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A guide to Edexcel GCSE Mathematics (9-1)

GCSE Mathematics is getting more demanding GCSE Maths is going to change and get more demanding for everyone: • The volume of subject content has increased.

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Text of A guide to Edexcel GCSE Mathematics (9-1)

Edexcel GCSE Mathematics (9-1)A guide to1What s in this guide?What s changing in GCSE Mathematics? 4-7 Understanding the changes to content: Foundation 8-9Understanding the changes to content: Higher 10-11Changes to assessment 12-15Sample Assessment Material 16-17What you can expect from us 18-233Hello and welcome to our guide to Edexcel GCSE Mathematics (9-1).GCSE Mathematics is getting more demandingGCSE Maths is going to change and get more demanding for everyone: The volume of subject content has increased. You may need more time to teach it. The demand of that content is increasing too, with harder topics being introduced. This is true for both your Foundation Tier students and Higher Tier students. The total time for the examinations is increasing, from 3 hours to 4 hours. All exams will be sat at the end of the course. There are fewer marks at the lower grades and more marks at the higher grades at both Foundation Tier and Higher Tier. A new grading structure is being introduced, from grade 9 to 1, to replace the familiar A* to G grading scale. In the assessments there s a greater emphasis on problem solving and mathematical reasoning, with more marks now being allocated to these higher-order skills. Students will be required to memorise formulae fewer formulae will be provided in these changes are designed to help students emerge from GCSE Maths with a level of confidence and fluency that will provide a genuine foundation for the rest of their learning and working all our support on gcsemaths2015guide1Working with you to meet the demands of GCSE MathematicsGCSE Maths may be changing, but the help and expertise that we offer isn t. To support you in making the most of these changes, we ll continue to provide you with: Carefully differentiated examination papers, written in a clear and unambiguous way, with opportunities for students to build their confidence as they progress through the paper. Clear mark schemes that provide opportunities for students to demonstrate their mathematical ability and that support consistent marking so all students achieve the grades they deserve. Help with understanding the increase in demand including exemplar student work, examiner commentaries and free training for marking mocks. Teaching and learning support to meet the demands of the new curriculum including immediate support for your Year 9 students to bridge the gap to the new GCSE Maths and differentiated resources that focus on building fluency, reasoning and problem-solving skills for students across all grades. Support for tracking your students progress including three sets of practice papers and a secure mock papers that your students won t have seen, from 2016 - 2019. Expert and local support from Graham, the Emporium and our Edexcel Maths team; we re here to listen and help: at the end of a phone, on email, or in person at local network and training course, the key to your students success isn t to be found in a qualification and the help we provide. Instead it s in what you do every day to develop their understanding, nurture their confidence and expose them to the range of mathematical experiences that will shape their success. And we ll do everything we can to support you in doing that, every step of the the changes to con tent: FoundationChanges to content at Foundation TierThe biggest change to content is at Foundation tier. There are new topics added to the Foundation tier for 2015, which in 2010 were assessed at Higher tier only. The list opposite is not exhaustive but includes all the major changes. Full, annotated tables for this and the following lists can be found on the GCSE Maths support both tiers, there will be new knowledge, skills and understanding that your students will be assessed on in the new GCSE Mathematics (9-1).98Topics new to Foundation tier (previously Higher tier only in 2010) Index laws: zero and negative powers (numeric and algebraic) Standard form Compound interest and reverse percentages Direct and indirect proportion (numeric and algebraic) Expand the product of two linear expressions Factorise quadratic expressions in the form x2 + bx + c Solve linear/linear simultaneous equations Solve quadratic equations by factorisation Plot cubic and reciprocal graphs, recognise quadratic and cubic graphs Trigonometric ratios in 2D right-angled triangles Fractional scale enlargements in transformations Lengths of arcs and areas of sectors of circles Mensuration problems Vectors (except geometric problems/proofs) Density Tree diagramsTopics new to both tiers Use inequality notation to specify simple error intervals Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically Fibonacci type sequences, quadratic sequences, geometric progressions Relate ratios to linear functions Interpret the gradient of a straight line graph as a rate of change Know the exact values of sin and cos for = 0 , 30 , 45 , 60 and 90 ; know the exact value of tan for = 0 , 30 , 45 and 60 FoundationFoundation tier papers will assess the different content domains in these proportions:(It s worth noting that there s a 3% tolerance for each domain area.)Ratio, Proportion and Rates of Change25%Number 25%Algebra 20%Statistics &Probability15%Geometry& Measures15%Half the marks at foundation tier will be testing Number and Ratio, proportion and changeThis is a now a standalone area of contentThese will be tested less than in 2010 Find more details, visit the changes to content: HigherTopics new to Higher tier Expand the products of more than two binomials Interpret the reverse process as the inverse function ; interpret the succession of two functions as a composite function (using formal function notation) Deduce turning points by completing the square Calculate or estimate gradients of graphs and areas under graphs, and interpret results in real-life cases (not including calculus) Simple geometric progressions including surds, and other sequences Deduce expressions to calculate the nth term of quadratic sequences Calculate and interpret conditional probabilities through Venn diagramsOmitted topics Trial and improvement Tessellations Isometric grids Imperial units of measure Questionnaires 3D coordinates Rotation and enlargement of functionsIn the specification, you will see the content has been divided into three levels: Standard: this content will be assessed at both Foundation and Higher tier; all students should be confident and competent with it. Underlined: this content will be assessed at both Foundation and Higher tier; higher-attaining students should be confident and competent with it. Bold: this content will be assessed at Higher tier only; the highest-attaining students should be confident and competent with tier papers will assess the different content domains in these proportions:Ratio, Proportion and Rates of Change20%Number 15%Statistics &Probability15%Geometry& Measures20%This is a now a standalone area of contentThese will be tested less than in 2010 More content has been added to Higher tier in order to stretch and challenge the most able students and better prepare them for studying A level Mathematics, so we ll see the introduction of new knowledge, skills and understanding that will be assessed at Higher tier content previously assessed in the current GCSE Mathematics has been omitted from the new GCSE Mathematics (9-1).Algebra 30%(It s worth noting that there s a 3% tolerance for each domain area.)This will be tested more than in 2010 Find more details, visit Edexcel GCSE in Mathematics (9 1) will be assessed through three equally-weighted written examination papers at either Foundation tier or Higher tier. Paper 1 is a non-calculator paper. Availability: May/June and November (for post-16 students only). First assessment: May/June 2017. Tiers of entry: Foundation and Higher (a student must take all 3 papers at the same tier). Grading: 9 1 overall, with questions targeted at grades 1 5 at Foundation tier and at grades 4 9 at Higher tier. See page 14 for more on the new grading, including how it relates to the current A* G grading. Types of questions: Each paper will have a range of question types, utilising both structured and unstructured questions. Take a look at pages 16 and 17 for examples. Questions in context: Some questions on the papers will be set in context (both mathematical and non-mathematical). Common questions between tiers: Grades 4 and 5 are the overlap grades between Foundation and Higher tiers, so common questions targeted at these grades will appear in the respective papers for each objectivesThe diagram below gives an overview of the three assessment objectives. The strands and elements are detailed in the specification. Every strand and element must be assessed in every examination series. We ve shown the marks allocated to these strands and elements clearly in our mark schemes. You can learn more at 1Non-calculator1 hour and 30 weightingPaper 2Calculator80 marks1 hour and 30 weightingPaper 3Calculator80 marks1 hour and 30 minutes weighting80 marksPaper 1Non-calculator1 hour and 30 weightingPaper 2Calculator80 marks1 hour and 30 weightingPaper 3Calculator80 marks1 hour and 30 minutes weighting80 marksFoundation(grades 1-5)Higher(grades 4-9)Changes to assessment: summaryAO1 is about using and applying standard techniques, similar to the current AO150% foundation40% higherAO2 has a different focus. It s about reasoning, interpreting and communicating mathematically25% foundation30% higherAO3 is about solving problems with a much greater focus on solving non-routine problems in mathematical and non- mathematical foundation30% higherIn 2015 there is less AO1 at Higher and roughly the same at Foundation compared to 2010. Quality of written communication (QWC) is also now included as part of AO2. In both tiers, there s now more focus on AO3 than in 2010. 2017 school performance measures The only GCSE Maths qualification that will count in the 2017 secondary school performance tables (due to be published in January 2018) will be the new GCSE in any earlier (pre-2017) results from the current GCSE in Mathematics nor any results from the Edexcel Level 1/Level 2 Certificate in Mathematics will be included in the 2017 secondary school performance will continue to be an overlapping tiers model at grades 4 and 5. Students who fall slightly below the grade 4 boundary on Higher tier may be awarded a grade have defined anchor points that provide broad proportions and alignments between the old A* G and the new 9 1 GCSE grading systems, which we ve shown papers now start at, and reach, a higher marks on current Foundation papers are allocated like this:Formulae sheetsStudents will need to memorise many of the formulae currently given in the formulae sheets at the front of the exam papers. These are: Volume of a prism Area of a trapezium The Quadratic equation (Higher tier only) The sine rule, cosine rule, and area of a triangle (Higher tier only).Here s the formulae sheet that will be provided:In the new Foundation papers, marks will be allocated like this:50% Targeted at F/G25% Targeted at grade E25% Targeted at grades D/C50%50%12lower 3upper 345Approximately equivalent to:G/FED-D+CC/B50%50%456789Approximately equivalent to:CC/BBAA/A*A/A*HigherHigher tier papers now start at a higher level than in the current GCSE, which starts at grade new Higher tier papers will cover 6 grades instead of 5, allowing for more differentiation at the top end of the grades. Previously, 25% of questions were targeted at A/A*, but now 50% of questions in each paper are targeted at the equivalent grades, 7 the new Higher papers, they will look like this:Pearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 201462*S47348A0224*Formulae SheetPerimeter, area, surface area and volume formulaeWhere r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone:Curved surface area of a cone = rlSurface area of a sphere = 4 r2Volume of a sphere = 43 r3Volume of a cone = 13 r2hKinematics formulaeWhere a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t= 0 and t is time:v = u + ats = ut + 12at2v2 = u2 + 2asChanges to assessment: gradingBottom of 1 aligned with bottom of GBottom two-thirds of C marksBottom two-thirds of C marksTop third of C marks / bottom third of B marksTop third of C marks / bottom third of B marksTop two-thirds of B marksTop 20% of A/A* marksPearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 20145014*S47349A01420*12 Ashten chooses three different whole numbers between 1 and 50 The first number is a prime number. The second number is 4 times the first number. The third number is 6 less than the second number. The sum of the three numbers is greater than 57 Find the three numbers.(Total for Question 12 is 3 marks)13 Given that 3(x c) = 2x + 5 where c is an integer, show that x cannot be a multiple of six.(Total for Question 13 is 3 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 201417115*S47353A01524*Turn over 12 A rectangular sheet of paper can be cut into two identical rectangular pieces in two different ways. When the original sheet of paper is cut one way, the perimeter of each of the two pieces is 50 cm. When the original sheet of paper is cut the other way, the perimeter of each of the two pieces is 64 cm. What is the perimeter of the original sheet of paper? (Total for Question 12 is 5 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 2014128*S47348A0824*7 The diagram shows a right-angled triangular prism A and a cuboid B. A B Show that the volume of B is 6 times the volume of A.(Total for Question 7 is 3 marks)4 cm10 cm5 cm6 cm5 cm20 cm671716At-a-glance: Sample Assessment MaterialFoundation and Higher tierHigher tier onlyFoundation tier onlyThe same clear layout of questions you re familiar withThis question shows problem solving in the new AO3Mark schemeMark schemeMark schemePearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 201460 Question Working Answer Mark type AO Notes 12 7 + 28 + 22 = 57 11, 44 and 38 P P A P1 for a correct process to develop algebraic expressions for each number and set up an inequality, x + 4x + 4x 6 > 57 or for a correct trial with a prime number P1 for a correct process to solve the inequality, x > (57 + 6) 9 (= 7) or for a correct trial with the prime number as 7 resulting in a sum of 57 A1 cao 13 3x 3c = 2x + 5 x = 3c + 5 Shown P P C P1 for a process to start a chain of reasoning P1 for a process to isolate terms in x C1 convincing explanation from x = 3c + 5 14 (a) 720 P P A P1 attempt to find the maximum biscuits for one of the ingredients, 5000 150 (= ) or 2500 75 (= ) or 3000 100 (= 30) or 320 10 (= 32) P1 for identifying butter as the limiting factor or 30 24 (= 720) seen A1 for 720 cao Pearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 2014186 Question Working Answer Mark AO Notes 10 (d) Complete explanation P C P1 for an argument in words or using symbols, in any two consecutive numbers one is even and one is odd and the square of an even number is even and the square of an odd number is odd The sum of an odd and an even number is odd C1 conclusion with a correct complete argument 11 (a) =P =P = 1005 P M A P1 for process to translate problem into algebraic form, =P M1 =P A1 1005 11 (b) Correct explanation C C1 for an explanation eg the original population size will be greater 12 Let h and w be the dimensions of the original rectangle h + 2w = 50 2h + w = 64 w = 12, h = 26 Perimeter = 2 12 + 2 26 76 cm P P P P A P1 for correct process to set up equations, +++wwhh and6422=+++hhww P1 for correct process to find value of one variable P1 for correct process to find value of other variable P1 for correct process to find numerical value of perimeter, 2 ('12' + '26') A1 cao Pearson Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 2014186 Question Working Answer Mark AO Notes 10 (d) Complete explanation P C P1 for an argument in words or using symbols, in any two consecutive numbers one is even and one is odd and the square of an even number is even and the square of an odd number is odd The sum of an odd and an even number is odd C1 conclusion with a correct complete argument 11 (a) =P =P = 1005 P M A P1 for process to translate problem into algebraic form, =P M1 =P A1 1005 11 (b) Correct explanation C C1 for an explanation eg the original population size will be greater 12 Let h and w be the dimensions of the original rectangle h + 2w = 50 2h + w = 64 w = 12, h = 26 Perimeter = 2 12 + 2 26 76 cm P P P P A P1 for correct process to set up equations, +++wwhh and6422=+++hhww P1 for correct process to find value of one variable P1 for correct process to find value of other variable P1 for correct process to find numerical value of perimeter, 2 ('12' + '26') A1 cao The new P mark is a mark that can be awarded to a proof, a process, a numerical solution to a problem, or for evaluation of Edexcel Level 1/Level 2 GCSE (9 1) in Mathematics Sample Assessment Materials Issue 1 September 2014 Pearson Education Limited 201431 Question Working Answer Mark AO Notes 7 Show M P C M1 for Use of correct formula for volume for triangular prism or cuboid, 14 10 5( 100)2 = or 6 20 5(= 600) P1 for beginning to construct chains of reasoning, 14 10 5( 100)2 = and 6 20 5 (= 600) C1 for completion of chains of reasoning, 600 100 = 6 8 1200 300 = 4 1200 400 = 3 1000 = 400 + 300 + 300 Correct diagram with correct layout M P C M1 for changing to consistent units, 1000 10 or 40 10 P1 for interpreting information and a process to fit tiles in floor area, may be seen on a sketch or may see a calculation C1 for diagram to communicate a correct layout with lengths clearly identified 9 Square 9 9 =81 Bottom triangle 245295= Top triangle 254296= Shaded area 81 27 cm2 P P P P1 for a process to establish the missing lengths on the perimeter of the shape P1 for a process to begin the problem by finding the area of one relevant shape P1 for complete process to find the shaded area, 9 9 (' ' + '27') Learn more and download our sample assessment material at gcsemaths2015guideStraightforward mark schemes to show what s required in student answers1918You know us for the support we provide to thousands of maths teachers across the UK and in international centres. We re confident the developments we ve made to our new GCSE Mathematics (9-1) will help you encourage your students to progress to capable and confident mathematicians, ready for whatever route they decide to you can expect from usYou can find all this support on our website. Download our accredited specifications and sample assessment materials. the changes and their impactWe re ready for the biggest change since GCSE Maths began, and you can be too. Content mappings from the current GCSE to the new GCSE, which clearly set out what new content has come in at both tiers. Examples of the sample assessment materials to help you understand how the assessment objectives and content relate to the questions. Examples of student work and examiner commentaries taken from the trials we ve run with a head start with your Year 9sWe ve produced a bank of useful documents to help you with starting to teach your Year 9s the new Edexcel GCSE Mathematics if you want to get started handy 3-year scheme of work will help you plan, as will our 1-year KS3-GCSE transition scheme of work for Year 9. You ll also find content mapping documents, so you can see how the new GCSE compares to the current qualification. We ll also provide: GCSE Baseline test These will help you understand the progress your students have made at Key Stage 3, and assess your students learning needs before you start teaching the GCSE. End of term tests These tests are aligned to both our schemes of work. They are designed to help you understand the progress your students have made at the end of term and can be used in conjunction with the GCSE baseline you can expect from usDelivering GCSE Maths from September 2015Designing your curriculum Schemes of work Produced by a group of innovative and forward-thinking teachers, and drawing on recent academic research, you can download a five-year scheme of work born out of a five-year curriculum, which combines Key Stages 3 and 4. You ll be able to extract 1, 2 and 3 year schemes of work from this, too. Planning: We ll provide Teaching time guidance to help you plan your timetableallocation for GCSE Maths. Our Getting Started Guide will also provide guidance about planning your teaching and learning for our new & Learning Formulae posters will help your students learn the formulae they ll have to remember. You re the experts - which is why we ll also have classroom resources by teachers, for teachers (take a look at our videos online for a quick taster!)Designing your curriculumTeaching & LearningTracking learner progress End of term assessments to help you to track your students progress, set targets, and to understand which tier of entry may be most appropriate. We ll provide a varied bank of new style questions and assessments for Higher and Foundation tiers to help build confidence and motivation. New and unseen secure mock papers, complete with mark schemes, will be available to use with your students towards the end of the course. ResultsPlus provides the most detailed analysis available of your students exam performance. Widely used by teachers across the country, this free online service helps you identify topics and skills where students could benefit from further learning, helping them gain a deeper understanding of maths. examWizard is a free exam preparation tool containing a bank of past Edexcel mathematics exam questions, mark schemes and examiners student progress232223The personal, local and collaborative support you re used toGraham and The Maths EmporiumRun by our in-house mathematics expert Graham Cumming, our email service tells you what you need to know, when you need to know it. This unique service will keep you updated with the latest information about Edexcel GCSE Mathematics (9-1) direct to your inbox! What s more, you can access and download documents (such as specifications, schemes of work and a vast archive of past papers) to support you in teaching our mathematics qualifications all for eventsOnline or face-to-face, these free launch events will help you learn about the new specification, and the support we re offering to help you make the transition. They re great opportunities to speak to one of our mathematics experts, NetworksOur established networks provide you with local opportunities to share ideas and receive support that has a more personal touch - from us, and from each Ready to Teach eventsEvents, delivered by subject experts and practicing teachers, to make sure you have all the information and ideas you need to start planning an effective course for your you can expect from usBrand new published resources from PearsonDesigning your curriculumOur brand-new paid-for resources are written specifically to tackle the demands of the new GCSE in will help you: teach the new Edexcel GCSE in Maths specification with confidence support your foundation tier and challenge your higher tier students nurture confidence in maths embed fluency, reasoning and problem differentiated resources give you the flexibility to meet the needs of your Foundation and Higher fluency problem solving reasoningAll information correct at time of going to print, will be subject to changeThese resources are not yet endorsed and will be subject to resources for Edexcel GCSE Maths (9-1) We re committed to helping teachers deliver our new Edexcel GCSE Maths (9-1) and students to achieve their full potential. To do this, we aim for our qualifications to be supported by a wide range of high-quality resources, produced by a range of publishers, including ourselves. It is not necessary to purchase endorsed resources, including those published by Pearson, to deliver our are working with a range of publishers who are looking towards getting their resources endorsed. Cambridge University Press: GCSE Mathematics for Edexcel Collins Education: Edexcel GCSE Maths Hodder Education: Mastering Mathematics for Edexcel GCSE Oxford University Press: Edexcel GCSE Maths Pearson: Edexcel GCSE MathematicsYou can find out more and order your free evaluation pack gcsemaths2015guideEdexcel GCSEMathematicsHigherStudent BookConfidence Fluency Problem-solving Progression11 - 19 PROGRESSIONALWAYS LEARNINGEdexcel GCSEMathematicsFoundationStudent Book11 - 19 PROGRESSIONConfidence Fluency Problem-solving ProgressionALWAYS LEARNINGGet in touchThe new GCSE Maths: you don t have to face it on your own. 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