/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":11,"initialQuestionWindow":[{"id":"9130d069-1f56-4520-b84b-3e77f3ce1ed2","revisionId":"d56ac9af-3400-4258-a38c-fa5c6cf21833","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"357fdea2-8c2b-4a6a-8e08-a654590cd5af","label":"a","content":"Simplify fully $\\frac{x^2 + 5x + 6}{x^2 + x - 6}$","markscheme":"- Factorise numerator and denominator: $\\frac{(x+2)(x+3)}{(x-2)(x+3)}$ M1\n- Simplify by cancelling $(x+3)$ to get $\\frac{x+2}{x-2}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Attempt to factorise both numerator and denominator into two brackets, with at least one quadratic factorised correctly.","code":"M"},{"id":"p2","marks":1,"description":"Correct simplified fraction after cancelling common factors.","code":"A"}],"finalAnswers":["\\frac{x+2}{x-2}"],"generatedAt":"2026-08-10T10:36:46.109Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"967f95d2-cfef-4cff-85d1-5f12f88b42e5","revisionId":"a88c0de2-2456-4223-b4a8-8af26ed428f0","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$x - 4 : x - 5 = 3x - 2 : x + 2$$","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"9f288371-3a79-498b-afda-ed987b149bd8","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x-4}{x-5} = \\frac{3x-2}{x+2}$ M1\n- Cross multiply: $(x-4)(x+2) = (x-5)(3x-2)$ M1\n- Expand and simplify to $2x^2 - 15x + 18 = 0$ M1\n- Solve to get $x = 1.5$ and $x = 6$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation using fractions $\\frac{x-4}{x-5} = \\frac{3x-2}{x+2}$","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies to remove fractions $(x-4)(x+2) = (x-5)(3x-2)$","code":"M"},{"id":"p3","marks":1,"description":"Expands brackets and simplifies to a quadratic equation $2x^2 - 15x + 18 = 0$","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic equation to find both $x = 1.5$ and $x = 6$","code":"A"}],"finalAnswers":["1.5, 6","x = 1.5, x = 6","6, 1.5"],"generatedAt":"2026-08-10T10:37:25.428Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"9b191aa8-f4dd-465b-a60a-6cb2924300bb","revisionId":"4e4fe94f-2295-42d2-b03b-70487e07dbb2","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"f024721b-082b-4343-9cd9-5792122aa977","label":"","content":"Write $\\frac{2x^2 + 7x + 3}{x^2 + x - 6}$ in the form $\\frac{ax + b}{x + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(2x+1)(x+3)$ M1\n- Factorise denominator: $(x+3)(x-2)$ M1\n- Cancel common factor $(x+3)$ to get $\\frac{2x+1}{x-2}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct factorisation of the numerator $2x^2 + 7x + 3$ into $(2x+1)(x+3)$.","code":"M"},{"id":"p2","marks":1,"description":"Correct factorisation of the denominator $x^2 + x - 6$ into $(x+3)(x-2)$.","code":"M"},{"id":"p3","marks":1,"description":"Cancellation of common factor $(x+3)$ to reach the final simplified form.","code":"A"}],"finalAnswers":["\\frac{2x+1}{x-2}"],"generatedAt":"2026-08-10T10:38:33.501Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initia

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions