/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":48,"initialQuestionWindow":[{"id":"b452c7f4-d413-4e9f-abe7-4f8a8d7e4729","revisionId":"17abdf65-519e-4a51-9a88-a06707c0cdee","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"c0c48164-add1-45a0-8c43-47536d4570c1","label":"a","content":"Simplify fully $\\frac{2x+10}{x-3} \\div \\frac{5x^2+24x-5}{x^2-3x}$","markscheme":"- Invert second fraction and multiply: $\\frac{2x+10}{x-3} \\times \\frac{x^2-3x}{5x^2+24x-5}$ M1\n- Factorise all terms: $\\frac{2(x+5)}{x-3} \\times \\frac{x(x-3)}{(5x-1)(x+5)}$ M1\n- Cancel common factors to get $\\frac{2x}{5x-1}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Applies the rule for division of fractions by inverting the second fraction.","code":"M"},{"id":"p2","marks":1,"description":"Factors the quadratic expression into two linear binomials correctly.","code":"M"},{"id":"p3","marks":1,"description":"Fully simplifies the algebraic fraction.","code":"A"}],"finalAnswers":["\\frac{2x}{5x-1}"],"generatedAt":"2026-08-10T10:36:26.850Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"b4b3f098-eda8-4216-bae8-6a887365b65a","revisionId":"8b93daea-0304-46a6-8fcb-f30d9800cddd","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"1484d0d8-91d8-4dc1-a761-fa6c5ce253fa","label":"a","content":"Simplify fully $\\frac{3x+3}{x+6} \\div \\frac{x^2-3x-4}{2x^2+17x+30}$","markscheme":"- Invert second fraction and multiply: $\\frac{3(x+1)}{x+6} \\times \\frac{(2x+5)(x+6)}{(x+1)(x-4)}$ M1\n- Factorise all terms correctly M1\n- Cancel common factors to get $\\frac{3(2x+5)}{x-4}$ or $\\frac{6x+15}{x-4}$ 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{3(2x+5)}{x-4}","\\frac{6x+15}{x-4}"],"generatedAt":"2026-08-10T10:37:28.597Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"cd6441bf-455c-4c64-a683-8455e3c1fb3b","revisionId":"b18e226c-87ab-49f3-98cf-f9774f61d837","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"22f2d59f-5974-4de4-a8bd-c3941d2e7304","label":"","content":"Solve $\\frac{8}{x + 3} + \\frac{3}{x - 2} = 2$","markscheme":"- Multiply by common denominator: $8(x - 2) + 3(x + 3) = 2(x + 3)(x - 2)$ M1\n- Expand and simplify: $11x - 7 = 2x^2 + 2x - 12$ M1\n- Rearrange to $2x^2 - 9x - 5 = 0$ M1\n- Factorise $(2x + 1)(x - 5) = 0$ to get $x = -0.5$ or $x = 5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply terms by $(x + 3)(x - 2)$. ","code":"M"},{"id":"p2","marks":1,"description":"Expand both sides of the equation correctly.","code":"M"},{"id":"p3","marks":1,"description":"Collect like terms to form the quadratic $2x^2 - 9x - 5 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solve the quadratic to obtain $x = -0.5$ (or $-1/2$) and $x = 5$.","code":"A"}],"finalAnswers":["x = -0.5, x = 5"],"generatedAt":"2026-08-10T10:36:34.176Z","modelVersion":"gemini-3-flash-preview

Algebraic Fractions

Question 46

Algebraic Fractions Questions

Algebraic Fractions

Question 46

Algebraic Fractions Questions