/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":45,"initialQuestionWindow":[{"id":"ab4659be-4d0d-44e0-b43f-1b830c59ad29","revisionId":"1af0de4b-d93f-410c-9402-575ac22c3bd0","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"55d25f81-c91f-4268-be35-e2a36bd0f979","label":"a","content":"Solve $\\frac{5}{y - 3} - \\frac{2}{y + 1} = 1$","markscheme":"- Multiply by common denominator: $5(y + 1) - 2(y - 3) = 1(y - 3)(y + 1)$ M1\n- Expand and simplify: $3y + 11 = y^2 - 2y - 3$ M1\n- Rearrange to $y^2 - 5y - 14 = 0$ M1\n- Factorise $(y - 7)(y + 2) = 0$ to get $y = 7$ or $y = -2$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply the equation by the common denominator $(y-3)(y+1)$.","code":"M"},{"id":"p2","marks":1,"description":"Expand the brackets and simplify the expressions on both sides.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange the expression into the quadratic form $y^2 - 5y - 14 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Factorise and solve the quadratic equation to find both $y$ values.","code":"A"}],"finalAnswers":["y = 7, y = -2"],"generatedAt":"2026-08-10T10:36:37.963Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ae9d8c75-4b9a-483e-8812-7b3088dfb19d","revisionId":"67ee7225-0533-4ee6-b3b4-3c8cbc98b88d","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"d56a44fc-bbd1-4e12-98a2-5f69af768781","label":"a","content":"Write $\\frac{x^2 + 8x + 12}{5x^2 + 13x + 6}$ in the form $\\frac{x + a}{bx + c}$ where $a$, $b$, and $c$ are integers.","markscheme":"- Factorise numerator: $(x + 6)(x + 2)$ M1\n- Factorise denominator: $(5x + 3)(x + 2)$ M1\n- Cancel common factor $(x + 2)$ to get $\\frac{x + 6}{5x + 3}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct factorisation of $x^2 + 8x + 12$ into $(x + 6)(x + 2)$.","code":"M"},{"id":"p2","marks":1,"description":"Correct factorisation of $5x^2 + 13x + 6$ into $(5x + 3)(x + 2)$.","code":"M"},{"id":"p3","marks":1,"description":"Simplification to $\\frac{x+6}{5x+3}$.","code":"A"}],"finalAnswers":["\\frac{x+6}{5x+3}"],"generatedAt":"2026-08-10T10:37:54.427Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"b452c7f4-d413-4e9f-abe7-4f8a8d7e4729","revisionId":"17abdf65-519e-4a51-9a88-a06707c0cdee","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"c0c48164-add1-45a0-8c43-47536d4570c1","label":"a","content":"Simplify fully $\\frac{2x+10}{x-3} \\div \\frac{5x^2+24x-5}{x^2-3x}$","markscheme":"- Invert second fraction and multiply: $\\frac{2x+10}{x-3} \\times \\frac{x^2-3x}{5x^2+24x-5}$ M1\n- Factorise all terms: $\\frac{2(x+5)}{x-3} \\times \\frac{x(x-3)}{(5x-1)(x+5)}$ M1\n- Cancel common factors to get $\\frac{2x}{5x-1}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Applies the rule for division of fractions by inverting the second fraction.","code":"M"},{"id":"p2","marks":1,"description":"Factors the quadratic expression into two linear binomials correctly.","code":"M"},{"id":"p3","marks":1,"description":"Fully simplifies the algebraic fraction.","code":"A"}],"finalAnswers":["\\frac{2x}{5x-1}"],"generatedAt":"2026-08-10T10:36:26.850Z","modelVersion":"gemini-3-flash-preview"},"explanation

Algebraic Fractions

Question 44

Algebraic Fractions Questions

Algebraic Fractions

Question 44

Algebraic Fractions Questions