/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":61,"initialQuestionWindow":[{"id":"8aefa908-c49d-46a2-9247-dd02c0e50f95","revisionId":"6a321364-ca4c-40f9-acff-b6a525993fbf","questionNumber":"13","questionType":"LA","specification":"Given that\n\n$$2x + 1 : x + 2 = x + 8 : 3x - 4$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"5e2d77f2-09ec-4a9f-97e1-797210041f20","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{2x+1}{x+2} = \\frac{x+8}{3x-4}$ M1\n- Cross multiply: $(2x+1)(3x-4) = (x+8)(x+2)$ M1\n- Expand and simplify to $x^2 - 3x - 4 = 0$ M1\n- Solve to get $x = 4$ or $x = -1$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts ratio to an algebraic fraction equation.","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies and expands brackets correctly.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $x^2 - 3x - 4 = 0$ or equivalent.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 4$ and $x = -1$.","code":"A"}],"finalAnswers":["4","-1"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"848156c2-c256-4f6f-8b89-af3f2ab121dd","revisionId":"b0494f19-9c06-4a4a-b6b0-70305c8018dc","questionNumber":"14","questionType":"LA","specification":"Given that\n\n$$x - 1 : 2x - 3 = x + 2 : 3x - 2$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"52d2ef47-dc1d-4f9a-be68-1d4f9716216a","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x-1}{2x-3} = \\frac{x+2}{3x-2}$ M1\n- Cross multiply: $(x-1)(3x-2) = (x+2)(2x-3)$ M1\n- Expand and simplify to $x^2 - 6x + 8 = 0$ M1\n- Solve to get $x = 2$ or $x = 4$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts ratio to an algebraic fraction equation.","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies and expands brackets correctly.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $x^2 - 6x + 8 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 2$ and $x = 4$.","code":"A"}],"finalAnswers":["2","4"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"9d209464-7ab2-4a44-9261-7675c305b949","revisionId":"e0c8116c-b798-40cd-bb37-3f17b140ce9d","questionNumber":"15","questionType":"LA","specification":"Given that\n\n$$x + 9 : 5x - 1 = x + 7 : 2x - 3$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"b0ce2aea-a518-46f2-b10a-58edbff7974a","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x+9}{5x-1} = \\frac{x+7}{2x-3}$ M1\n- Cross multiply: $(x+9)(2x-3) = (x+7)(5x-1)$ M1\n- Expand and simplify to $3x^2 + 19x + 20 = 0$ M1\n- Solve to get $x = -4/3$ or $x = -5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts ratio to an algebraic fraction equation.","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies and expands brackets correctly.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $3x^2 + 19x + 20 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = -4/3$ and $x = -5$.","code":"A"}],"finalAnswers":["-4/3","-5"],"generatedAt":"2026-08-10T10:27

Algebraic Fractions

Question 59

Algebraic Fractions Questions

Algebraic Fractions

Question 59

Algebraic Fractions Questions