/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":10,"initialQuestionWindow":[{"id":"669d940d-3383-4891-8833-36e34a72dcb6","revisionId":"f437be35-60a3-41ca-a42c-6346e1d08596","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"5c45db98-9416-4ced-937d-96384472ca5f","label":"a","content":"Simplify fully $\\frac{5x^2 - 10x}{x^2 - 4}$","markscheme":"- Factorise numerator and denominator: $\\frac{5x(x-2)}{(x-2)(x+2)}$ M1\n- Simplify by cancelling $(x-2)$ to get $\\frac{5x}{x+2}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorise numerator as $5x(x-2)$ and denominator as $(x-2)(x+2)$ or $(x+2)(x-2)$.","code":"M"},{"id":"p2","marks":1,"description":"Simplify by cancelling the common factor $(x-2)$ to reach the final answer.","code":"A"}],"finalAnswers":["\\frac{5x}{x+2}"],"generatedAt":"2026-08-10T10:38:59.601Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"9130d069-1f56-4520-b84b-3e77f3ce1ed2","revisionId":"d56ac9af-3400-4258-a38c-fa5c6cf21833","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"357fdea2-8c2b-4a6a-8e08-a654590cd5af","label":"a","content":"Simplify fully $\\frac{x^2 + 5x + 6}{x^2 + x - 6}$","markscheme":"- Factorise numerator and denominator: $\\frac{(x+2)(x+3)}{(x-2)(x+3)}$ M1\n- Simplify by cancelling $(x+3)$ to get $\\frac{x+2}{x-2}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Attempt to factorise both numerator and denominator into two brackets, with at least one quadratic factorised correctly.","code":"M"},{"id":"p2","marks":1,"description":"Correct simplified fraction after cancelling common factors.","code":"A"}],"finalAnswers":["\\frac{x+2}{x-2}"],"generatedAt":"2026-08-10T10:36:46.109Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"967f95d2-cfef-4cff-85d1-5f12f88b42e5","revisionId":"a88c0de2-2456-4223-b4a8-8af26ed428f0","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$x - 4 : x - 5 = 3x - 2 : x + 2$$","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"9f288371-3a79-498b-afda-ed987b149bd8","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x-4}{x-5} = \\frac{3x-2}{x+2}$ M1\n- Cross multiply: $(x-4)(x+2) = (x-5)(3x-2)$ M1\n- Expand and simplify to $2x^2 - 15x + 18 = 0$ M1\n- Solve to get $x = 1.5$ and $x = 6$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation using fractions $\\frac{x-4}{x-5} = \\frac{3x-2}{x+2}$","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies to remove fractions $(x-4)(x+2) = (x-5)(3x-2)$","code":"M"},{"id":"p3","marks":1,"description":"Expands brackets and simplifies to a quadratic equation $2x^2 - 15x + 18 = 0$","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic equation to find both $x = 1.5$ and $x = 6$","code":"A"}],"finalAnswers":["1.5, 6","x = 1.5, x = 6","6, 1.5"],"generatedAt":"2026-08-10T10:37:25.428Z","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":null,"calculatorUse":null},{"id":"1beaa2b3-8fba-4912-a538-851dead9b005","diffic

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions