/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":50,"initialQuestionWindow":[{"id":"cd6441bf-455c-4c64-a683-8455e3c1fb3b","revisionId":"b18e226c-87ab-49f3-98cf-f9774f61d837","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"22f2d59f-5974-4de4-a8bd-c3941d2e7304","label":"","content":"Solve $\\frac{8}{x + 3} + \\frac{3}{x - 2} = 2$","markscheme":"- Multiply by common denominator: $8(x - 2) + 3(x + 3) = 2(x + 3)(x - 2)$ M1\n- Expand and simplify: $11x - 7 = 2x^2 + 2x - 12$ M1\n- Rearrange to $2x^2 - 9x - 5 = 0$ M1\n- Factorise $(2x + 1)(x - 5) = 0$ to get $x = -0.5$ or $x = 5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply terms by $(x + 3)(x - 2)$. ","code":"M"},{"id":"p2","marks":1,"description":"Expand both sides of the equation correctly.","code":"M"},{"id":"p3","marks":1,"description":"Collect like terms to form the quadratic $2x^2 - 9x - 5 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solve the quadratic to obtain $x = -0.5$ (or $-1/2$) and $x = 5$.","code":"A"}],"finalAnswers":["x = -0.5, x = 5"],"generatedAt":"2026-08-10T10:36:34.176Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"dac36d2a-60e9-4ac1-98e4-ac1ce7284e70","revisionId":"e32c0bf2-dbeb-439b-8b8f-bd47ac2e96de","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$3x + 2 : 2x + 1 = 5x + 4 : 3x + 2$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"6fb67845-7b2a-40a5-ad21-9f7de181fd56","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{3x+2}{2x+1} = \\frac{5x+4}{3x+2}$ M1\n- Cross multiply: $(3x+2)^2 = (2x+1)(5x+4)$ M1\n- Expand and simplify to $x^2 + x = 0$ M1\n- Solve to get $x = 0$ or $x = -1$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation $\\frac{3x+2}{2x+1} = \\frac{5x+4}{3x+2}$ or equivalent.","code":"M"},{"id":"p2","marks":1,"description":"Cross-multiplies correctly to get $(3x+2)^2 = (2x+1)(5x+4)$.","code":"M"},{"id":"p3","marks":1,"description":"Expands and simplifies terms to reach a quadratic equation, e.g., $x^2 + x = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Correctly solves the quadratic equation to find $x = 0$ and $x = -1$.","code":"A"}],"finalAnswers":["x = 0, x = -1","0, -1"],"generatedAt":"2026-08-10T10:38:09.418Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"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}],"subjectCode":"gcse_maths","summaries":[{"id":"d09aae9a-bc4b-4819-84a5-

Algebraic Fractions

Question 48

Algebraic Fractions Questions

Algebraic Fractions

Question 48

Algebraic Fractions Questions