null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"ab951b00-5383-4003-aa0b-e12bf06fe687","label":"a","content":"Solve the equation\n\n$$\\frac{7}{y + 15} + \\frac{15}{y + 7} = 1$$","markscheme":"- Multiply by common denominator: $7(y + 7) + 15(y + 15) = (y + 15)(y + 7)$ M1\n- Expand and simplify to quadratic: $22y + 274 = y^2 + 22y + 105$ M1\n- Rearrange to $y^2 - 169 = 0$ M1\n- Solve to get $y = 13$ or $y = -13$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Establish the equation $7(y + 7) + 15(y + 15) = (y + 15)(y + 7)$. ","code":"M"},{"id":"p2","marks":1,"description":"Expand and simplify the linear and quadratic expressions correctly on both sides.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange to the form $y^2 - 169 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Identify the two solutions $y = 13$ and $y = -13$.","code":"A"}],"finalAnswers":["y = 13, y = -13","y = \\pm 13"],"generatedAt":"2026-08-10T10:37:15.241Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"766d0f92-1e9f-4984-876c-1e16af770945","revisionId":"9a2b0f0a-d919-45db-9dde-5f88f108877a","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$x + 1 : 2 = 2x + 5 : x + 4$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"3d3cfbb7-0921-45db-9660-d73e7829191c","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x+1}{2} = \\frac{2x+5}{x+4}$ M1\n- Cross multiply: $(x+1)(x+4) = 2(2x+5)$ M1\n- Expand and simplify to $x^2 + x - 6 = 0$ M1\n- Solve to get $x = 2$ or $x = -3$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation as a ratio of fractions: $\\frac{x+1}{2} = \\frac{2x+5}{x+4}$","code":"M"},{"id":"p2","marks":1,"description":"Correctly cross-multiplies to get $(x+1)(x+4) = 2(2x+5)$.","code":"M"},{"id":"p3","marks":1,"description":"Expands both sides and simplifies to a standard quadratic form, e.g., $x^2 + x - 6 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic correctly to find both values of $x$.","code":"A"}],"finalAnswers":["x = 2, x = -3","x = 2 and x = -3"],"generatedAt":"2026-08-10T10:37:05.663Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"90ebd2c4-370d-4424-a9a6-3c99f22c395d","revisionId":"86e84cdc-e177-4e0d-baeb-f5454155d654","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"62fe4e1e-c475-455f-ac04-a5ecc4d2ab6a","label":"a","content":"Solve $\\frac{4}{n + 1} + \\frac{5}{2n - 1} = 3$","markscheme":"- Multiply by common denominator: $4(2n - 1) + 5(n + 1) = 3(n + 1)(2n - 1)$ M1\n- Expand and simplify: $13n + 1 = 6n^2 + 3n - 3$ M1\n- Rearrange to $6n^2 - 10n - 4 = 0$ (or $3n^2 - 5n - 2 = 0$) M1\n- Factorise $(3n + 1)(n - 2) = 0$ to get $n = -\\frac{1}{3}$ or $n = 2$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply by common denominator $(n+1)(2n-1)$.","code":"M"},{"id":"p2","marks":1,"description":"Expand and simplify the linear and quadratic terms.","code":"M"},{"id":"p3","marks":1,"description":"Equate to zero and rearrange to a quadratic equation.","code":"M"},{"id":"p4","marks":1,"description":"Solve the resulting quadratic to find both solutions.","code":"A"}],"finalAnswers":["n = -\\frac{1}{3}, n = 2","-0.33, 2"],"generatedAt":"2026-08-10T10:36:35.739Z","modelVersion":"gemini-3-flash-preview"},"explana

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions