/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":47,"initialQuestionWindow":[{"id":"ae9d8c75-4b9a-483e-8812-7b3088dfb19d","revisionId":"67ee7225-0533-4ee6-b3b4-3c8cbc98b88d","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"d56a44fc-bbd1-4e12-98a2-5f69af768781","label":"a","content":"Write $\\frac{x^2 + 8x + 12}{5x^2 + 13x + 6}$ in the form $\\frac{x + a}{bx + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(x + 6)(x + 2)$ M1\n- Factorise denominator: $(5x + 3)(x + 2)$ M1\n- Cancel common factor $(x + 2)$ to get $\\frac{x + 6}{5x + 3}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct factorisation of $x^2 + 8x + 12$ into $(x + 6)(x + 2)$.","code":"M"},{"id":"p2","marks":1,"description":"Correct factorisation of $5x^2 + 13x + 6$ into $(5x + 3)(x + 2)$.","code":"M"},{"id":"p3","marks":1,"description":"Simplification to $\\frac{x+6}{5x+3}$.","code":"A"}],"finalAnswers":["\\frac{x+6}{5x+3}"],"generatedAt":"2026-08-10T10:37:54.427Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"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}],"subjectC

Algebraic Fractions

Question 45

Algebraic Fractions Questions

Algebraic Fractions

Question 45

Algebraic Fractions Questions