/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":54,"initialQuestionWindow":[{"id":"be550440-afc7-4a71-b6a3-9779b693586d","revisionId":"0c7854b1-87e9-44a5-bf00-d836bdda3241","questionNumber":"6","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"972309d7-959a-4fc3-b3b8-a6a559b7a32d","label":"0","content":"Write $\\frac{x^2 + 7x - 18}{2x^2 - x - 6}$ in the form $\\frac{x + a}{bx + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(x+9)(x-2)$ M1\n- Factorise denominator: $(2x+3)(x-2)$ M1\n- Cancel common factor $(x-2)$ to get $\\frac{x+9}{2x+3}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correctly factorises the quadratic numerator.","code":"M"},{"id":"p2","marks":1,"description":"Correctly factorises the quadratic denominator.","code":"M"},{"id":"p3","marks":1,"description":"Final answer $\\frac{x+9}{2x+3}$.","code":"A"}],"finalAnswers":["\\frac{x+9}{2x+3}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"0904d9ed-910b-4e89-98a4-a2c0af0ce71a","revisionId":"4d3eca48-728c-451a-8ea9-c1b2befac229","questionNumber":"7","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"c2232f1d-e417-44cc-955a-8809d2f0891b","label":"0","content":"Simplify fully $\\frac{3x+6}{x-4} \\div \\frac{2x^2+9x+10}{x^2-4x}$","markscheme":"- Invert second fraction and multiply: $\\frac{3x+6}{x-4} \\times \\frac{x^2-4x}{2x^2+9x+10}$ M1\n- Factorise all terms: $\\frac{3(x+2)}{x-4} \\times \\frac{x(x-4)}{(2x+5)(x+2)}$ M1\n- Cancel common factors to get $\\frac{3x}{2x+5}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Inverts the divisor and changes to multiplication.","code":"M"},{"id":"p2","marks":1,"description":"Factorises at least two expressions correctly.","code":"M"},{"id":"p3","marks":1,"description":"Final answer $\\frac{3x}{2x+5}$.","code":"A"}],"finalAnswers":["\\frac{3x}{2x+5}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"929ab195-159e-4cd5-969e-3111a7c595e4","revisionId":"9ec99fc7-b325-41a7-93f1-2398693e9a26","questionNumber":"8","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"5264b7b9-b053-4b0c-9c8f-13964e19c08a","label":"0","content":"Simplify fully $\\frac{2x-2}{x+5} \\div \\frac{x^2-4x+3}{2x^2+13x+15}$","markscheme":"- Invert second fraction and multiply: $\\frac{2(x-1)}{x+5} \\times \\frac{(2x+3)(x+5)}{(x-3)(x-1)}$ M1\n- Factorise all terms correctly M1\n- Cancel common factors to get $\\frac{2(2x+3)}{x-3}$ or $\\frac{4x+6}{x-3}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Inverts the divisor and changes to multiplication.","code":"M"},{"id":"p2","marks":1,"description":"Factorises at least two expressions correctly.","code":"M"},{"id":"p3","marks":1,"description":"Final answer $\\frac{2(2x+3)}{x-3}$ or equivalent.","code":"A"}],"finalAnswers":["\\frac{2(2x+3)}{x-3}","\\frac{4x+6}{x-3}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"subjectCode":"gcse_maths","summaries":[{"id":"d09aae9a-bc4b-4819-84a5-d2f7793bd6b4","difficultyBand":"hard","calculatorUse

Algebraic Fractions

Question 52

Algebraic Fractions Questions

Algebraic Fractions

Question 52

Algebraic Fractions Questions