/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":36,"initialQuestionWindow":[{"id":"0037d4ef-91cd-4e27-9b27-af35e88cb62a","revisionId":"d029b8ce-9a7a-409b-a4ad-b0aa93d95d3e","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"4061a06d-06bb-4270-9693-bca2fe1c6b9f","label":null,"content":"Simplify fully $\\frac{a + 10}{a^2 - 100}$","markscheme":"- Factorise denominator: $\\frac{a+10}{(a+10)(a-10)}$ M1\n- Simplify by cancelling $(a+10)$ to get $\\frac{1}{a-10}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorises the denominator using difference of two squares","code":"M"},{"id":"p2","marks":1,"description":"Provides the final correct simplified form","code":"A"}],"finalAnswers":["\\frac{1}{a-10}"],"generatedAt":"2026-08-10T10:38:25.402Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"037a8862-fc30-4c2f-8353-36537b2d42bf","revisionId":"5ba9db04-ce52-4161-b456-89f76d75550a","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$4x - 1 : 2x + 1 = x + 1 : x - 1$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"113e95d1-06a7-4343-a386-25d516cab26d","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{4x-1}{2x+1} = \\frac{x+1}{x-1}$ M1\n- Cross multiply: $(4x-1)(x-1) = (x+1)(2x+1)$ M1\n- Expand and simplify to $2x^2 - 8x = 0$ M1\n- Solve to get $x = 0$ or $x = 4$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation as a ratio of fractions: $\\frac{4x-1}{2x+1} = \\frac{x+1}{x-1}$","code":"M"},{"id":"p2","marks":1,"description":"Correctly cross-multiplies to get $(4x-1)(x-1) = (x+1)(2x+1)$.","code":"M"},{"id":"p3","marks":1,"description":"Expands both sides and simplifies to a standard quadratic form, e.g., $2x^2 - 8x = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic correctly to find both values of $x$.","code":"A"}],"finalAnswers":["x = 0, x = 4","x = 0 and x = 4"],"generatedAt":"2026-08-10T10:37:07.083Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"0c917b15-fa38-4545-a451-1239cf2d0e10","revisionId":"4c5f0c0a-31f7-401a-a3e4-ba771a9d773b","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"d25b6b39-ef4f-4e09-a183-593041332ae0","label":"a","content":"Work out the values of $x$ for which\n\n$$\\frac{4}{x} + \\frac{3}{x - 2} = 1$$","markscheme":"- Multiply by common denominator: $4(x - 2) + 3x = x(x - 2)$ M1\n- Expand and simplify to quadratic: $7x - 8 = x^2 - 2x$ M1\n- Rearrange to $x^2 - 9x + 8 = 0$ M1\n- Solve to get $x = 1$ or $x = 8$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply through by $x(x - 2)$ to eliminate denominators.","code":"M"},{"id":"p2","marks":1,"description":"Simplify the expansion to reach a quadratic equation in any form.","code":"M"},{"id":"p3","marks":1,"description":"Correctly rearrange into standard quadratic form $x^2 - 9x + 8 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"State both final solutions for $x$.","code":"A"}],"finalAnswers":["x = 1, x = 8","x = 8, x = 1"],"generatedAt":"2026-08-10T10:37:17.075Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"subjectCode":"gcse_maths",

Algebraic Fractions

Question 35

Algebraic Fractions Questions

Algebraic Fractions

Question 35

Algebraic Fractions Questions