a quadratic equation

7 Inequalities

8 Arithmetic series

9 Coordinate geometry

10 Graphs of functions

11 Graphs of simple loci


13 Direct and inverse proportion

14 Transformations of functions

15 Area under a curve

16 Surds

Assessment overview

One written paper for each award is taken at the end of the course.

The Level 2 award:

o is assessed through a 1 hour and 30 minutes examination set and marked by Edexcel.

o Calculators are not allowed

o The total number of marks for the paper is 80.

The Level 3 award:

o is assessed through a 2 hour examination set and marked by Edexcel.



Each qualification is awarded at pass or unclassified.

Available in January and June.

First assessment: June 2013.



5

Edexcel Level 2 Award in Algebra

Overview

Content overview

This qualification contains:

1 Roles of symbols


3 Formulae

4 Linear equations

5 Graph sketching

6 Linear inequalities

7 Number sequences

8 Gradients of straight line graphs

9 Straight line graphs

10 Graphs for real life situations

11 Simple quadratic functions


Assessment overview

One written paper for is taken at the end of the course.

The Level 2 award:

o is assessed through a 1 hour and 30 minutes examination set and marked by Edexcel.





First assessment: June 2013.

Calculators are not allowed in the assessment.



6

Level 2

What students need to learn:

Topic Concepts and skills

1. Roles of symbols 1. Distinguish between the roles played by letter symbols in algebra using the correct notation

2 Distinguish in meaning between the words equation, formula and expression

3. Write an expression to represent a situation in ‘real life’

2. Algebraic manipulation 1. Collect like terms

2. Multiply a single term over a bracket

3. Factorise algebraic expressions by taking out all common factors

4. Use index laws for multiplication, division and raising a power to a power

3. Formulae

1. Substitute numbers into a formula

2. Change the subject of a formula where the subject only appears once

4. Linear equations 1. Solve linear equations with integer coefficients where the variable appears on either side or on both sides of the equation

2. Solve linear equations which include brackets, those that have negative signs occurring anywhere in the equation, those with negative and fractional solutions and those with fractional coefficients

5. Graph sketching 1. Sketch graphs of quadratic functions, considering orientation and labelling the point of intersection with the y-axis, considering what happens to y for large positive and negative values of x

6. Linear inequalities 1. Show inequalities on a number line, using solid circles to show inclusive inequalities and open circles to show exclusive inequalities

2. Write down an inequality shown on a number line

3. Solve simple linear inequalities in one variable



7


7. Number sequences

1. Generate terms of a sequence using term-to-term definition or using position-to-term definition

2. Find and use the nth term of a linear arithmetic sequence

8. Gradients of straight line graphs

1. Find the gradient of a straight line graph

2. Interpret the gradient of real-life graphs

9. Straight line graphs 1. Recognise, plot and draw graphs of the form y = mx + c

2. Given a straight line graph, find its equation

10 Graphs for real-life situations

1. Understand that straight and curved graphs can represent real-life situations

2. Draw, and interpret information from graphs of real-life situations

11 Simple quadratic functions 1. Plot graphs of simple quadratic functions

2 Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function


1. Draw distance-time graphs and speed-time graphs

2. Interpret distance-time graphs and speed-time graphs

3 Understand that the gradient of a distance-time graph represents speed

4. Find speed and distance from information on a travel graph



8



9

Edexcel Level 3 Award in Algebra

Overview

Content overview

This qualification contains:

1. Roles of symbols

2. Algebraic manipulation

3. Formulae

4. Simultaneous equations

5. Quadratic equations

6. Roots of a quadratic equation

7. Inequalities

8. Arithmetic series

9. Coordinate geometry

10. Graphs of functions

11. Graphs of simple loci

12. Distance-time and speed-time graphs

13. Direct and inverse proportion

14. Transformations of functions

15. Area under a curve

16. Surds

Assessment overview

One written paper is taken at the end of the course.

The Level 3 award:

o is assessed through a 2 hour examination set and marked by Edexcel.






Calculators are not allowed in the assessment.

The content of the Level 2 Award in Algebra is assumed knowledge and this content may be assessed in the Level 3 award.



10

Level 3

What students need to learn:

The content of the Level 2 Award in Algebra is assumed knowledge and this content may be assessed in the Level 3 award.


1. Roles of symbols 1. Distinguish between the roles played by letter symbols in algebra using the correct notation, and between the words equation, formula identity and expression

2. Algebraic manipulation

1. Multiply two linear expressions

2. Factorise expressions including quadratics and the difference of two squares, taking out all common factors

3. Use index laws to include fractional and negative indices

4. Simplify algebraic fractions

5. Complete the square in a quadratic expression

3. Formulae 1. Substitute numbers into formulae

2. Change the subject of a formula

4. Simultaneous equations

1. Solve simultaneous equations in two unknowns, where one may be quadratic, where one may include powers up to 2

5. Quadratic equations 1. Solve quadratic equations by factorisation or by using the formula or by completing the square

2. Know and use the quadratic formula

6. Roots of a quadratic equation

1. Understand the role of the discriminant in quadratic equations

2. Understand the sum and the product of the roots of a quadratic equation



11


7. Inequalities 1. Solve linear inequalities, and quadratic inequalities

2. Represent linear inequalities in two variables on a graph

8. Arithmetic series

1. Find and use the general term of arithmetic series

2. Find and use sum of an arithmetic series

9. Coordinate geometry 1. Forms of the equation of a straight line graph

2. Conditions for straight lines to be parallel or perpendicular to each other

10. Graphs of functions 1. Recognise, draw and sketch graphs of linear, quadratic, cubic, reciprocal, exponential and circular functions, and understand tangents and normals

2. Sketch graphs of quadratic, cubic, and reciprocal functions, considering asymptotes, orientation and labelling points of intersection with axes and turning points

3. Use graphs to solve equations

11. Graphs of simple loci 1. Construct the graphs of simple loci eg circles and parabolas

12. Distance-time and speed-time graphs

1. Draw and interpret distance-time graphs and speed-time graphs

2. Understand that the gradient of a distance-time graph represents speed and that the gradient of a speed-time graph represents acceleration

3. Understand that the area under the graph of a speed-time graph represents distance travelled

13. Direct and inverse proportion

1. Set up and use equations to solve word and other problems using direct and inverse proportion and relate algebraic solutions to graphical representations of the equations

14. Transformations of functions

1. Apply to the graph of y = f(x) transformations of y = f(x) ± a, y = f(±ax), y = f(x ± a), y = ±af(x) for any function in x



12


15. Area under a curve 1. Find the area under a curve using the trapezium rule

16. Surds 1. Use and manipulate surds, including rationalising the denominator of a fraction

written in the form a

b c



13

Assessment

Assessment summary

Level 2

Paper code: AAL20

One written paper.

The paper is assessed through a 1 hour and 30 minute examination, set and marked by Edexcel.


Calculators are not allowed

The qualification is awarded at pass or unclassified.

Level 3

Paper code: AAL30

One written paper.

The paper is assessed through a 2 hour examination, set and marked by Edexcel.


Calculators are not allowed.

The qualification is awarded at pass or unclassified.



14

Assessment objectives and weightings

Level 2 % in Award

AO1: demonstrate knowledge, understanding and skills in algebraic symbols and manipulation

25%-35%

AO2: demonstrate knowledge, understanding and skills in solving equations and inequalities and using substitution

35%-45%

AO3: demonstrate knowledge, understanding and skills in interpreting, drawing and sketching graphs and using graphs to solve equations

25%-35%

TOTAL 100%

Level 3 % in Award

AO1: demonstrate knowledge, understanding and skills in algebraic symbols and manipulation

25%-35%

AO2: demonstrate knowledge, understanding and skills in solving equations, and inequalities and using substitution

25%-35%

AO3: demonstrate knowledge, understanding and skills in interpreting, drawing and sketching graphs and using graphs to solve equations

35%-45%

TOTAL 100%



15

Relationship of assessment objectives to papers

Assessment objective Paper number

AO1 AO2 AO3 Total for AO1, AO2 and AO3

Level 2 25%-35% 35%-45% 25%-35% 100%

Level 3 25%-35% 25%-35% 35%-45% 100%

Entering your students for assessment

Student entry

Students are entered at either Level 2 or Level 3.

Details of how to enter students for These qualifications can be found in Edexcel’s Information Manual, copies of which (in CD format) are sent to all active Edexcel centres. The information can also be found on Edexcel’s website: www.edexcel.com

Access arrangements and special considerations

Edexcel’s policy on access arrangements and special considerations for GCE, GCSE, International GCSE, and Entry Level qualifications aims to enhance access to the qualifications for students with disabilities and other difficulties without compromising the assessment of skills, knowledge, understanding or competence.

The access arrangements and special arrangements for these qualification will comply with this policy.

Please see the Edexcel website (www.edexcel.com/sfc) for:

the Joint Council for Qualifications (JCQ) policy Access Arrangements, Reasonable Adjustments and Special Considerations 2010-2011

the forms to submit for requests for access arrangements and special considerations

dates for submission of the forms.

Requests for access arrangements and special considerations must be addressed to:

Special Requirements Edexcel One90 High Holborn London WC1V 7BH



16

Assessing your students

The first assessment opportunity for these qualifications will take place in the June 2013 series and in each January and June series thereafter for the lifetime of the qualifications.

Your students’ assessment opportunities

All papers June 2013

January 2014

June 2014

January 2015

Level 2 and Level 3

Awarding and reporting

The awarding and certification processes for these qualifications will comply with the current GCSE/GCE Code of Practice, which is published by the Office of Qualifications and Examinations Regulation (Ofqual). The Level 2 and Level 3 Awards qualifications will be pass only.

The first certification opportunity for the Edexcel Level 2 and Level 3 Awards in Algebra will be June 2013.

Students whose level of achievement is below the minimum judged by Edexcel to be of sufficient standard to be recorded on a certificate will receive an unclassified (U) result.

Language of assessment

Assessment of These qualifications will be available in English only. Assessment materials will be published in English only and all work submitted for examination must be produced in English.

Malpractice and plagiarism

For up-to-date advice on malpractice and plagiarism, please refer to the JCQ’s Suspected Malpractice in Examinations and Assessments: Policies and Procedures document on the JCQ website: www.jcq.org.uk.

http://www.jcq.org.uk/�



17

Student recruitment

Edexcel’s access policy concerning recruitment to our qualifications is that:

they must be available to anyone who is capable of reaching the required standard

they must be free from barriers that restrict access and progression

equal opportunities exist for all students.

Prior learning

For level 2, this qualification builds on the content, knowledge and skills developed in the Key Stage 3 Programme of Study for Mathematics as defined by the National Curriculum Orders for England.

For level 3, this qualification builds on the content, knowledge and skills taught as part of GCSE mathematics.

Guided learning hours

The number of guided learning hours (GLH) required for each qualification is 60-70 GLH.

These qualifications can be co-taught as part of other mathematics programmes, so the delivery time allocated may be more or less than this, according to delivery plans and individual learner needs.



18

Progression

At level 2, this qualification support progression to:

GCSE in Mathematics (see Appendix 3)

International GCSEs in Mathematics (see Appendix 4)

Level 1/Level 2 Certificate in Mathematics (see Appendix 4)

GCE AS Level Mathematics (see Appendix 5)

further level 2 qualifications in other subjects, such as chemistry, biology, psychology and electronics

further education or employment where mathematical skills are required.

At level 3, this qualification supports progression to:

GCE AS and A Level Mathematics (see Appendix 5)

further level 2 and level 3 qualifications in other subjects, such as biology, chemistry, psychology and electronics

undergraduate degrees in numerate disciplines, such as the biosciences

further education or employment where mathematical skills are required.



19

Level descriptors

The following level descriptions indicate the level of attainment characteristic of the given level. They give a general indication of the required learning outcomes at each specified level. The descriptors should be interpreted in relation to the content outlined in the specification; they are not designed to define that content. The level awarded will depend in practice upon the extent to which the candidate has met the Assessment Objectives overall. Shortcomings in some aspects of the examination may be balanced by better performance in others.

Level 2

Candidates find and describe in symbols the next term or the nth term of a sequence, where the rule is linear. They multiply two expressions of the form (x + n) and they simplify the corresponding quadratic expressions. They represent inequalities using a number line. They formulate and solve linear equations with whole number coefficients. They manipulate simple algebraic formulae, equations and expressions. They use trial and improvement to solve cubic equations. They factorise simple expressions. Candidates sketch quadratic graphs and label them correctly. Candidates draw linear and quadratic graphs. They understand the role of m and c in y = mx + c. They interpret distance-time graphs from real-life situations.

Level 3

Candidates understand and use direct and inverse proportion. They manipulate algebraic formulae, equations and expressions, finding common factors and multiplying two linear expressions. In simplifying algebraic expressions, they use rules of indices for negative and fractional values. In finding formulae that approximately connect data, candidates express general laws in symbolic form. Candidates solve quadratic equations and

understand the role of a, b and c in .02 cbxax They draw and sketch a range of functions and understand tangents and normals. They manipulate and use surds.



20

Support and training

Edexcel support services

Edexcel has a wide range of support services to help you implement this qualification successfully.

ResultsPlus – ResultsPlus is an application launched by Edexcel to help subject teachers, senior management teams, and students by providing detailed analysis of examination performance. Reports that compare performance between subjects, classes, your centre and similar centres can be generated in ‘one-click’. Skills maps that show performance according to the specification topic being tested are available for some subjects. For further information about which subjects will be analysed through ResultsPlus, and for information on how to access and use the service, please visit www.edexcel.com/resultsplus.

Ask the Expert – To make it easier for you to raise a query with us online, we have merged our Ask Edexcel and Ask the Expert services.

There is now one easy-to-use web query form that will allow you to ask any question about the delivery or teaching of Edexcel qualifications. You’ll get a personal response, from one of our administrative or teaching experts, sent to the email address you provide.

We’ll also be doing lots of work to improve the quantity and quality of information in our FAQ database, so you’ll be able find answers to many questions you might have by searching before you submit the question to us.

Examzone – The Examzone site is aimed at students sitting external examinations and gives information on revision, advice from examiners and guidance on results, including remarking, resitting and progression opportunities. Further services for students – many of which will also be of interest to parents – will be available in the near future. Links to this site can be found on the main homepage at www.examzone.co.uk.

Training

A programme of professional development and training courses, covering various aspects of the specification and examination, will be arranged by Edexcel. Full details can be obtained from our website: www.edexcel.com

http://www.examzone.co.uk/�

http://www.edexcel.org.uk/�



21

Appendices

Appendix 1: Wider curriculum 23

Appendix 2: Codes 25

Appendix 3: Mapping to GCSE Mathematics content 27

Appendix 4: Mapping to International GCSE and Level 1/ Level 2 Certificate in Mathematics qualifications 39

Appendix 5: Mapping of GCE AS Level Core Mathematics 1 (C1) 43



22



23

Appendix 1: Wider curriculum

Signposting and development suggestions

Issue Paper Opportunities for development

Spiritual All papers

Moral All papers

Ethical All papers

Social All papers

Legislative All papers

Economic All papers

Cultural All papers

Sustainable All papers

Health and safety All papers

European initiatives All papers

These qualifications will enable centres to provide courses in mathematics that will allow students to discriminate between truth and falsehood. As candidates explore mathematical models of the real world there will be many naturally arising moral and cultural issues, environmental and health and safety considerations and aspects of European developments for discussion, for example:

use and abuse of statistics in the media

financial and business mathematics

how mathematics is used to communicate climate change

cultural and historical roots of mathematics

use of mathematics in cultural symbols and patterns.



24



25

Appendix 2: Codes

Type of code Use of code Code number

National Qualifications Framework (NQF) codes

Each qualification title is allocated a National Qualifications Framework (NQF) code.

The National Qualifications Framework (NQF) code is known as a Qualification (QN). This is the code that features in the DfE Funding Schedule, Section 96, and is to be used for all qualification funding purposes. The QN is the number that will appear on the student’s final certification documentation.

The QN for the qualifications in this publication are:

Level 2: 600/6631/3

Level 3: 600/6632/5

Cash-in codes The cash-in code is used as an entry code to aggregate the student’s scores to obtain the overall grade for the qualification. Centres will need to use the entry codes only when entering students for their qualification.

Level 2: AAL20

Level 3: AAL30

Entry codes The entry codes are used to:

enter a student for assessment

aggregate the student’s paper scores to obtain the overall grade for the qualification.

Please refer to the Information Manual, available on the Edexcel website.



26

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fact

ori

se q

uad

rati

c exp

ress

ion

s in

clu

din

g t

he

dif

fere

nce

of

two

sq

uare

s an

d

sim

plify

rati

on

al

exp

ress

ion

s

U

se inst

ance

s of

index

law

s,

incl

udin

g u

se o

f fr

act

ion

al,

ze

ro a

nd

neg

ati

ve p

ower

s,

and p

ower

s ra

ised

to a

pow

er

Pro

gre

ssio

n

Op

po

rtu

nit

ies

O

nce

stu

den

ts h

ave

mas

tere

d t

he

skill

s ab

ove

, le

arnin

g

can b

e ex

tended

to

incl

ude

expre

ssio

ns

and u

sing

algeb

raic

man

ipula

tion t

o s

olv

e pro

ble

ms.

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

29

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s

Ref

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

1.

Subst

itute

num

ber

s in

to a

form

ula

Opport

unity

to e

xten

d t

his

to

incl

ude:

su

bst

ituting p

osi

tive

and

neg

ativ

e

num

ber

s in

to e

xpre

ssio

ns

such

as

3x2 +

4 a

nd 2

x3

Subst

itute

num

ber

s in

to a

fo

rmula

3.

Fo

rmu

lae

2.

Chan

ge

the

subje

ct o

f a

form

ula

wher

e th

e su

bje

ct o

nly

appea

rs

once

Opport

unity

to e

xten

d t

his

to

incl

ude:

ca

ses

wher

e th

e su

bje

ct is

on b

oth

sid

es o

f th

e origin

al f

orm

ula

, or

wher

e a

pow

er o

f th

e su

bje

ct

appea

rs (

Hig

her

tie

r G

CSE).

A f

D

eriv

e a

form

ula

, su

bst

itute

num

ber

s in

to a

form

ula

and

chan

ge

the

subje

ct o

f a

form

ula

Chan

ge

the

subje

ct o

f a

form

ula

in

clu

din

g c

ase

s w

here

th

e s

ub

ject

is

on

b

oth

sid

es

of

the o

rig

inal

form

ula

, o

r w

here

a

pow

er

of

the s

ub

ject

ap

pears

Pro

gre

ssio

n

Op

po

rtu

nit

ies

O

nce

stu

den

ts h

ave

mas

tere

d t

he

skill

s ab

ove

, le

arnin

g

can b

e

ex

tended

to

incl

ude

der

ivin

g f

orm

ula

e an

d u

sing

fo

rmula

e fr

om

mat

hem

atic

s an

d o

ther

subje

cts

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

30

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s

Ref

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

1.

Solv

e lin

ear

equat

ions

with inte

ger

co

effici

ents

wher

e th

e va

riab

le a

ppea

rs o

n

eith

er s

ide

or

on b

oth

si

des

of

the

equat

ion

Solv

e lin

ear

equat

ions,

with

inte

ger

coef

fici

ents

, in

whic

h

the

unkn

ow

n a

ppea

rs

on e

ither

sid

e or

on b

oth

sides

of

the

equat

ion

4.

Lin

ear

equ

ati

on

s

2.

Solv

e lin

ear

equat

ions

whic

h incl

ude

bra

cket

s, t

hose

that

hav

e neg

ativ

e si

gns

occ

urr

ing a

nyw

her

e in

th

e eq

uat

ion,

those

w

ith n

egat

ive

and

frac

tional

solu

tions

and t

hose

with

frac

tional

coef

fici

ents

A d

Set

up a

nd s

olv

e si

mple

equat

ions

incl

ud

ing

si

mu

ltan

eo

us

eq

uati

on

s in

tw

o

un

kn

ow

ns

Solv

e lin

ear

equat

ions

that

in

clude

bra

cket

s, t

hose

that

hav

e neg

ativ

e si

gns

occ

urr

ing a

nyw

her

e in

the

equat

ion,

and t

hose

with a

neg

ativ

e so

lution

Solv

e lin

ear

equat

ions

in

one

unkn

own,

with inte

ger

or

frac

tional

coef

fici

ents

Pro

gre

ssio

n

Op

po

rtu

nit

ies

O

nce

stu

den

ts h

ave

mas

tere

d t

he

skill

s ab

ove

, le

arnin

g

can b

e ex

tended

to

incl

ude

solv

ing s

imultan

eous

equat

ions

both

alg

ebra

ical

ly a

nd g

raphic

ally

.

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

31

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s

Ref

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

5.

Gra

ph

sk

etc

hin

g

1.

Ske

tch g

raphs

of

quad

ratic

funct

ions,

co

nsi

der

ing o

rien

tation

and lab

ellin

g t

he

poin

t of

inte

rsec

tion w

ith

the

y-ax

is,

consi

der

ing

what

hap

pen

s to

y f

or

larg

e posi

tive

and

neg

ativ

e va

lues

of

x

A

t

Gen

erat

e poin

ts a

nd

plo

t gra

phs

of

sim

ple

quad

ratic

funct

ions,

an

d u

se t

hes

e to

fin

d

appro

xim

ate

solu

tions

G

ener

ate

poin

ts a

nd p

lot

gra

phs

of

sim

ple

quad

ratic

funct

ions,

then

more

gen

eral

quad

ratic

funct

ions

2.

Show

ineq

ual

itie

s on a

num

ber

lin

e, u

sing

solid

circl

es t

o s

how

in

clusi

ve ineq

ual

itie

s an

d o

pen

circl

es t

o

show

exc

lusi

ve

ineq

ual

itie

s.

3.

Write

dow

n a

n

ineq

ual

ity

show

n o

n a

num

ber

lin

e

6.

Lin

ear

ineq

ual-

itie

s

4.

Solv

e si

mple

lin

ear

ineq

ual

itie

s in

one

variab

le

Opport

unity

to e

xten

d t

his

to

incl

ude

show

ing ineq

ual

itie

s in

tw

o v

aria

ble

s on a

gra

ph

(Hig

her

tie

r G

CSE).

A g

Solv

e lin

ear

ineq

ual

itie

s in

one

or

two

var

iable

s, a

nd

repre

sent

the

solu

tion s

et o

n a

num

ber

lin

e o

r co

ord

inate

gri

d

Solv

e si

mple

lin

ear

ineq

ual

itie

s in

one

variab

le,

and r

epre

sent

the

solu

tion

set

on a

num

ber

lin

e

U

se t

he

corr

ect

nota

tion

to

show

incl

usi

ve a

nd e

xclu

sive

in

equal

itie

s

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

32

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s R

ef

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

1.

Gen

erat

e te

rms

of

a se

quen

ce u

sing t

erm

-to

-ter

m d

efin

itio

n o

r usi

ng p

osi

tion-t

o-t

erm

def

initio

n

Opport

unity

to e

xten

d t

his

to

incl

ude:

des

crib

ing t

he

term

to-

term

def

initio

n o

f a

sequen

ce in w

ord

s

find a

spec

ific

ter

m in a

se

quen

ce

usi

ng t

he

posi

tion-t

o-t

erm

an

d t

erm

-to-

term

rule

s

id

entify

ing w

hic

h t

erm

s ca

nnot

be

in a

seq

uen

ce.

A i

Gen

erat

e te

rms

of

a se

quen

ce u

sing

term

-to-t

erm

and

posi

tion-t

o-t

erm

def

initio

ns

of

the

sequen

ce

G

ener

ate

sim

ple

seq

uen

ces

of

num

ber

s, s

quar

ed

inte

ger

s an

d s

equen

ces

der

ived

fro

m d

iagra

ms

7.

Nu

mb

er

seq

uen

ces

2.

Find a

nd u

se t

he

nth

term

of

a lin

ear

arithm

etic

seq

uen

ce

A

j

Use

lin

ear

expre

ssio

ns

to

des

crib

e th

e nt

h ter

m

of

an a

rith

met

ic

sequen

ce

Fi

nd t

he

nth t

erm

of

an

arithm

etic

seq

uen

ce

U

se t

he

nth t

erm

of

an

arithm

etic

seq

uen

ce

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

33

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s R

ef

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

A m

U

nders

tan

d t

hat

the f

orm

y

= m

x +

c re

pre

sen

ts

a s

traig

ht

lin

e a

nd

that

m is

the

gra

die

nt

of

the lin

e

an

d c

is

the v

alu

e o

f th

e y

- in

terc

ept

Fin

d t

he g

rad

ien

t of

a

stra

igh

t lin

e f

rom

its

eq

uati

on

1.

Find t

he

gra

die

nt

of

a st

raig

ht

line

gra

ph

Opport

unity

to e

xten

d t

his

to:

under

stan

din

g t

he

gra

die

nts

of par

alle

l an

d

per

pen

dic

ula

r lin

es (

Hig

her

tier

GCSE).

A l

Rec

ognis

e an

d p

lot

equat

ions

that

co

rres

pond t

o

stra

ight-

line

gra

phs

in t

he

coord

inat

e pla

ne,

incl

udin

g

findin

g g

radie

nts

Fi

nd

the

grad

ient of

a s

trai

ght lin

e fr

om a

gra

ph

Fin

d t

he g

rad

ien

t o

f lin

es

giv

en

by e

qu

ati

on

s o

f th

e

form

y =

mx

+ c

A l

Rec

ognis

e an

d p

lot

equat

ions

that

co

rres

pond t

o

stra

ight-

line

gra

phs

in t

he

coord

inat

e pla

ne,

incl

udin

g

findin

g g

radie

nts

A

naly

se p

rob

lem

s an

d u

se

gra

die

nts

to

in

terp

ret

ho

w

on

e v

ari

ab

le c

han

ges

in

rela

tio

n t

o a

no

ther

8.

Gra

die

nts

o

f st

raig

ht

lin

e

gra

ph

s

2.

Inte

rpre

t th

e gra

die

nt

of

real

-life

gra

phs

A s

D

iscu

ss,

plo

t an

d

inte

rpre

t gra

phs

(whic

h m

ay b

e non

-lin

ear)

model

ling r

eal

situ

atio

ns

In

terp

ret

info

rmat

ion p

rese

nte

d

in a

ran

ge

of lin

ear

and n

on-

linea

r gra

phs

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

34

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s R

ef

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

1.

Rec

ognis

e, p

lot

and

dra

w g

raphs

of th

e fo

rm y

= m

x +

c

O

pport

unity

to e

xten

d t

his

to

incl

ude

plo

ttin

g a

nd

dra

win

g g

raphs

of

funct

ions

D

raw

, la

bel

and s

cale

axe

s

Rec

ognis

e th

at e

quat

ions

of

the

form

y =

mx

+ c

corr

espond t

o st

raig

ht-

line

gra

phs

in t

he

coord

inat

e pla

ne

Pl

ot

and d

raw

gra

phs

of

stra

ight

lines

with e

quat

ions

of

the

form

y =

mx

+ c

9.

Str

aig

ht

lin

e

gra

ph

s

2.

Giv

en a

str

aight

line

gra

ph,

find its

eq

uat

ion

A

m

Un

ders

tan

d t

hat

the f

orm

y

= m

x +

c re

pre

sen

ts a

st

raig

ht

lin

e a

nd

th

at

m is

the

gra

die

nt

of

the lin

e

an

d c

is

the v

alu

e

of

the y

- in

terc

ep

t

In

terp

ret

an

d a

naly

se a

st

raig

ht

lin

e g

rap

h

U

nd

ers

tan

d t

hat

the f

orm

y

= m

x +

c re

pre

sen

ts a

st

raig

ht

lin

e

Pro

gre

ssio

n

Op

po

rtu

nit

ies

O

nce

stu

den

ts h

ave

mas

tere

d t

he

skill

s ab

ove

, le

arnin

g

can b

e ex

tended

to

incl

ude

anal

ysin

g p

roble

ms

usi

ng

stra

ight

line

gra

phs.

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

35

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s R

ef

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

1.

Under

stan

d t

hat

st

raig

ht

and c

urv

ed

gra

phs

can r

epre

sent

real

-life

situ

atio

ns

A

r

Const

ruct

lin

ear,

q

uad

rati

c an

d

oth

er

funct

ions

from

re

al-l

ife

pro

ble

ms

and p

lot

thei

r co

rres

pondin

g g

raphs

D

raw

str

aight

line

gra

phs

for

real

-life

situ

atio

ns

–

read

y re

ckoner

gra

phs

–

conve

rsio

n g

raphs

–

fuel

bill

s

–

fixe

d c

har

ge

(sta

ndin

g

char

ge)

and c

ost

per

unit

10

. Gra

ph

s fo

r re

al-

life

si

tuati

on

s

2.

Dra

w,

and inte

rpre

t in

form

atio

n f

rom

gra

phs

of

real

-life

situ

atio

ns

A

s

Dis

cuss

, plo

t an

d

inte

rpre

t gra

phs

(whic

h m

ay b

e non

-lin

ear)

model

ling r

eal

situ

atio

ns

In

terp

ret

stra

ight

line

gra

phs

for

real

-life

situ

atio

ns

–

read

y re

ckoner

gra

phs

–

conve

rsio

n g

raphs

–

fuel

bill

s

–

fixe

d c

har

ge

(sta

ndin

g

char

ge)

and c

ost

per

unit

In

terp

ret

info

rmat

ion p

rese

nte

d

in a

ran

ge

of lin

ear

and n

on-

linea

r gra

phs

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

36

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s R

ef

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

1.

Plot

gra

phs

of

sim

ple

quad

ratic

funct

ions

Gen

erat

e poin

ts a

nd p

lot

gra

phs

of

sim

ple

quad

ratic

funct

ions,

then

more

gen

eral

quad

ratic

funct

ions

11

. Sim

ple

q

uad

rati

c fu

nct

ion

s

2.

Find a

ppro

xim

ate

solu

tions

of a

quad

ratic

equat

ion

from

the

gra

ph o

f th

e co

rres

pondin

g

quad

ratic

funct

ion

A t

G

ener

ate

poin

ts a

nd

plo

t gra

phs

of

sim

ple

quad

ratic

funct

ions,

an

d u

se t

hes

e to

fin

d

appro

xim

ate

solu

tions

Fi

nd a

ppro

xim

ate

solu

tions

of

a quad

ratic

equat

ion f

rom

the

gra

ph o

f th

e co

rres

pondin

g

quad

ratic

funct

ion

Pro

gre

ssio

n

Op

po

rtu

nit

ies

Once

stu

den

ts h

ave

mas

tere

d t

he

skill

s ab

ove

, le

arnin

g

can b

e ex

tended

to

incl

ude:

–

Sel

ect

and u

se t

he

corr

ect

mat

hem

atic

al t

echniq

ues

to

dra

w q

uad

ratic

gra

phs

–

Find t

he

inte

rsec

tion p

oin

ts o

f th

e gra

phs

of a

linea

r an

d q

uad

ratic

funct

ion,

know

ing t

hat

thes

e ar

e th

e ap

pro

xim

ate

solu

tions

of

the

corr

espondin

g

sim

ultan

eous

equat

ions

repre

senting t

he

linea

r an

d

quad

ratic

funct

ions

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

37

Level

2 A

ward

in

Alg

eb

ra

GC

SE M

ath

em

ati

cs –

Alg

eb

ra c

on

ten

t

To

pic

C

on

cep

ts a

nd

skil

ls

Pro

gre

ssio

n O

pp

ort

un

itie

s R

ef

C

on

ten

t d

esc

rip

tor

Co

nce

pts

an

d s

kills

12

. Dis

tan

ce-

tim

e a

nd

sp

eed

-ti

me

gra

ph

s

1.

Dra

w d

ista

nce

-tim

e gra

phs

and s

pee

d-

tim

e gra

phs

A

r

Const

ruct

lin

ear,

q

uad

rati

c an

d

oth

er

funct

ions

from

re

al-l

ife

pro

ble

ms

and p

lot

thei

r co

rres

pondin

g g

raphs

D

raw

str

aight

line

gra

phs

for

real

-life

situ

atio

ns

–

Dis

tance

-tim

e gra

phs

2.

Inte

rpre

t dis

tance

-tim

e gra

phs

and

spee

d-t

ime

gra

phs

Inte

rpre

t dis

tance

-tim

e gra

phs

3.

Under

stan

d t

hat

the

gra

die

nt

of a

dis

tance

-tim

e gra

ph r

epre

sents

sp

eed

4.

Find s

pee

d a

nd

dis

tance

fro

m

info

rmat

ion o

n a

tra

vel

gra

ph

A s

D

iscu

ss,

plo

t an

d

inte

rpre

t gra

phs

(whic

h m

ay b

e non

-lin

ear)

model

ling r

eal

situ

atio

ns

In

terp

ret

info

rmat

ion p

rese

nte

d

in a

ran

ge

of lin

ear

and n

on-

linea

r gra

phs



38



39

Appendix 4: Mapping to International GCSE and Level 1/ Level 2 Certificate in Mathematics qualifications

Below is a sub-set of the content (relating to Algebra) within the International GCSE Mathematics A and the Level 1/level 2 Certificate in Mathematics qualifications. The content common across the above specifications and the Level 2 Award in Algebra is shown in purple.

There are opportunities to progress from content within Level 2 Award in Algebra to content within the International and Certificate specifications. These possible progression opportunities are shown in green.

Higher tier International GCSE and Certificate content is shown in bold.

2. Equations, Formulae and Identities

2.1 Use of Symbols

understand that symbols may be used to represent numbers in equations or variables in expressions and formulae (Ref 1.1)

understand that algebraic expressions follow the generalised rules of arithmetic

use index notation for positive integer powers (Ref 2.4)

use index laws in simple cases (Ref 2.4)

use index notation involving fractional powers

2.2 Algebraic Manipulation

evaluate expressions by substituting numerical values for letters

collect like terms (Ref 2.1)

multiply a single term over a bracket (Ref 2.2)

take out single common factors (Ref 2.3)

expand the product of two linear expressions

understand the concept of a quadratic expression and be able to factorise such expressions

manipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadratic



40

2.3 Expressions and Formulae

understand that a letter may represent an unknown number or a variable (Ref 1.1)

use correct notational conventions for algebraic expressions and formulae

substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae (Ref 3.1)

use formulae from mathematics and other real life contexts expressed initially in words or diagrammatic form and converting to letters and symbols

understand the process of manipulating formulae to change the subject where the subject may appear twice or a power of the subject occurs (Ref 3.2 only where subject appears once)

2.4 Linear Equations

solve linear equations with integer or fractional coefficients in one unknown in which the unknown appears on either side or both sides of the equation (Ref 4.1, 4.2)

set up simple linear equations from data given

2.5 Proportion

set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations

2.4 Simultaneous Linear Equations

calculate the exact solution of two simultaneous equations in two unknowns

interpret the equations as lines and the common solution as the point of intersection

2.6 Quadratic Equations

solve quadratic equations by factorisation

solve quadratic equations by using the quadratic formula

form and solve quadratic equations from data given in a context

solve simultaneous equations in two unknowns, one equation being linear and the other equation being quadratic

2.8 Inequalities

understand and use the symbols >, <, and

understand and use the convention for open and closed intervals on a number line (Ref 6.1)

solve simple linear inequalities in one variable and represent the solution set on a number line (Ref 6.3)

represent simple linear inequalities on rectangular cartesian graphs

identify regions on rectangular cartesian graphs defined by simple linear inequalities

solve quadratic inequalities in one unknown and represent the solution set on a number line

identify harder examples of regions defined by linear inequalities



41

3. Sequences, Functions and Graphs

3.1 Sequences

generate terms of a sequence using term-to-term and position-to-term definitions of the sequence (Ref 7.1)

find subsequent terms of an integer sequence

Use linear expressions to describe the nth term of an arithmetic sequence (Ref 7.2)

3.2 Graphs

interpret information presented in a range of linear and non-linear graphs (Ref 10.1)

understand and use conventions for rectangular cartesian coordinates

plot points (x, y) in any of the four quadrants of a graph

locate points with given coordinates

determine the coordinates of points identified by geometrical information

determine the coordinates of the midpoint of a line segment given the coordinates of the two end points

draw and interpret straight line conversion graphs

understand the concept of a gradient of a straight line (Ref 8.1, 8.2)

recognise that equations of the form y = mx + c are straight line graphs (Ref 9.1, 9,2)

generate points and plot graphs of linear and quadratic functions (Ref 9.1. 11.1)

plot and draw 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

or: y = Ax3 + Bx2 + Cx + D + E/x + F/x2

in which

(i) the constants are numerical and at least three of them are zero

(ii) the letters x and y can be replaced with any other two letters

find the gradients of non-linear graphs

Find the intersection points of two graphs, one linear (y1) and one non-linear (y2), and recognise that the solutions correspond to the solutions of y2 – y1 = 0 (Ref 5.1)

Calculate a gradient of a straight line given two coordinates (Ref 8.1)

Recognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y axis at the point (0, c) (Ref 9.1)

find the equation of a straight line parallel to a given line



42

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

43

Appen

dix

5:

Map

pin

g of

GC

E A

S Le

vel C

ore

Mat

hem

atic

s 1 (

C1)

Progre

ssio

n in t

erm

s of

conte

nt

and s

kills

is

illust

rate

d in t

he

grid b

elow

, fr

om

the

Leve

l 2 t

o L

evel

3 A

war

ds

in A

lgeb

ra t

o C

ore

Mat

hem

atic

s 1

within

GCE A

S a

nd A

lev

el M

athem

atic

s.

Level

2 A

ward

in

Alg

eb

ra

Level

3 A

ward

in

Alg

eb

ra

Co

re M

ath

em

ati

cs 1

1.

Alg

eb

ra a

nd

fu

nct

ion

s

2.4

U

se index

law

s fo

r m

ultip

licat

ion,

div

isio

n a

nd r

aisi

ng p

ow

er t

o a

pow

er

2.3

U

se index

law

s to

incl

ude

frac

tional

an

d n

egat

ive

indic

es

Law

s o

f in

dic

es

for

all r

ati

on

al exp

on

en

ts.

16.1

U

se a

nd m

anip

ula

te s

urd

s, incl

udin

g

rational

isin

g t

he

den

om

inat

or

of a

frac

tion w

ritt

en in t

he

form

a

bc

Use

an

d m

an

ipu

lati

on

of

surd

s.

11.1

Pl

ot

gra

phs

of

sim

ple

quad

ratic

funct

ions

11.2

Fi

nd a

ppro

xim

ate

solu

tions

of a

quad

ratic

equat

ion f

rom

the

gra

ph o

f th

e co

rres

pondin

g q

uad

ratic

funct

ion

10.1

Rec

ognis

e, d

raw

and s

ketc

h g

raphs

of

linea

r, q

uad

ratic,

cubic

, re

cipro

cal,

exponen

tial

and c

ircu

lar

funct

ions,

an

d u

nder

stan

d t

angen

ts a

nd

norm

als

10.2

Ske

tch g

raphs

of quad

ratic,

cubic

, an

d r

ecip

roca

l fu

nct

ions,

con

sider

ing

asym

pto

tes,

orien

tation a

nd lab

elin

g

poin

ts o

f in

ters

ection w

ith a

xes

and

turn

ing p

oints

Qu

ad

rati

c fu

nct

ion

s an

d t

heir

gra

ph

s.

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

44

Level

2 A

ward

in

Alg

eb

ra

Level

3 A

ward

in

Alg

eb

ra

Co

re M

ath

em

ati

cs 1

1.

Alg

eb

ra a

nd

fu

nct

ion

s co

ntinued

6.1

U

nder

stan

d t

he

role

of

the

dis

crim

inan

t in

quad

ratic

equat

ions

Th

e d

iscr

imin

an

t o

f a q

uad

rati

c fu

nct

ion

.

5.1

Solv

e quad

ratic

equat

ions

by

fact

orisa

tion o

r by

com

ple

ting t

he

squar

e

5.2

Know

and u

se t

he

quad

ratic

form

ula

Co

mp

leti

ng

th

e s

qu

are

. S

olu

tio

n o

f q

uad

rati

c eq

uati

on

s.

4.1

Solv

e si

multan

eous

equat

ions

in

two u

nkn

owns,

wher

e one

may

be

quad

ratic,

wher

e one

may

incl

ude

pow

ers

up t

o 2

.

Sim

ult

an

eo

us

eq

uati

on

s: a

naly

tica

l so

luti

on

by s

ub

stit

uti

on

.

6.3

Solv

e si

mple

lin

ear

ineq

ual

itie

s in

one

variab

le

7.1

Solv

e lin

ear

ineq

ual

itie

s, a

nd

quad

ratic

ineq

ual

itie

s

So

luti

on

of

lin

ear

an

d q

uad

rati

c in

eq

ualiti

es.

2.1

Colle

ctio

n o

f lik

e te

rms

2.2

M

ultip

licat

ion o

f a

single

ter

m o

ver

a bra

cket

2.3

Fa

ctorise

alg

ebra

ic e

xpre

ssio

ns

by

taki

ng o

ut

all co

mm

on f

acto

rs

2.4

U

se index

law

s fo

r m

ultip

licat

ion,

div

isio

n a

nd r

aisi

ng a

pow

er t

o a

pow

er

2.1

M

ultip

ly t

wo lin

ear

expre

ssio

ns

2.2

Fa

ctorise

exp

ress

ions

incl

udin

g

quad

ratics

and t

he

diffe

rence

of

two

squar

es,

taki

ng o

ut

all co

mm

on

fact

ors

2.3

U

se index

law

s to

incl

ude

frac

tional

an

d n

egat

ive

indic

es

2.4

Sim

plif

y al

geb

raic

fra

ctio

ns

Alg

eb

raic

man

ipu

lati

on

of

po

lyn

om

ials

, in

clu

din

g e

xp

an

din

g b

rack

ets

an

d

collect

ing

lik

e t

erm

s, f

act

ori

sati

on

.

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

45

Level

2 A

ward

in

Alg

eb

ra

Level

3 A

ward

in

Alg

eb

ra

Co

re M

ath

em

ati

cs 1

1.

Alg

eb

ra a

nd

fu

nct

ion

s co

ntinued

5.1

Ske

tch g

raphs

of

quad

ratic

funct

ions,

consi

der

ing o

rien

tation

and lab

ellin

g t

he

poin

t of

inte

rsec

tion

with t

he

y-ax

is,

consi

der

ing w

hat

hap

pen

s to

y f

or

larg

e posi

tive

and

neg

ativ

e va

lues

of x

5.2

Pl

ot

gra

phs

of

sim

ple

quad

ratic

funct

ions

5.3

Fi

nd a

ppro

xim

ate

solu

tions

of a

quad

ratic

equat

ion f

rom

the

gra

ph o

f th

e co

rres

pondin

g q

uad

ratic

funct

ion

10.1

Rec

ognis

e, d

raw

and s

ketc

h g

raphs

of

linea

r, q

uad

ratic,

cubic

, re

cipro

cal,

exponen

tial

and c

ircu

lar

funct

ions,

an

d u

nder

stan

d t

angen

ts a

nd

norm

als

10.2

Ske

tch g

raphs

of quad

ratic,

cubic

, an

d r

ecip

roca

l fu

nct

ions,

con

sider

ing

asym

pto

tes,

orien

tation a

nd lab

elin

g

poin

ts o

f in

ters

ection w

ith a

xes

and

turn

ing p

oints

10.3

U

se g

raphs

to s

olv

e eq

uat

ions

Gra

ph

s o

f fu

nct

ion

s; s

ketc

hin

g c

urv

es

defi

ned

by s

imp

le e

qu

ati

on

s. G

eo

metr

ical

inte

rpre

tati

on

of

alg

eb

raic

so

luti

on

of

eq

uati

on

s. U

se o

f in

ters

ect

ion

po

ints

of

gra

ph

s o

f fu

nct

ion

s to

so

lve e

qu

ati

on

s.

14.1

Apply

to t

he

gra

ph o

f y

= f

(x)

tran

sform

atio

ns

of

y =

f(x

) ±

a,

y =

f(±

ax),

y =

f(x

± a

), y

= ±

af(x

) fo

r an

y fu

nct

ion in x

Kn

ow

led

ge o

f th

e e

ffect

of

sim

ple

tr

an

sfo

rmati

on

s o

n t

he g

rap

h o

f y

= f(

x) a

s re

pre

sen

ted

by y

= a

f(x)

, y =

f(x)

+ a

,

y =

f(x

+ a)

, y =

f(ax

).

UG

031210 –

Spec

ific

atio

n –

Edex

cel Le

vel 2 a

nd L

evel

3 A

war

d in A

lgeb

ra –

Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

rson E

duca

tion L

imited

2012

46

Level

2 A

ward

in

Alg

eb

ra

Level

3 A

ward

in

Alg

eb

ra

Co

re M

ath

em

ati

cs 1

2.

Co

ord

inate

geo

metr

y in

th

e (

x, y

) p

lan

e

8.1

Fi

nd t

he

gra

die

nt

of

a st

raig

ht

line

gra

ph

9.1

Rec

ognis

e, p

lot

and d

raw

gra

phs

of

the

form

y =

mx

+ c

9.2

G

iven

a s

trai

ght

line

gra

ph,

find its

eq

uat

ion

9.1

Fo

rms

of

the

equat

ion o

f a

stra

ight

line

gra

ph

Eq

uati

on

of

a s

traig

ht

lin

e,

incl

ud

ing

th

e

form

s y

– y 1

= m

(x –

x1)

and

ax

+ by

+ c

= 0

9.2

Conditio

ns

for

stra

ight

lines

to b

e par

alle

l or

per

pen

dic

ula

r to

eac

h

oth

er

Co

nd

itio

ns

for

two

str

aig

ht

lin

es

to b

e

para

llel o

r p

erp

en

dic

ula

r to

each

oth

er.

3.

Seq

uen

ces

an

d s

eri

es

7.1

G

ener

ate

term

s of

a se

quen

ce u

sing

term

to t

erm

def

initio

n o

r usi

ng

posi

tion t

o t

erm

def

initio

n

S

eq

uen

ces,

in

clu

din

g t

ho

se g

iven

by a

fo

rmu

la f

or

the n

th t

erm

an

d t

ho

se

gen

era

ted

by a

sim

ple

rela

tion

of

the f

orm

x n

+1 =

f(x n

).

7.2

Fi

nd a

nd u

se t

he

nth t

erm

of

a lin

ear

arithm

etic

seq

uen

ce

A

rith

meti

c se

ries,

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ula

fo

r th

e s

um

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n n

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ral n

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.

UG

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Spec

ific

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n –

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cel Le

vel 2 a

nd L

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Issu

e 1 –

Sep

tem

ber

2012 ©

Pea

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tion L

imited

2012

47

Pro

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ssio

n t

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nd

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ati

cs

Core

Mat

hem

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requires

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ed in C

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hem

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C1).

Lik

ewis

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for

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1,

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for

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puls

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athem

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4 c

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the

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bov

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can b

e in

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ed t

hat

the:

Le

vel 2 A

lgeb

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ds

support

pro

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Db260912G

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D_L2

3_ALG

EBRA.D

OC.1

–54/4

Further copies of this publication are available from Edexcel Publications, Adamsway, Mansfield, Notts, NG18 4FN Telephone 01623 467467 Fax 01623 450481 Email: [email protected] Publications Code UG031210 September 2012 For more information on Edexcel and BTEC qualifications please visit our website: www.edexcel.com Pearson Education Limited. Registered in England and Wales No. 872828 Registered Office: Edinburgh Gate, Harlow, Essex CM20 2JE. VAT Reg No GB 278 537121

mailto:[email protected]�

http://www.edexcel.com/�

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