null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"53f10bf4-f2d8-43b8-b38a-056c1740fef0","label":"a","content":"Write $\\frac{x^2 - 2x - 15}{2x^2 + x - 15}$ in the form $\\frac{x + a}{bx + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(x - 5)(x + 3)$ M1\n- Factorise denominator: $(2x - 5)(x + 3)$ M1\n- Cancel common factor $(x + 3)$ to get $\\frac{x - 5}{2x - 5}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Factorise the numerator into $(x - 5)(x + 3)$. Or one correct factor in a factorisation attempt.","code":"M"},{"id":"p2","marks":1,"description":"Factorise the denominator into $(2x - 5)(x + 3)$. Or one correct factor in a factorisation attempt.","code":"M"},{"id":"p3","marks":1,"description":"Final simplified fraction obtained by cancelling common factor.","code":"A"}],"finalAnswers":["\\frac{x-5}{2x-5}"],"generatedAt":"2026-08-10T10:37:50.987Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ad6e0894-ab2e-4bd7-b533-15f78b776fb0","revisionId":"b0be5fc0-0c06-4c2d-9e10-3f5ba8bb1063","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$x + 2 : 4 = 3x - 1 : x + 3$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"12f27786-d7ac-491d-9f6b-413b5765e100","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x+2}{4} = \\frac{3x-1}{x+3}$ M1\n- Cross multiply: $(x+2)(x+3) = 4(3x-1)$ M1\n- Expand and simplify to $x^2 - 7x + 10 = 0$ M1\n- Solve to get $x = 2$ or $x = 5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the initial equation from the ratio: $\\frac{x+2}{4} = \\frac{3x-1}{x+3}$","code":"M"},{"id":"p2","marks":1,"description":"Correctly cross multiplies the algebraic fractions: $(x+2)(x+3) = 4(3x-1)$","code":"M"},{"id":"p3","marks":1,"description":"Expands brackets and simplifies to reach a standard quadratic equation $x^2 - 7x + 10 = 0$","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic equation to find two correct values for $x$.","code":"A"}],"finalAnswers":["x = 2, x = 5","2, 5"],"generatedAt":"2026-08-10T10:38:47.958Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ae08c1ec-647e-46b8-857b-70618d83ac4d","revisionId":"e75199c7-beef-4882-b0fa-f1356015f0f2","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"efa1a041-663a-4de5-8fc9-f52ba42660a4","label":"a","content":"Simplify fully $\\frac{x^2 + 7x}{x^2 + 10x + 21}$","markscheme":"- Factorise numerator and denominator: $\\frac{x(x+7)}{(x+7)(x+3)}$ M1\n- Simplify by cancelling $(x+7)$ to get $\\frac{x}{x+3}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorise numerator and denominator: $\\frac{x(x+7)}{(x+7)(x+3)}$","code":"M"},{"id":"p2","marks":1,"description":"Simplify by cancelling $(x+7)$ to get $\\frac{x}{x+3}$","code":"A","acceptable":["x/(x+3)"]}],"finalAnswers":["\\frac{x}{x+3}"],"generatedAt":"2026-08-10T10:39:04.320Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3f","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-bb02-81

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions