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It structures learning into numbered sections covering arithmetic and factor work, multiples, primes, LCM and HCF, rounding and bounds, fractions and mixed numbers, ordering, operations, and links to decimals. The book then develops ratio, proportion, dividing in ratios, percentages and percentage change, expressions including simplifying, expanding, factorising and algebraic fractions, and advances through powers, roots, formulas, equations, and further algebraic 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exponential, circle and trigonometric), interpreting and drawing real-life graphs, functions, differentiation, and matrices and sets.","https://schema.org",{"og:url":83,"og:type":119,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":121,"canonical":83},"index,follow",{"doc_id":123,"site_id":62},207047,1788597679,{"code":4,"msg":5,"data":126},{"doc_id":123,"user_id":127,"nickname":87,"user_avatar":128,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":129,"file_id":130,"file_url":131,"file_type":132,"file_size":133,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":134,"language":135,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":67,"update_tm":124,"read_time":139},18829141979164,"https://eur-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","GCSE  \nMATHEMATICSTEXTBOOK  \nFOR THE NEW 9-1 COURSE  \nHIGHER TIER  \nNumber,Ratio and Algebra  \nSection 1—Arithmetic,Multiples  \nand Factors  \n1.1 Calculations …………………………………………………………………………2  \n1.2 Multiples and Factors ………………………………………………5  \n1.3 Prime Numbers and Prime Factors……………………7  \n1.4 LCM and HCF ………………………………………………………9  \nSection 2—Approximations  \n2.1 Rounding…………………………………………………………………12  \n2.2 Upper and Lower Bounds……………………………………14  \nSection 3—Fractions  \n3.1 Equivalent Fraction. ……………………………………………17  \n3.2 Mixed Numbers………………………………………………………18  \n3.3 Ordering Fraction. ………………………………………………19  \n3.4 Adding and Subtracting Fractions …………………21  \n3.5 Multiplying and Dividing Fraction. ……………22  \n3.6 Fractions and Decimals…………………………………………24  \n3.7 Fractions Problems……………………………………………………27  \nSection 4—Ratio and Proportion  \n4.1 Ratios…………………………………………………………………………………29  \n4.2 Dividing in a Given Rati……………………………………32  \n4.3 More Ratio Problems…………………………………………………34  \n4.4 Proportion………………………………………………………………35  \n4.5 Ratio and Proportion Problems. ……………………38  \nSection 5—Percentages  \n5.1 Percentages……………………………………………………………40  \n5.2 Percentages,Fractions and Decimals …………42  \n5.3 Percentage Increase and Decrease …………………4  \n5.4 Compound Percentage Change………………………46  \n5.5 Percentages Problem. …………………………………………49  \nSection 6—Expressions  \n6.1 Simplifying Expressions ………………………………51  \n6.2 Expanding Brackets ……………………………………………52  \n6.3 Factorising—Common Factors…………………56  \n6.4 Factorising—Quadratics………………………………57  \n6.5 Algebraic Fractions…………………………………………59  \n6.6 Expressions Problem. …………………………………………63  \nSection 7—Powers and Roots  \n7.1 Squares, Cubes and Roots ………………………………65  \n7.2 Indices and Index Laws ………………………………………66  \n7.3 Standard Form……………………………………………………………71  \n7.4 Surds…………………………………………………………………………………73  \nSection 8-Formulas  \n8.1 Writing Formulas …………………………………………………77  \n8.2 Substituting into a Formula………………………78  \n8.3 Rearranging Formulas ………………………………………80  \n8.4 Formulas Problems……………………………………………81  \nSection 9—Equations  \n9.1 Solving Equation………………………………………………83  \n9.2 Writing Equations………………………………………………85  \n9.3 Iterative Methods………………………………………………………87  \n9.4 Equations Problem. ………………………………………………89  \n9.5 Identities……………………………………………………………………………91  \nSection 10— Direct and Inverse  \nProportion  \n10.1 Direct Proportion………………………………………………92  \n10.2 Inverse Proportion………………………………………………94  \n10.3 Direct and Inverse Proportion  \nProblems…………………………………………………………………………96  \nSection 11—Quadratic Equations  \n11.1 Solving Quadratics by Factorising………………98  \n11.2 Completing the Square…………………………………100  \n11.3 The Quadratic Formula…………………………………102  \n11.4 Quadratic Equations Problems ……………………104  \nSection 12—Simultaneous Equations  \n12.1 Simultaneous Equation…………………………………106  \n12.2 More Simultaneous Equations ……………………108  \nSection 13—Inequalities  \n13.1 Inequalities ……………………………………………………10  \n13.2 Quadratic Inequalities ……………………………………11  \n13.3 Graphing Inequalities …………………………………13  \n13.4 Linear Programming……………………………………15  \nSection 14—Sequences  \n14.1 Term to Term Rules……………………………………………18  \n14.2 Using the nth Term…………………………………………121  \n14.3 Finding the nth Term………………………………………123  \nSection 15—Straight-Line Graphs  \n15.1 Straight-Line Graph……………………………………127  \n15.2 Gradients………………………………………………………………………129  \n15.3 Equations of Straight-Line Graphs……………131  \n15.4 Parallel and Perpendicular Lines………………133  \n15.5 Line Segments ………………………………………………………135  \n15.6 Straight-Line Graphs Problem……………………138  \nSection 16—Other Types of Graph  \n16.1 Quadratic Graphs ……………………………………………140  \n16.2 Cubic Graphs ……………………………………………………142  \n16.3 Reciprocal Graphs …………………………………………144  \n16.4 More Reciprocal Graphs………………………………145  \n16.5 Exponential Graphs …………………………………………147  \n16.6 Circle Graph. …………………………………………………148  \n16.7 Trigonometric Graphs …………………………………149  \n16.8 Transforming Graphs………………………………………151  \n16.9 Graphs Problem……………………………………………154  \nSection 17—Using Graphs  \n17.1 Interpreting Real-Life Graph. ……………","cbCailUIY1PqEYrY","https://ap.wps.com/l/cbCailUIY1PqEYrY","pdf",29864485,447,"English","# Section 1: Arithmetic, Multiples and Factors\n## 1.1 Calculations\n## 1.2 Multiples and Factors\n## 1.3 Prime Numbers and Prime Factors\n## 1.4 LCM and HCF\n# Section 2: Approximations\n## 2.1 Rounding\n## 2.2 Upper and Lower Bounds\n# Section 3: Fractions\n## 3.1 Equivalent Fraction\n## 3.2 Mixed Numbers\n## 3.3 Ordering Fraction\n## 3.4 Adding and Subtracting Fractions\n## 3.5 Multiplying and Dividing Fraction\n## 3.6 Fractions and Decimals\n## 3.7 Fractions Problems\n# Section 4: Ratio and Proportion\n## 4.1 Ratios\n## 4.2 Dividing in a Given Rati\n## 4.3 More Ratio Problems\n## 4.4 Proportion\n## 4.5 Ratio and Proportion Problems\n# Section 5: Percentages\n## 5.1 Percentages\n## 5.2 Percentages, Fractions and Decimals\n## 5.3 Percentage Increase and Decrease\n## 5.4 Compound Percentage Change\n## 5.5 Percentages Problem\n# Section 6: Expressions\n## 6.1 Simplifying Expressions\n## 6.2 Expanding Brackets\n## 6.3 Factorising—Common Factors\n## 6.4 Factorising—Quadratics\n## 6.5 Algebraic Fractions\n## 6.6 Expressions Problem\n# Section 7: Powers and Roots\n## 7.1 Squares, Cubes and Roots\n## 7.2 Indices and Index Laws\n## 7.3 Standard Form\n## 7.4 Surds\n# Section 8: Formulas\n## 8.1 Writing Formulas\n## 8.2 Substituting into a Formula\n## 8.3 Rearranging Formulas\n## 8.4 Formulas Problems\n# Section 9: Equations\n## 9.1 Solving Equation\n## 9.2 Writing Equations\n## 9.3 Iterative Methods\n## 9.4 Equations Problem\n## 9.5 Identities\n# Section 10: Direct and Inverse Proportion\n## 10.1 Direct Proportion\n## 10.2 Inverse Proportion\n## 10.3 Direct and Inverse Proportion Problems\n# Section 11: Quadratic Equations\n## 11.1 Solving Quadratics by Factorising\n## 11.2 Completing the Square\n## 11.3 The Quadratic Formula\n## 11.4 Quadratic Equations Problems\n# Section 12: Simultaneous Equations\n## 12.1 Simultaneous Equation\n## 12.2 More Simultaneous Equations\n# Section 13: Inequalities\n## 13.1 Inequalities\n## 13.2 Quadratic Inequalities\n## 13.3 Graphing Inequalities\n## 13.4 Linear Programming\n# Section 14: Sequences\n## 14.1 Term to Term Rules\n## 14.2 Using the nth Term\n## 14.3 Finding the nth Term\n# Section 15: Straight-Line Graphs\n## 15.1 Straight-Line Graph\n## 15.2 Gradients\n## 15.3 Equations of Straight-Line Graphs\n## 15.4 Parallel and Perpendicular Lines\n## 15.5 Line Segments\n## 15.6 Straight-Line Graphs Problem\n# Section 16: Other Types of Graph\n## 16.1 Quadratic Graphs\n## 16.2 Cubic Graphs\n## 16.3 Reciprocal Graphs\n## 16.4 More Reciprocal Graphs\n## 16.5 Exponential Graphs\n## 16.6 Circle Graph\n## 16.7 Trigonometric Graphs\n## 16.8 Transforming Graphs\n## 16.9 Graphs Problem\n# Section 17: Using Graphs\n## 17.1 Interpreting Real-Life Graph\n## 17.2 Drawing Real-Life Graph\n## 17.3 Solving Simultaneous Equations Graphically\n## 17.4 Solving Quadratic Equations Graphically\n## 17.5 Sketching Quadratic Graphs\n# Section 18: Functions\n## 18.1 Functions\n## 18.2 Composite Functions\n## 18.3 Inverse Functions\n## 18.4 Functions Problems\n# Section 19: Differentiation\n## 19.1 Differentiating Powers of x\n## 19.2 Finding Gradients\n## 19.3 Maximum and Minimum Point\n## 19.4 Using Differentiation\n# Section 20: Matrices\n## 20.1 Matrix Addition and Subtraction\n## 20.2 Matrix Multiplication\n## 20.3 Inverse Matrices and Determinants\n# Section 21: Sets\n## 21.1 Sets\n## 21.2 Venn Diagrams\n## 21.3 Unions and Intersections\n## 21.4 Complement of a Se\n## 21.5 Subsets\n## 21.6 Sets Problems\n# Geometry and Measures\n## Section 22: Angles and 2D Shapes\n## Section 23: Circle Geometry\n## Section 24: Units, Measuring and Estimating\n## Section 25: Compound Measures","[{\"question\":\"What topics are covered in the Number, Ratio and Algebra part of the GCSE 9-1 course textbook?\",\"answer\":\"It covers arithmetic calculations, multiples and factors, prime numbers and prime factors, LCM and HCF, rounding and bounds, fractions and decimals, ratios and proportion, and percentages including percentage change.\"},{\"question\":\"How does the book handle algebraic skills like expressions and equations?\",\"answer\":\"It includes simplifying and expanding expressions, factorising (including common factors and quadratics), algebraic fractions, forming and rearranging formulas, and solving equations including iterative methods and identities.\"},{\"question\":\"What graph and advanced algebra areas are included in later sections?\",\"answer\":\"Later sections cover straight-line graphs, gradients, equations of lines, other graph types (quadratic, cubic, reciprocal, exponential, circle and trigonometric), interpreting and drawing real-life graphs, functions, differentiation, and matrices and sets.\"}]","GCSE Mathematics Textbook for the New 9-1 Course - Number, Ratio and Algebra - Section 1 to Section 25 | PDF",1126]