168982-specification-gcse-mathematics-j560

GCSE (9-1) Specification MATHEMATICS J560 For first assessment in 2017 ocr.org.uk/gcsemaths Version 1.1 (April 2018)

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Contents ii iii Introducing… GCSE (9–1) Mathematics (from September 2015) iv Teaching and learning resources Professional Development 1 1 1 Why choose an OCR GCSE (9–1) in Mathematics? 2 3 1a. Why choose an OCR qualification? 3 1b. Why choose an OCR GCSE (9–1) in Mathematics? 1c. What are the key features of this specification? 4 1d. How do I find out more information? 4 5 2 The specification overview 47 2a. OCR’s GCSE (9–1) in Mathematics (J560) 48 2b. Content of GCSE (9–1) in Mathematics (J560) 48 2c. Prior knowledge, learning and progression 48 48 3 Assessment of OCR GCSE (9–1) in Mathematics 49 50 3a. Forms of assessment 50 3b. Assessment availability 51 3c. Retaking the qualification 3d. Assessment objectives (AOs) 52 3e. Tiers 52 3f. Synoptic assessment 53 3g. Calculating qualification results 53 54 4 Admin: what you need to know 54 54 4a. Pre-assessment 4b. Accessibility and special consideration 55 4c. External assessment arrangements 55 4d. Results and certificates 56 4e. Post-results services 56 4f. Malpractice 56 5 Appendices i 5a. Grade descriptors 5b. Overlap with other qualifications 5c. Avoidance of bias Summary of Updates © OCR 2016 GCSE (9–1) in Mathematics

Introducing… GCSE (9–1) Mathematics (from September 2015) We’ve developed an inspiring, motivating and coherent Meet the team mathematics specification for the entire ability range. It emphasises and encourages: We have a dedicated team of Mathematics Subject Advisors working on our mathematics qualifications. • Sound understanding of concepts If you need specialist advice, guidance or support, • Fluency in procedural skill get in touch as follows: • Competency to apply mathematical skills in a 01223 553998 range of contexts [email protected] @OCR_Maths • Confidence in mathematical problem solving. © OCR 2016 ii GCSE (9–1) in Mathematics

Teaching and learning resources We recognise that the introduction of a new Plenty of useful resources specification can bring challenges for implementation and teaching. Our aim is to help you at every stage and You’ll have four main types of subject-specific teaching we’re working hard to provide a practical package of and learning resources at your fingertips: support in close consultation with teachers and other experts, so we can help you to make the change. • Delivery Guides Designed to support progression for all • Transition Guides Our resources are designed to provide you with a • Topic Exploration Packs range of teaching activities and suggestions so you can select the best approach for your particular students. • Lesson Elements. You are the experts on how your students learn and our aim is to support you in the best way we can. Along with subject-specific resources, you’ll also have access to a selection of generic resources that focus We want to… on skills development and professional guidance for teachers. • Support you with a body of knowledge that grows throughout the lifetime of the Skills Guides – we’ve produced a set of Skills Guides specification that are not specific to Mathematics, but each covers a topic that could be relevant to a range of qualifications • Provide you with a range of suggestions so you – for example, communication, legislation and can select the best activity, approach or context research. Download the guides at ocr.org.uk/ for your particular students skillsguides • Make it easier for you to explore and interact Active Results – a free online results analysis service with our resource materials, in particular to to help you review the performance of individual develop your own schemes of work students or your whole school. It provides access to detailed results data, enabling more comprehensive • Create an ongoing conversation so we can analysis of results in order to give you a more accurate develop materials that work for you. measurement of the achievements of your centre and individual students. For more details refer to ocr.org.uk/activeresults © OCR 2016 iii GCSE (9–1) in Mathematics

Professional Development Take advantage of our improved Professional These events are designed to help prepare you for first Development Programme, designed with you in mind. teaching and to support your delivery at every stage. Whether you want to come to events, look at our new digital training or search for training materials, you can Watch out for details at cpdhub.ocr.org.uk. find what you’re looking for all in one place at the CPD Hub. To receive the latest information about the training we’ll be offering, please register for GCSE email An introduction to the new specifications updates at ocr.org.uk/updates. We’ll be running events to help you get to grips with our GCSE Mathematics qualification. © OCR 2016 iv GCSE (9–1) in Mathematics

1 Why choose an OCR GCSE (9–1) in Mathematics? 1a. Why choose an OCR qualification? Choose OCR and you’ve got the reassurance that We provide a range of support services designed to 1 you’re working with one of the UK’s leading exam help you at every stage, from preparation through to boards. Our new GCSE (9–1) in Mathematics course the delivery of our specifications. This includes: has been developed in consultation with teachers, employers and Higher Education to provide students • A wide range of high-quality creative resources with a qualification that’s relevant to them and meets including: their needs. o Delivery Guides o Transition Guides We’re part of the Cambridge Assessment Group, o Topic Exploration Packs Europe’s largest assessment agency and a department o Lesson Elements of the University of Cambridge. Cambridge Assessment o …and much more. plays a leading role in developing and delivering assessments throughout the world, operating in over • Access to Subject Advisors to support you 150 countries. through the transition and throughout the lifetimes of the specifications. We work with a range of education providers, including schools, colleges, workplaces and other institutions • CPD/Training for teachers to introduce the in both the public and private sectors. Over 13,000 qualifications and prepare you for first teaching. centres choose our A levels, GCSEs and vocational qualifications including Cambridge Nationals and • Active Results – our free results analysis service Cambridge Technicals. helps you review the performance of individual students or across your whole school. Our Specifications • ExamBuilder – our new free online past papers We believe in developing specifications that help you service that enables you to build your own test bring the subject to life and inspire your students to papers from past OCR exam questions. achieve more. http://www.ocr.org.uk/exambuilder We’ve created teacher-friendly specifications based on All GCSE (9–1) qualifications offered by OCR are extensive research and engagement with the teaching accredited by Ofqual, the Regulator for qualifications community. They’re designed to be straightforward offered in England. The QN for this qualification is and accessible so that you can tailor the delivery of QN 601/4606/0. the course to suit your needs. We aim to encourage learners to become responsible for their own learning, confident in discussing ideas, innovative and engaged. © OCR 2016 1 GCSE (9–1) in Mathematics

1b. Why choose an OCR GCSE (9–1) in Mathematics? OCR’s GCSE (9–1) in Mathematics provides a broad, Learner-focused coherent, satisfying and worthwhile course of study. • OCR’s specification and assessment will consist 1 It encourages learners to develop confidence in, of mathematics fit for the modern world and and a positive attitude towards mathematics and to presented in authentic contexts. recognise the importance of mathematics in their own lives and to society. It also provides a strong • It will allow learners to develop mathematical mathematical foundation for learners who go on to independence built on a sound base of study mathematics at a higher level, post-16. conceptual learning and understanding. Aims and learning outcomes • OCR will target support and resources to develop fluency, reasoning and problem solving skills. OCR’s GCSE (9–1) in Mathematics enables learners to: • It will be a springboard for future progress and • develop fluent knowledge, skills and achievement in a variety of qualifications across understanding of mathematical methods and subjects along with employment. concepts Teacher-centred • acquire, select and apply mathematical techniques to solve problems • OCR will provide an extensive teacher support package, including high-quality flexible • reason mathematically, make deductions and resources, particularly for the new GCSE (9–1) inferences and draw conclusions subject areas and assessment objectives. • comprehend, interpret and communicate • OCR’s support and resources will focus on mathematical information in a variety of forms empowering teachers, exploring teaching appropriate to the information and context. methods and classroom innovation alongside more direct content-based resources. OCR’s GCSE (9–1) in Mathematics is: • OCR’s assessment will be solid and dependable, Worthwhile recognising positive achievement in candidate learning and ability. • Research, international comparisons and engagement with both teachers and the wider Dependable education community have been used to enhance the reliability, validity and appeal of our • OCR’s high-quality assessments are backed up assessment tasks in mathematics. by sound educational principles and a belief that the utility, richness and power of mathematics • It will encourage the teaching of interesting should be made evident and accessible to all mathematics, aiming for mastery leading to learners. positive exam results. • An emphasis on learning and understanding mathematical concepts underpinned by a sound, reliable and valid assessment. © OCR 2016 2 GCSE (9–1) in Mathematics

1c. What are the key features of this specification? • A simple assessment model, featuring 3 papers • A flexible support package for teachers formed at each tier, of equal length with identical through listening to teachers’ needs, allowing 1 mark allocations and identical weightings of teachers to easily understand the requirements Assessment Objectives and subject content. of the qualification and present the qualification • A specification developed by teachers to learners. specifically for teachers, laying out the required • A team of OCR Subject Advisors, who centres content clearly in terms of both topic area can contact for subject and assessment queries. and difficulty, facilitating learners’ progression • Part of a wide range of OCR mathematics through the content. assessments, allowing progression into a range • An exciting package of free resources, developed of further qualifications, from A and AS Level in conjunction with teachers and through Mathematics and Further Mathematics to Free research by Cambridge Assessment, taking Standing Mathematics Qualifications, Core learners from Key Stage 3 right the way through Maths, Level 3 certificates and more. GCSE, which can be adapted as required by • A mock exams package to assess the progression teachers and shaped to their learners’ needs. of learners and easily pick up on topics requiring further teaching. 1d. How do I find out more information? If you are already using OCR specifications you can Find out more? contact us at: www.ocr.org.uk  Get in touch with one of our Subject Advisors: Email: [email protected]  If you are not already a registered OCR centre then Customer Contact Centre: 01223 553998 you can find out more information on the benefits of Teacher support: www.ocr.org.uk  becoming one at: www.ocr.org.uk  © OCR 2016 3 GCSE (9–1) in Mathematics

2 The specification overview 2a. OCR’s GCSE (9–1) in Mathematics (J560) Learners are entered for either Foundation tier (Paper 1, Paper 2 and Paper 3) or Higher tier (Paper 4, Paper 5 and Paper 6). Qualification Overview Assessment Overview 2 Foundation tier, grades 5 to 1 Written paper 33 13– % 100 marks of total • Paper 1 (Foundation tier) GCSE J560/01 1 hour 30 minutes Calculator permitted • Paper 2 (Foundation tier) Written paper 33 31– % J560/02 100 marks of total GCSE 1 hour 30 minutes Calculator not permitted • Paper 3 (Foundation tier) Written paper 33 31– % J560/03 100 marks of total GCSE 1 hour 30 minutes Calculator permitted Higher tier, grades 9 to 4 Written paper 33 13– % 100 marks of total • Paper 4 (Higher tier) GCSE J560/04 1 hour 30 minutes Calculator permitted • Paper 5 (Higher tier) Written paper 33 31– % J560/05 100 marks of total GCSE 1 hour 30 minutes Calculator not permitted • Paper 6 (Higher tier) Written paper 33 31– % J560/06 100 marks of total GCSE 1 hour 30 minutes Calculator permitted © OCR 2016 4 GCSE (9–1) in Mathematics

2b. Content of GCSE (9–1) in Mathematics (J560) The content of this specification. • allows for easier movement from Foundation 2 tier to Higher tier by showing how the required • This is a linear qualification. The content is content for the former progresses to the latter arranged by topic area and exemplifies the level of demand for different tiers, but centres are All exemplars contained in the specification are for free to teach the content for the appropriate tier illustration only and do not constitute an exhaustive in the order most appropriate to their learners’ list. needs. Where content in one column is not further • Any topic area may be assessed on any exemplified in the column(s) to its right, that content component, as relevant at that tier. may be assessed at a higher level of demand than given, as appropriate for learners attaining a higher • The content of this specification is presented grade. The expectation is that themes will be in three columns, representing a progression developed further and connections explored even within the content strands. when not explicitly stated. • The columns are cumulative so that the Formulae expectation of a Foundation tier learner is exemplified by the first two columns and The assessment for this specification will not include that of a Higher tier learner is the sum of the a formula sheet. All formulae which learners are statements in all three columns. required to know are given in the specification under 6.02d. • Many higher tier learners will already be confident and competent with the content of All other formulae required will be given in the the first column when they begin their GCSE assessment. (9–1) course. It may therefore not be necessary to cover this content explicitly with all learners, Units and measures though all learners will be assessed on this content at an appropriate level of demand. Learners should be familiar with and calculate with appropriate units: 24-hour and 12-hour clock; • Learners should build on all of the content from seconds (s), minutes (min), hours (h), days, months earlier key stages. Knowledge of the content of and years including the relation between consecutive Key Stages 1 and 2 is therefore assumed, but will units (1 year = 365 days); £ and pence; $ and cents; not be assessed directly. € and cents; degrees; standard units of mass, length, area, volume and capacity, and related compound The division of content into three columns is intended units. Learners should be able to convert between to give an indication of the progression in conceptual units efficiently. Learners should be able to use rulers and procedural difficulty in each content strand. and protractors to measure the lengths of lines and the sizes of angles. This structure: Calculators • helps teachers to target teaching appropriately If no reference is made in the specification to • promotes assessment for learning by presenting calculator use then learners are expected to be able the content as a progression not simply the end to use both calculator and non-calculator methods. All point content may be assessed on either the calculator or non-calculator papers. • allows teachers to start this GCSE (9–1) course at a level which is appropriate to their learners, without feeling that they have to spend time on content with which their learners are familiar © OCR 2016 5 GCSE (9–1) in Mathematics

Sketching and plotting curves • A plot is drawn on squared or graph paper This specification makes a distinction between for a given range of values by calculating sketching and plotting curves. the coordinates of points on the curve and connecting them as appropriate. Where a table • A sketch shows the most important features of of values is given it will include sufficient points a curve. It does not have to be to scale, though to determine the curve. Where such a table is axes should be labelled and the graph should not given, the number of points required is left interact with the axes correctly. A sketch should to the discretion of the learner. 2 fall within the correct quadrants and show the correct long-term behaviour. A sketch only needs Statement References to be labelled with x-intercepts, y-intercepts, turning points or other features when requested Individual references for the statements of this in the assessment. A sketch does not require specification are included in the column headed ‘GCSE graph or squared paper. The assessment for this (9–1) Content Ref.’. Corresponding statements from the specification will expect a sketch to be drawn Department for Education (DfE) Mathematics – GCSE freehand. subject content and assessment objectives document are included in the column headed ‘DfE Ref.’. © OCR 2016 6 GCSE (9–1) in Mathematics

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content qualification will enabl Ref. Number Operations and Integers learners to… Calculations with integers OCR 1 Four rules Use non-calculator met calculate the sum, diffe 1.01 product and quotient o positive and negative w 1.01a numbers. 1.02 Whole number theory Understand and use the 1.02a Definitions and terms odd, even, prime, facto (divisor), multiple, com 1.02b Prime numbers factor (divisor), commo multiple, square, cube, Understand and use pla value. Identify prime numbers than 20. Express a whole numbe product of its prime fac e.g. 24 = 2 # 2 # 2 # 3 Understand that each n can be expressed as a p of prime factors in only way. 7

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. thods to N2 erence, of N2, whole N4, N6 e terms Identify prime numbers. or N4, mmon Use power notation in N6 on expressing a whole number as , root. a product of its prime factors. e.g. 600 = 23 # 3 # 52 ace s less er as a ctors. 3 number product y one 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content qualification will enabl 8 GCSE (9–1) in Mathematics Ref. Highest Common Factor (HCF) and learners to… Lowest Common Multiple (LCM) 1.02c Find the HCF and LCM o whole numbers by listin 1.03 Combining arithmetic operations 1.03a Priority of operations Know the conventional for performing calculati 1.04 Inverse operations involving brackets, four 1.04a Inverse operations rules and powers, roots reciprocals. Know that addition and subtraction, multiplicati division, and powers an are inverse operations use this to simplify and calculations, for examp reversing arithmetic in thinking of a number” o “missing digit” problem e.g. 223 – 98 = 223 + 2 – 10 25 × 12 = 50 × 6 = 100 × [see also Calculation an estimation of powers a roots, 3.01b]

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. of two ng. Find the HCF and LCM of two N4 whole numbers from their prime factorisations. l order N3 tions r N3, s and N6 d tion and nd roots, and d check ple, in “I’m or ms. 00 = 125 × 3 = 300 nd and

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content qualification will enabl Ref. Fractions, Decimals and Percentages learners to… Fractions OCR 2 Equivalent fractions Recognise and use equ between simple fractio 2.01 mixed numbers. 2.01a e.g. 2 = 1 6 3 2 1 = 5 2 2 2.01b Calculations with fractions Add, subtract, multiply divide simple fractions and improper), includin mixed numbers and ne fractions. e.g. 1 1 + 3 2 4 5 # 3 6 10 -3 # 4 5 2.01c Fractions of a quantity Calculate a fraction of a quantity. 2 e.g. 5 of £3.50 Express one quantity as fraction of another. [see also Ratios and fra 5.01c] 9

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. uivalence N3 ons and y and Carry out more complex [see also Algebraic fractions, N2, (proper 6.01g] N8 calculations, including the use ng egative of improper fractions. e.g. 2 + 5 5 6 2 + 1 # 3 3 2 5 a Calculate with fractions N12, greater than 1. R3, R6 sa actions, 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content qualification will enabl 10 GCSE (9–1) in Mathematics Ref. Decimal fractions learners to… Decimals and fractions 2.02 Express a simple fractio 2.02a a terminating decimal o versa, without a calcula 2 e.g. 0.4 = 5 2.02b Addition, subtraction and multiplication Understand and use pla 2.02c of decimals value in decimals. Division of decimals Add, subtract and multi decimals including nega decimals, without a cal Divide a decimal by a w number, including nega decimals, without a cal e.g. 0.24 ' 6 2.03 Percentages Convert between fracti 2.03a Percentage conversions decimals and percentag 1 e.g. 4 = 0.25 = 25% 1 1 = 150% 2

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. on as Use division to convert a Convert a recurring decimal to N10, or vice N2 ator. simple fraction to a decimal. an exact fraction or vice versa. 1 41 e.g. 6 = 0.16666… e.g. 0.4o 1o = 99 ace Without a calculator, divide a N2 decimal by a decimal. N2 tiply ative e.g. 0.3 ' 0.6 lculator. whole ative lculator. tions, R9 ges.

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content qualification will enabl Ref. learners to… 2.03b Percentage calculations Understand percentage 2.03c ‘number of parts per hu 2.04 Calculate a percentage 2.04a quantity, and express o 2.04b quantity as a percentag another, with or withou calculator. Percentage change Increase or decrease a q by a simple percentage, including simple decima fractional multipliers. Apply this to simple orig value problems and sim interest. e.g. Add 10% to £2.50 b either finding 10% adding, or by multi by 1.1 or 110100 Calculate original p an item costing £10 50% discount. Ordering fractions, decimals and percentages Ordinality Order integers, fraction Symbols decimals and percentag 4 3 e.g. 5 , 4 , 0.72, –0.9 Use 1, 2, G, H, =, 11

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. e is R9, undred’. N12 of a one R9, ge of N12 ut a N1, quantity Express percentage change N2, , as a decimal or fractional R9 al or multiplier. Apply this to N1 percentage change problems ginal (including original value mple problems). by [see also Growth and decay, % and 5.03a] tiplying price of 0 after a ns, ges. ,! 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content qualification will enabl 12 GCSE (9–1) in Mathematics Ref. Indices and Surds learners to… Powers and roots OCR 3 Index notation Use positive integer ind write, for example, 3.01 2 # 2 # 2 # 2 = 24 3.01a Calculate positive integ powers and exact roots 3.01b Calculation and estimation of powers e.g. 24 = 16 and roots 9=3 3.01c Laws of indices 3 8=2 Recognise simple powe 3, 4 and 5. e.g. 27 = 33 [see also Inverse operati 1.04a] [see also Simplifying pr and quotients, 6.01c]

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. dices to Use negative integer indices to Use fractional indices N6, represent reciprocals. to represent roots and N7 ger combinations of powers and s. roots. N6, N7 ers of 2, Calculate with integer powers. Calculate fractional powers. - 1 -3 e.g. 3 = 8 = 1 = 1 2 e.g. 16 4 _4 16i3 8 Calculate with roots. Estimate powers and roots. e.g. 51 to the nearest whole number tions, Know and apply: N7, roducts A4 am # an = am + n am ' an = am - n _amin = amn [see also Calculations with numbers in standard form, 3.02b, Simplifying products and quotients, 6.01c]

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content qualification will enabl Ref. Standard form learners to… Standard form 3.02 Interpret and order num expressed in standard f 3.02a Convert numbers to an standard form. 3.02b Calculations with numbers in standard e.g. 1320 = 1.32 # 103 form 0.00943 = 9.43 # 3.03 Use a calculator to perf 3.03a Exact calculations calculations with numb 3.03b Exact calculations standard form. Manipulating surds Use fractions in exact calculations without a calculator. 13

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. mbers N9 form. nd from 3, # - 3 10 form Add, subtract, multiply and N9 bers in divide numbers in standard form, without a calculator. [see also Laws of indices, Use surds in exact calculations N2, 3.01c] without a calculator. N8 Use multiples of π in exact N8 calculations without a calculator. Simplify expressions with surds, including rationalising denominators. e.g. 12 = 2 3 1= 3 3 3 1= 3 –1 3+1 2 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content qualification will enabl 14 GCSE (9–1) in Mathematics Ref. Approximation and Estimation learners to… Approximation and estimation OCR 4 Rounding Round numbers to the whole number, ten, hun 4.01 etc. or to a given numb of significant figures (sf 4.01a decimal places (dp). 4.01b Estimation Estimate or check, with a calculator, the result o calculation by using sui approximations. e.g. Estimate, to one significant figure, the co 2.8 kg of potatoes at 68 per kg.

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. nearest Round answers to an N15 ndred, appropriate level of accuracy. N14 ber f) or Estimate or check, without a calculator, the result of more hout complex calculations including of a roots. itable Use the ost of symbol ≈ appropriately. 8p e.g. 2.9 . 10 0.051 # 0.62

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content Upper and lower bounds qualification will enabl Ref. learners to… 4.01c OCR 5 Ratio, Proportion and Rates Of Change Find the ratio of quanti 5.01 Calculations with ratio the form a : b and simp 5.01a Equivalent ratios Find the ratio of quanti the form 1 : n. e.g. 50 cm : 1.5 m = 50 =1:3 15

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. Use inequality notation to Calculate the upper and lower N15, write down an error interval bounds of a calculation using N16 for a number or measurement numbers rounded to a known rounded or truncated to a degree of accuracy. given degree of accuracy. e.g. Calculate the area of a e.g. If x = 2.1 rounded to 1 dp, rectangle with length and then 2.05 G x 1 2.15. width given to 2 sf. If x = 2.1 truncated to 1 dp, Understand the difference then 2.1 G x 1 2.2. between bounds of discrete and continuous quantities. Apply and interpret limits of accuracy. e.g. If you have 200 cars to the nearest hundred then the number of cars n satisfies: 150 G n 1 250 and 150 G n G 249. tities in R4, plify. R5 tities in 0 : 150 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content Division in a given ratio qualification will enabl 16 GCSE (9–1) in Mathematics Ref. learners to… 5.01b Split a quantity into two given the ratio of the p e.g. £2.50 in the ratio 2 Express the division of quantity into two parts ratio. Calculate one quantity another, given the ratio two quantities. 5.01c Ratios and fractions Interpret a ratio of two as a fraction of a whole e.g. £9 split in the ratio gives parts 2 # £9 and 3 [see also Fractions of a quantity, 2.01c] 5.01d Solve ratio and proportion problems Solve simple ratio and proportion problems. e.g. Adapt a recipe for 6 people. Understand the relation between ratio and linea functions.

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. o parts R5, parts. Split a quantity into three or R6 2:3 more parts given the ratio of the parts. N11, a R5, s as a R6, R8 from o of the R5, R8 o parts e. o2:1 1 # £9 . 3 6 for 4 nship ar

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content qualification will enabl Ref. Direct and inverse proportion learners to… Direct proportion 5.02 Solve simple problems involving quantities in d 5.02a proportion including al proportions. e.g. Using equality of r if y ? x , then y1 = y2 y1 = y2 . x1 x2 5.02b Inverse proportion Currency conversi problems. [see also Similar shapes Solve simple word prob involving quantities in i proportion or simple al proportions. e.g. speed–time contex (if speed is doubled, tim halved). 17

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. direct Solve more formal problems Formulate equations and solve R7, lgebraic involving quantities in direct problems involving a quantity R10, proportion (i.e. where y ? x ). in direct proportion to a power R13 or root of another quantity. Recognise that if y = kx, where ratios, k is a constant, then y is proportional to x. = x1 or x2 ion Solve more formal problems Formulate equations and R10, solve problems involving a R13 s, 9.04c] involving quantities in inverse quantity in inverse proportion blems 1 to a power or root of another inverse proportion (i.e. where y ? x ). quantity. lgebraic Recognise that if y = k , xts x me is where k is a constant, then y is inversely proportional to x. 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content qualification will enabl 18 GCSE (9–1) in Mathematics Ref. Discrete growth and decay learners to… Growth and decay 5.03 Calculate simple intere including in financial co 5.03a OCR 6 Algebra Understand and use the 6.01 Algebraic expressions concepts and vocabula 6.01a Algebraic terminology and proofs of expressions, equatio formulae, inequalities, 6.01b Collecting like terms in sums and and factors. differences of terms Simplify algebraic expre by collecting like terms e.g. 2a + 3a = 5a

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. est Solve problems step-by- Express exponential growth or R9, ontexts. step involving multipliers decay as a formula. R16 over a given interval, for example, compound interest, e.g. Amount £A subject to depreciation, etc. compound interest of 10% p.a. on £100 as e.g. A car worth £15 000 new A = 100 # 1.1n . depreciating by 30%, 20% and 15% respectively in Solve and interpret answers in three years. growth and decay problems. [see also Percentage change, [see also Exponential 2.03c] functions, 7.01d, Formulate algebraic expressions, 6.02a] e Recognise the difference Use algebra to construct A3, ary between an equation and an proofs and arguments. A6 ons, identity, and show algebraic expressions are equivalent. e.g. prove that the sum terms of three consecutive e.g. show that integers is a multiple of 3. essions s. (x + 1) 2 + 2 = x2 + 2x + 3 Use algebra to construct arguments. A1, A3, A4

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content Simplifying products and quotients qualification will enabl Ref. learners to… 6.01c Simplify algebraic prod and quotients. 6.01d Multiplying out brackets e.g. a # a # a = a3 2a # 3b = 6ab 6.01e Factorising a2 # a3 = a5 3a3 ' a = 3a2 [see also Laws of indice 3.01c] Simplify algebraic expre by multiplying a single over a bracket. e.g. 2 (a + 3b) = 2a + 6 2 (a + 3b) + 3 (a - Take out common facto e.g. 3a - 9b = 3 (a - 3 2x + 3x2 = x (2 + 3 6.01f Completing the square 19

le Foundation tier learners Higher tier learners should DfE ducts should also be able to… additionally be able to… Ref. Simplify algebraic products N3, A1, and quotients using the laws A4 of indices. -5 1 e.g. # - 3 = 2a 2 a2 2a 2a2 b3 ' - 3 b = 1 a5 b2 2 4a es, essions Expand products of two Expand products of more than A1, term binomials. two binomials. A3, A4 6b e.g. e.g. 2b) = 5a (x - 1) (x - 2) = x2 - 3x + 2 A1, (a + 2b) (a - b) = a2 + ab - 2b2 (x + 1) (x - 1) (2x + 1) A3, = 2x3 + x2 - 2x - 1 A4 ors. Factorise quadratic expressions Factorise quadratic expressions A11, 3b) of the form x2 + bx + c . of the form ax2 + bx + c (where A18 3x) e.g. x2 - x - 6 = (x - 3) (x + 2) a ≠ 0 or 1) x2 - 16 = (x - 4) (x + 4) x2 - 3 = _x - 3i_x + 3i e.g. 2x2 + 3x - 2 = (2x - 1) (x + 2) Complete the square on a quadratic expression. e.g. x2 + 4x - 6 = (x + 2) 2 - 10 2x2 + 5x + 1 = 2dx + 5 2 - 17 4 8 n 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content Algebraic fractions qualification will enabl 20 GCSE (9–1) in Mathematics Ref. learners to… 6.01g 6.02 Algebraic formulae 6.02a Formulate algebraic expressions 6.02b Substitute numerical values into Substitute positive num formulae and expressions into simple expressions formulae to find the va the subject. e.g. Given that v = u + v when t = 1, a = 2 u=7

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. Simplify and manipulate A1, A4 algebraic fractions. n 1 + e.g. Write n - 1 + n 1 as a single fraction. Simplify n2 + 2n . n2 + n - 2 Formulate simple formulae [See, for example, Direct A3, and expressions from real- proportion, 5.02a, Inverse A5, world contexts. proportion, 5.02b, Growth and A21, decay, 5.03a] R10 e.g. Cost of car hire at £50 per day plus 10p per mile. A2, A5 The perimeter of a rectangle when the length is 2 cm more than the width. mbers Substitute positive or negative s and alue of numbers into more complex at, find formulae, including powers, 2 and roots and algebraic fractions. e.g. v = u2 + 2as with u = 2.1, s = 0.18, a = -9.8 .

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content Change the subject of a formula qualification will enabl Ref. learners to… 6.02c Rearrange formulae to the subject, where the appears once only. e.g. Make d the subjec formula c = πd . Make x the subjec formula y = 3x - 6.02d Recall and use standard formulae Recall and use: Circumference of a circ 2πr = πd Area of a circle πr2 21

le Foundation tier learners Higher tier learners should DfE change should also be able to… additionally be able to… Ref. subject A4, ct of the Rearrange formulae to change [Examples may include A5 ct of the the subject, including cases manipulation of algebraic 2. where the subject appears fractions, 6.01g] A2, twice, or where a power A3, cle or reciprocal of the subject A5 appears. e.g. Make t the subject of the formulae (i) s = 1 at2 2 (ii) v = x t (iii) 2ty = t + 1 Recall and use: Recall and use: Pythagoras’ theorem The quadratic formula a2 + b2 = c2 x = -b ! b2 - 4ac 2a Trigonometry formulae Sine rule o a o sin i = h , cos i = h , tan i = a a=b= c sin A sin B sin C Cosine rule a2 = b2 + c2 - 2bc cos A Area of a triangle 1 ab sin C 2 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content Use kinematics formulae qualification will enabl 22 GCSE (9–1) in Mathematics Ref. learners to… 6.02e Use: v = u + at 1 s = ut + 2 at2 v2 = u2 + 2as where a is constant acceleration, u is initial velocity, v is final veloci s is displacement from when t = 0 and t is time 6.03 Algebraic equations Solve linear equations i 6.03a Linear equations in one unknown unknown algebraically. e.g. Solve 3x - 1 = 5 6.03b Quadratic equations

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. A2, A3, A5 l ity, position e taken. in one Set up and solve linear [Examples may include A3, . equations in mathematical and manipulation of algebraic A17, non-mathematical contexts, fractions, 6.01g] A21 including those with the unknown on both sides of the Know the quadratic formula. A18 equation. Rearrange and solve quadratic e.g. Solve 5 (x - 1) = 4 - x equations by factorising, Interpret solutions in context. completing the square or using Solve quadratic equations with coefficient of x2 equal to 1 by the quadratic formula. factorising. e.g. Solve x2 - 5x + 6 = 0 . e.g. 2x2 = 3x + 5 Find x for an x cm by 2 - 2 = 1 (x + 3) cm rectangle of x x+1 area 40cm2 .

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content Simultaneous equations qualification will enabl Ref. learners to… 6.03c 6.03d Approximate solutions using a graph Use a graph to find the 6.03e Approximate solutions by iteration approximate solution o linear equation. 23

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. e A19, of a Set up and solve two linear Set up and solve two A21 simultaneous equations in two simultaneous equations (one variables algebraically. linear and one quadratic) in A11, two variables algebraically. A17, e.g. Solve simultaneously A18, 2x + 3y = 18 and e.g. Solve simultaneously A19 y = 3x - 5 x2 + y2 = 50 and 2y = x + 5 A20, Use graphs to find Know that the coordinates R16 approximate roots of of the points of intersection quadratic equations and the of a curve and a straight approximate solution of two line are the solutions to the linear simultaneous equations. simultaneous equations for the line and curve. Find approximate solutions to equations using systematic sign-change methods (for example, decimal search or interval bisection) when there is no simple analytical method of solving them. Specific methods will not be requested in the assessment. 2

© OCR 2016 GCSE (9–1) Subject content Initial learning for this content qualification will enabl 24 GCSE (9–1) in Mathematics Ref. Algebraic inequalities learners to… Inequalities in one variable 6.04 Understand and use the symbols 1, G, 2 and H 6.04a 6.04b Inequalities in two variables

2 le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. e Solve linear inequalities in one Solve quadratic inequalities in N1, H variable, expressing solutions one variable. A3, on a number line using the e.g. x2 - 2x 1 3 A22 conventional notation. e.g 2x + 1 H 7 Express solutions in set notation. 34 56 e.g. #x | x H 3- 1 1 3x - 5 G 10 #x | 2 1 x G 5- 2345 [See also Polynomial and exponential functions, 7.01c] Solve (several) linear A22 inequalities in two variables, representing the solution set on a graph. [See also Straight line graphs, 7.02a]

© OCR 2016 GCSE (9–1) Subject content Initial learning for this GCSE (9–1) in Mathematics content qualification will enabl Ref. Language of functions learners to… Functions 6.05 Interpret, where appro simple expressions as 6.05a functions with inputs a outputs. e.g. y = 2x + 3 as x ×2 +3 6.06 Sequences Generate a sequence b 6.06a Generate terms of a sequence spotting a pattern or us a term-to-term rule giv algebraically or in word e.g. Continue the sequ 1, 4, 7, 10, ... 1, 4, 9, 16, ... Find a position-to-term simple arithmetic sequ algebraically or in word e.g. 2, 4, 6, … 2n 3, 4, 5, … n + 2 25

le Foundation tier learners Higher tier learners should DfE should also be able to… additionally be able to… Ref. opriate, Interpret the reverse process A7 and as the ‘inverse function’. y Interpret the succession of two functions as a ‘composite function’. [Knowledge of function notation will not be required] [see also Translations and reflections, 7.03a] by Generate a sequence from a Use subscript notation for A23, sing formula for the nth term. position-to-term and term-to- A25 ven e.g. nth term = n2 + 2n gives term rules. ds. uences 3, 8, 15, … e.g. xn = n + 2 xn + 1 = 2xn - 3 m rule for Find a formula for the nth term Find a formula for the nth term uences, of an arithmetic sequence. of a quadratic sequence. ds. e.g. 40, 37, 34, 31, … 43 – 3n e.g. 0, 3, 10, 21, … un = 2n2 - 3n + 1 2