[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207698-en":3,"doc-seo-207698-105":30,"detail-sidebar-cat-0-en-105":82},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207698,962088006270,"eBook King","https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",4,"Exam","Aiming for Grade 9 - Revision Booklet - GCSE Edexcel Maths","GCSE Edexcel Maths revision booklet focused on key Grade 9 topics, with structured questions for practice and confidence-building. It covers surds and simplifying techniques, rationalising denominators, expanding and simplifying expressions, and solving algebraic problems. It also includes algebraic proofs, covering parity, divisibility, factorisation and expanding brackets. Further sections address graph transformations, circle equations, sequences, completing the square, functions, simultaneous equations and quadratic inequalities. Geometry and data probability skills support exam-style readiness.","GCSE EDEXCEL MATHS  \nAiming for Grade 9  \nREVISION BOOKLET  \nName:    \nContents  \nPage:  \nNumber:  \nSurds 3  \nAlgebraic proofs 7  \nAlgebra:  \nTransformations of graphs 13  \nEquations of circles 17  \nQuadratic and other sequences 19  \nCompleting the square 22  \nInverse and composite functions 25  \nExpanding more than two binomials 28  \nNonlinear simultaneous equations 30  \nSolving quadratic inequalities 34  \nShape, Space and Measure:  \nCircle theorems 36  \nVectors 40  \nSine and cosine rules 48  \nArea under graphs 52  \nData Handling:  \nHistograms 57  \nMoving averages 65  \nProbability:  \nSet theory 68  \nRatio and Proportion:  \nProportion 71  \nPercentages – reverse 75  \nSurds  \nThings to remember:  \n􀁸 √ means square root;  \n􀁸 To simplify surds, find all its factors;  \n􀁸 To rationalise the denominator, find an equivalent fraction where the denominator is rational.  \nQuestions:  \n1. Work out  \n(5 + √3)(5− √3)  \n√22  \nGive your answer in its simplest form.  \n(Total 3 marks)  \n1  \n2. (a) Rationalise the denominator of ~~  ~~  \n√3  \n    (1)  \n(b) Expand (2 + √3)(1 + √3)    \nGive your answer in the form 􀜽 + 􀜾√3 where a and b are integers.  \n……………………………………  \n(2)  \n(Total 3 marks)  \n1  \n3. (a) Rationalise the denominator of ~~  ~~√7  \n(2)  \n(b) (i) Expand and simplify (√3 + √15)2    \nGive your answer in the form 􀜽 + 􀜾√3 where a and b are integers.  \n(ii) All measurements on the triangle are in centimetres.  \nABC is a right-angled triangle.  \nk is a positive integer.  \nA 􀂗􀀖 􀀎 􀂗􀀔􀀘 C  \nB  \nFind the value of k.  \nDiagram NOT accurately drawn  \nk =    \n(5)  \n(Total 7 marks)  \n4. Expand and simplify (√3 − √2)(√3 − √2)  \n(Total 2 marks)  \n5. (a) Write down the value of 491⁄2  \n……………………………………  \n    ( 1)  \n(b) Write √45 in the form 􀝇√5, where k is an integer.  \n……………………………………  \n(1)  \n(Total 2 marks)  \n√18 + 10    \n6. Write ~~   ~~ in the form 􀜽 + 􀜾√2 where a and b are integers.  \n√2  \na =    \nb =    \n(Total 2 marks)  \n7. Expand and simplify (2 + √3)(7 − √3)  \nGive your answer in the form 􀜽 + 􀜾√3 where a and b are integers.  \n(Total 3 marks)  \n(4 + √2) (4 − √2)  \n8. Rationalise the denominator of ~~   ~~  \n√7  \nGive your answer in its simplest form.  \n……………………………………  \n(Total for question = 3 marks)  \n(4 − √3)(4 + √3)    \n9. Show that ~~   ~~ simplifies to √13  \n√13  \n(Total for question = 2 marks)  \nAlgebraic Proofs  \nThings to remember:  \n􀁸 Start by expanding the brackets, then factorise.  \n􀁸 Remember the following:  \n1. 2n 􀃆 even number  \n2. 2n + 1 􀃆 odd number  \n3. a(bn + c) 􀃆 multiple of a  \n4. Consecutive numbers are numbers that appear one after the other.  \nQuestions:  \n1. (a) Expand and simplify x(x + 1)(x − 1)  \n(2)  \nIn a list of three consecutive positive integers at least one of the numbers is even and oneof the numbers is a multiple of 3  \nn is a positive integer greater than 1  \n(b) Prove that n³ − n is a multiple of 6 for all possible values of n.  \n(2)  \n261 − 1 is a prime number.  \n(c) Explain why 261 + 1 is a multiple of 3  \n(2)  \n(Total for question = 6 marks)  \n2. Prove that  \n(2n + 3)² –(2n – 3)² is a multiple of 8  \nfor all positive integer values of n.  \n(Total for Question is 3 marks)  \n3. (a) Expand and simplify (y − 2)(y − 5)  \n(2)  \n*(b) Prove algebraically that  \n(2n + 1)² − (2n + 1) is an even number  \nfor all positive integer values of n.  \n(3)  \n(Total for Question is 5 marks)  \n4. * Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.  \n(Total for Question is 4 marks)  \n5. (a) Factorise x² + 7x  \n(1)  \n(b) Factorise y² – 10y + 16  \n……………………………………  \n(2)  \n*(c) (i) Factorise 2t² + 5t + 2  \n……………………………………  \n(ii) t is a positive whole number.  \nThe expression 2t² + 5t + 2 can never have a value that is a prime number.  \nExplain why.  \n............................................................................................................................  \n..................................................................................","cbCaid0Hn1eOj8N7","https://ap.wps.com/l/cbCaid0Hn1eOj8N7","pdf",1969851,1,78,"English","en",105,"# Surds\n## Things to remember\n## Questions\n# Algebraic proofs\n## Things to remember\n## Questions\n# Algebra\n## Transformations of graphs\n## Equations of circles\n## Quadratic and other sequences\n## Completing the square\n## Inverse and composite functions\n## Expanding more than two binomials\n## Nonlinear simultaneous equations\n## Solving quadratic inequalities\n# Shape, Space and Measure\n## Circle theorems\n## Vectors\n## Sine and cosine rules\n## Area under graphs\n# Data Handling\n## Histograms\n## Moving averages\n# Probability\n## Set theory\n# Ratio and Proportion\n## Proportion\n## Percentages - 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