/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":9,"initialQuestionWindow":[{"id":"65038096-a2f3-4ac6-a5d9-40c46647dce0","revisionId":"999a6d5f-ffaf-427d-9c90-c9f9f5e25ec4","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"ba13d3d6-4b7e-42e9-929f-411b684cba9f","label":"a","content":"Write $\\frac{x^2 + 5x - 14}{3x^2 - x - 10}$ in the form $\\frac{x + a}{bx + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(x + 7)(x - 2)$ M1\n- Factorise denominator: $(3x + 5)(x - 2)$ M1\n- Cancel common factor $(x - 2)$ to get $\\frac{x + 7}{3x + 5}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Attempt to factorise the quadratic numerator into two linear brackets.","code":"M"},{"id":"p2","marks":1,"description":"Attempt to factorise the quadratic denominator into two linear brackets.","code":"M"},{"id":"p3","marks":1,"description":"Correct simplification by cancelling the common factor $(x - 2)$.","code":"A"}],"finalAnswers":["\\frac{x+7}{3x+5}"],"generatedAt":"2026-08-10T10:37:47.610Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"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}],"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","difficultyBand":null,"calculatorUse":null},{"id":"1c8bd641-25fd-4953-bb02-81a3a0eb8d60","difficultyBand":null,"calculatorUse":null},{"id":"317a6bef-5a53-470e-bd04-7f

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions