/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":33,"initialQuestionWindow":[{"id":"e3fb214f-ccd6-4c46-92c8-cb894ef5281f","revisionId":"66b2fa4a-069e-4841-91cc-f4215ce92b62","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"76609f1c-1fac-4d51-842a-aa2ef585aea4","label":"","content":"Solve $\\frac{2}{x + 2} + \\frac{5}{x - 1} = 2$","markscheme":"- Multiply by common denominator: $2(x - 1) + 5(x + 2) = 2(x + 2)(x - 1)$ M1\n- Expand and simplify: $7x + 8 = 2(x^2 + x - 2)$ M1\n- Rearrange to $2x^2 - 5x - 12 = 0$ M1\n- Solve $(2x + 3)(x - 4) = 0$ to get $x = -1.5$ or $x = 4$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiplies throughout by $(x + 2)(x - 1)$ to eliminate denominators.","code":"M"},{"id":"p2","marks":1,"description":"Expands and simplifies terms on both sides of the equation.","code":"M"},{"id":"p3","marks":1,"description":"Correctly rearranges the equation into the form $2x^2 - 5x - 12 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds the correct solutions $x = -1.5$ (or $-3/2$) and $x = 4$.","code":"A"}],"finalAnswers":["x = -1.5, x = 4","-1.5, 4","x = -3/2, x = 4"],"generatedAt":"2026-08-10T10:38:06.780Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"e5ea4ae3-2180-43e1-9a4b-abe584af8e88","revisionId":"4dc1c70c-081e-4e9e-820a-6d8ea7db11ed","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"2ec5ef6d-986d-4a99-ab2c-08e7924c2edd","label":"a","content":"Simplify fully $\\frac{4x-8}{x+5} \\div \\frac{2x^2-x-6}{x^2+5x}$","markscheme":"- Invert second fraction and multiply: $\\frac{4x-8}{x+5} \\times \\frac{x^2+5x}{2x^2-x-6}$ M1\n- Factorise all terms: $\\frac{4(x-2)}{x+5} \\times \\frac{x(x+5)}{(2x+3)(x-2)}$ M1\n- Cancel common factors to get $\\frac{4x}{2x+3}$ 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 the linear and quadratic expressions correctly.","code":"M"},{"id":"p3","marks":1,"description":"Identifies and cancels common factors to reach the final simplified fraction.","code":"A"}],"finalAnswers":["\\frac{4x}{2x+3}"],"generatedAt":"2026-08-10T10:36:25.416Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"f6a13619-31ca-4a2d-9c74-fb8cfe46b0ad","revisionId":"12795737-e99f-46e6-9223-5ac6a18becb0","questionNumber":"3","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"a197f479-b2a2-49fd-b9cc-37c0a5a68ac3","label":"0","content":"Simplify fully $\\frac{3x^2 + 9x}{x^2 - 9}$","markscheme":"- Factorise numerator and denominator: $\\frac{3x(x+3)}{(x-3)(x+3)}$ M1\n- Simplify by cancelling $(x+3)$ to get $\\frac{3x}{x-3}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorises both numerator and denominator correctly.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $\\frac{3x}{x-3}$.","code":"A"}],"finalAnswers":["\\frac{3x}{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":n

Algebraic Fractions

Question 32

Algebraic Fractions Questions

Algebraic Fractions

Question 32

Algebraic Fractions Questions