l,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e773f1ef-9513-4a88-8700-b48d03482af4","label":"a","content":"Simplify fully $\\frac{3x-6}{x+4} \\div \\frac{x^2-x-2}{2x^2+9x+4}$","markscheme":"- Invert second fraction and multiply: $\\frac{3(x-2)}{x+4} \\times \\frac{(2x+1)(x+4)}{(x-2)(x+1)}$ M1\n- Factorise all terms correctly M1\n- Cancel common factors to get $\\frac{3(2x+1)}{x+1}$ or $\\frac{6x+3}{x+1}$ 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+1)}{x+1}","\\frac{6x+3}{x+1}"],"generatedAt":"2026-08-10T10:37:22.545Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"3394cd8d-61ac-4414-8133-45ded4fcc42a","revisionId":"8cefa9b3-1e8b-4e24-a29c-5414f7f9eed7","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e7c1ca3c-be8c-468f-a84e-02b3fe601252","label":"","content":"Solve $\\frac{6}{x - 2} - \\frac{2}{x + 3} = 1$","markscheme":"- Multiply by common denominator: $6(x + 3) - 2(x - 2) = (x - 2)(x + 3)$ M1\n- Expand and simplify: $4x + 22 = x^2 + x - 6$ M1\n- Rearrange to $x^2 - 3x - 28 = 0$ M1\n- Factorise $(x - 7)(x + 4) = 0$ to get $x = 7$ or $x = -4$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply the entire equation by the common denominator $(x - 2)(x + 3)$. ","code":"M"},{"id":"p2","marks":1,"description":"Correctly expand both the numerator terms and the product of the denominators.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange the equation into a standard quadratic form $ax^2 + bx + c = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solve the quadratic equation to find two correct values for $x$.","code":"A"}],"finalAnswers":["x = 7, x = -4"],"generatedAt":"2026-08-10T10:36:28.042Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"3ddd763e-87b5-4e51-a425-e07e163b102d","revisionId":"4e24d4f1-d733-4e5b-b4b9-5011b5b6419b","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$2x + 2 : x + 3 = x + 1 : x - 1$$","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e4649d8d-ea48-4378-8374-d1e95e78b53a","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{2x+2}{x+3} = \\frac{x+1}{x-1}$ M1\n- Cross multiply: $(2x+2)(x-1) = (x+1)(x+3)$ M1\n- Expand and simplify to $x^2 - 4x - 5 = 0$ M1\n- Solve to get $x = 5$ or $x = -1$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation as a ratio of fractions: $\\frac{2x+2}{x+3} = \\frac{x+1}{x-1}$","code":"M"},{"id":"p2","marks":1,"description":"Correctly cross-multiplies to get $(2x+2)(x-1) = (x+1)(x+3)$ or equivalent.","code":"M"},{"id":"p3","marks":1,"description":"Expands both sides and simplifies to a standard quadratic form, e.g., $x^2 - 4x - 5 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic correctly to find both values of $x$.","code":"A"}],"finalAnswers":["x = 5, x = -1","x = 5 and x = -1"],"generatedAt":"2026-08-10T10:37:04.260Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"f

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions