/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":52,"initialQuestionWindow":[{"id":"c79b6a21-5784-4635-a8e3-7c76920a4c54","revisionId":"23665853-5ba6-4ce3-aaf9-420e2b5127eb","questionNumber":"4","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"f883b562-3f55-427c-afcb-73e6d99c20a4","label":"0","content":"Simplify fully $\\frac{x + 4}{x^2 - 16}$","markscheme":"- Factorise denominator: $\\frac{x+4}{(x+4)(x-4)}$ M1\n- Simplify by cancelling $(x+4)$ to get $\\frac{1}{x-4}$ 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":"Final answer $\\frac{1}{x-4}$.","code":"A"}],"finalAnswers":["\\frac{1}{x-4}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"c98f89fb-7228-4edc-809f-d1606093996a","revisionId":"0d2a6c12-db14-4644-a8bf-8a431d9b71e9","questionNumber":"5","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"e1a1095c-6e54-42d7-9a76-9850aadadb27","label":"0","content":"Write $\\frac{3x^2 + 11x - 4}{x^2 + 3x - 4}$ in the form $\\frac{ax + b}{x + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(3x-1)(x+4)$ M1\n- Factorise denominator: $(x+4)(x-1)$ M1\n- Cancel common factor $(x+4)$ to get $\\frac{3x-1}{x-1}$ 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 $\\frac{3x-1}{x-1}$.","code":"A"}],"finalAnswers":["\\frac{3x-1}{x-1}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"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}],"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-bb02-81a3a0eb8d60","difficultyBand":"hard","calculatorUse":null},{"id":"317a6bef-5a53-470e-bd04-7f50a8b0cbd0","difficultyBand":"hard","calculatorUse":null},{"id":"3394cd8d-61ac-4414-8133-45ded4fcc42a","

Algebraic Fractions

Question 50

Algebraic Fractions Questions

Algebraic Fractions

Question 50

Algebraic Fractions Questions