and":null,"totalMarks":3,"sourceTitle":"Factorising Harder Quadratics","calculatorUse":null,"parts":[{"id":"5b44b71d-3ab0-43fa-964b-7e3fc0a5e380","label":"a","content":"Solve $5x^2 - 37x - 24 = 0$","markscheme":"- Factorises the quadratic into $(5x + 3)(x - 8)$ M1\n- Sets factors to zero to find solutions M1\n- Final answers $x = -\\frac{3}{5}$ and $x = 8$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correctly factorises the quadratic into $(5x + 3)(x - 8)$.","code":"M"},{"id":"p2","marks":1,"description":"Sets factors to zero to solve for $x$.","code":"M"},{"id":"p3","marks":1,"description":"Final answers $x = -\\frac{3}{5}$ and $x = 8$.","code":"A"}],"finalAnswers":["x = -3/5, x = 8"],"generatedAt":"2026-05-07T02:06:38.085Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"factorising","label":"Factorise then solve","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"5x^2-37x-24=0"},{"latex":"(5x+3)(x-8)=0"}]},"order":0,"title":"Factorise the quadratic","description":"The cross-products are negative 40x and positive 3x, which add to negative 37x. This correct factorisation earns the first method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"(5x+3)(x-8)=0"},{"latex":"5x+3=0"},{"latex":"x-8=0"}]},"order":1,"title":"Set each factor zero","description":"A product is zero when at least one factor is zero, so set each factor equal to zero; this earns the second method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=eqone}{5x+3=0}"},{"latex":"\\htmlData{anchor=solone}{x=-\\frac{3}{5}}"},{"latex":"\\htmlData{anchor=eqtwo}{x-8=0}"},{"latex":"\\htmlData{anchor=soltwo}{x=8}"}],"connections":[{"to":"solone","from":"eqone","color":"orange","label":"subtract 3; divide by 5"},{"to":"soltwo","from":"eqtwo","color":"green","label":"add 8"}]},"order":2,"title":"Solve both equations","description":"Rearrange each equation. Obtaining both final solutions earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-21T03:19:22.648Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"23334b17-ffaa-487c-be33-f6d1c6a211c3","revisionId":"c71a6ead-49cf-4bb1-b2f7-8e0b5db481dd","questionNumber":"13","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":"Factorising Harder Quadratics","calculatorUse":null,"parts":[{"id":"60f8c2b9-3cb9-47a9-b616-ed220cfd1065","label":"a","content":"Factorise $6x^2 + 17x + 12$","markscheme":"- Identifies factors of $ac = 72$ that sum to 17 (8 and 9) M1\n- Final answer $(3x + 4)(2x + 3)$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies factors of 72 that sum to 17.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $(3x + 4)(2x + 3)$.","code":"A"}],"finalAnswers":["(3x + 4)(2x + 3)"],"generatedAt":"2026-05-07T02:06:38.085Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"split_middle_term","label":"Split the middle term","steps":[{"type":"text","order":0,"title":"Multiply outer coefficients","content":"For a quadratic of the form $ax^2+bx+c$, multiply $a$ and $c$. Here, $6\\times12=72$.\n\nWe now need two factors of $72$ that add to the middle coefficient, $17$.","highlights":[{"text":"Factorise $6x^2 + 17x + 12$","location":"specification"}]},{"type":"text","order":1,"title":"Choose the factor pair","content":"The pair $8$ and $9$ works because $8\\times9=72$ and $8+9=17$.\n\nIdentifying this pair earns the **M1** mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=start}{6x^2+17x+12}"},{"latex":"6x^2+\\htmlData{anchor=split}{8x+9x}+12"},{"latex":"\\htmlData{anchor=groups}{2x(3x+4)+3(3x+4)}"},{"latex":"\\htmlData{anchor=factorised}{(3x+4)(2x+3)}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"split"},{"color":"green"

Factorising Harder Quadratics Questions

Factorising Harder Quadratics Questions

Factorising Harder Quadratics Questions

Factorising Harder Quadratics Questions