/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":18,"initialQuestionWindow":[{"id":"620d8196-5a9c-469d-966a-bd3787fb0225","revisionId":"ab10fb72-c796-45c2-b0b6-be37f183d369","questionNumber":"2","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"2d318019-d537-4fd3-9e46-c6e5119a67cb","label":"0","content":"Simplify fully $\\frac{x^2 - x - 12}{x^2 - 9x + 20}$","markscheme":"- Factorise numerator and denominator: $\\frac{(x+3)(x-4)}{(x-5)(x-4)}$ M1\n- Simplify by cancelling $(x-4)$ to get $\\frac{x+3}{x-5}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorises both numerator and denominator correctly.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $\\frac{x+3}{x-5}$.","code":"A"}],"finalAnswers":["\\frac{x+3}{x-5}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"1e7e0a35-5dbf-40cf-b304-dca3a7ed7f6f","revisionId":"d2393b31-1f63-4e61-8d15-52ce086b72ad","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"6c302f76-1c02-4375-a7e6-2082088c8087","label":null,"content":"Simplify fully $\\frac{y + 8}{y^2 - 64}$","markscheme":"- Factorise denominator: $\\frac{y+8}{(y+8)(y-8)}$ M1\n- Simplify by cancelling $(y+8)$ to get $\\frac{1}{y-8}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorises the denominator as $(y+8)(y-8)$","code":"M"},{"id":"p2","marks":1,"description":"Simplifies to $\\frac{1}{y-8}$","code":"A"}],"finalAnswers":["\\frac{1}{y-8}"],"generatedAt":"2026-08-10T10:38:23.593Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"4340ab24-271e-41f9-84cb-b63ea6f576ee","revisionId":"ba48644c-8f2a-478f-9441-675b209b3ebc","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"ba13de7d-4092-4015-acc1-4c21fba35a14","label":"a","content":"Simplify fully $\\frac{5x-15}{x+2} \\div \\frac{x^2-4x+3}{3x^2+7x+2}$","markscheme":"- Invert second fraction and multiply: $\\frac{5(x-3)}{x+2} \\times \\frac{(3x+1)(x+2)}{(x-3)(x-1)}$ M1\n- Factorise all terms correctly M1\n- Cancel common factors to get $\\frac{5(3x+1)}{x-1}$ or $\\frac{15x+5}{x-1}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Evidence of inverting the second fraction and changing to multiplication.","code":"M"},{"id":"p2","marks":1,"description":"Correct factorisation of all four algebraic expressions.","code":"M"},{"id":"p3","marks":1,"description":"Full simplification resulting in the correct single fraction.","code":"A"}],"finalAnswers":["\\frac{5(3x+1)}{x-1}","\\frac{15x+5}{x-1}"],"generatedAt":"2026-08-10T10:37:25.157Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3e","subjectCode":"gcse_maths","summaries":[{"id":"d09aae9a-bc4b-4819-84a5-d2f7793bd6b4","difficultyBand":"hard","calculatorUse":null},{"id":"1beaa2b3-8fba-4912-a538-851dead9b005","difficultyBand":"hard","calculatorUse":null},{"id":"1c8bd641-25fd-4953-bb02-81a3a0eb8d60","difficultyBand":"hard","calculatorUse":null},{"id":"317a6bef-5a53-470e-bd04-7f50a8b0cbd0","difficultyBand":"hard","calculatorUse":null},{"id":"3394cd8d-61ac-4414-8133-45ded4fcc42a","difficultyBand":"hard","calculatorUse":null},{

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions