me":"- Substitutes values: $2(7) - (7)(3) = 14 - 21$ M1\n- Final answer: $-7$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correct substitution of $j=7$ and $k=3$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of -7.","code":"A"}],"finalAnswers":["-7"],"generatedAt":"2026-05-07T01:46:44.062Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"substitution","label":"Substitute the values","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"A=2j-jk"},{"latex":"A=\\htmlData{anchor=substituted}{\\color{@sky}{2(7)-(7)(3)}}"},{"latex":"A=\\htmlData{anchor=result}{\\color{@green}{14-21}}"}],"connections":[{"to":"result","from":"substituted","color":"sky","label":"multiply"}]},"order":1,"title":"Substitute carefully","description":"Use j = 7 and k = 3, keeping brackets around the substituted values so the multiplication is clear. This substitution and product calculation earns M1: it shows both the substitution and the products evaluated."},{"type":"text","order":2,"title":"Subtract","content":"Now subtract $21$ from $14$:\n\n$$A=14-21=-7$$\n\nThis earns A1 for the final answer, $A=-7$."}]}],"generatedAt":"2026-07-21T04:49:21.784Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"75aad16e-b795-4d5d-bf80-6965408a2216","revisionId":"1cf184b6-8964-4a0e-93d5-face74941362","questionNumber":"20","questionType":"LA","specification":"$$w = 5x^2 + 3$\n$x = -3$","difficulty":2,"difficultyBand":null,"totalMarks":2,"sourceTitle":"Substitution","calculatorUse":null,"parts":[{"id":"1e6ffea0-2c35-475a-bdec-15eb71b269bd","label":"0","content":"Work out the value of $w$.","markscheme":"- Substitutes value and squares: $5(-3)^2 + 3 = 5(9) + 3$ M1\n- Final answer: $48$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correct substitution and squaring of $x=-3$ (resulting in 9).","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 48.","code":"A"}],"finalAnswers":["48"],"generatedAt":"2026-05-07T01:46:44.062Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"substitute_then_evaluate","label":"Substitute then evaluate","steps":[{"type":"text","order":0,"title":"Substitute the value","content":"Put $x=-3$ into the formula for $w$. Keep the negative number in brackets before applying the square.\n\nThis substitution and squaring is the key method mark (M1).","highlights":[{"text":"$$x = -3$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"w=5\\left(-3\\right)^2+3"},{"latex":"w=5\\left(9\\right)+3"},{"latex":"w=45+3"},{"latex":"w=\\htmlData{anchor=answer}{\\color{@orange}{48}}\\quad\\text{(final accuracy mark, A1)}"}],"highlights":[{"color":"orange","style":"text-color-with-background","anchor":"answer"}]},"order":1,"title":"Square before multiplying","description":"Square the substituted negative number before multiplying by 5."}]}],"generatedAt":"2026-07-21T04:21:58.760Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"5e853ad3-5cfc-4e20-809a-9a1aada5eb98","revisionId":"b07953d6-b18d-4c8f-8bed-bc7086a76d7e","questionNumber":"21","questionType":"LA","specification":"$$A = \\frac{1}{2}bh$","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":"Substitution","calculatorUse":null,"parts":[{"id":"b8b0cfb0-f50f-4005-a13c-368d7c7ecb05","label":"0","content":"Work out the value of $A$ when $b = 3$ and $h = 8$","markscheme":"- Substitutes values: $\\frac{1}{2}(3)(8)$ M1\n- Final answer: $12$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correct substitution of $b=3$ and $h=8$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 12.","code":"A"}],"finalAnswers":["12"],"generatedAt":"2026-

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