e different literal factors together. B1 for the final answer."}]}],"generatedAt":"2026-07-21T03:56:19.686Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"e323ee98-e472-40e9-bf87-dd1e72b08302","label":"b","content":"Simplify $15p^3 \\div 3p^4$","markscheme":"- Award method mark for $5$ or $p^{-1}$ M1\n- Final answer $5p^{-1}$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly divides coefficients to get 5 or applies index law to get $p^{-1}$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $5p^{-1}$ or $\\frac{5}{p}$.","code":"A"}],"finalAnswers":["5p^{-1}","\\frac{5}{p}"],"generatedAt":"2026-05-07T01:51:00.219Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"index_laws","label":"Use index laws","steps":[{"type":"text","order":0,"title":"Split the division","content":"Treat the numbers and the powers of $p$ separately:\n\n$$15p^3 \\div 3p^4=\\left(15\\div3\\right)\\left(p^3\\div p^4\\right).$$\n\nFor powers with the same base, division means **subtract the exponents**."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=start}{15p^3\\div3p^4}"},{"latex":"\\htmlData{anchor=middle}{5p^{3-4}}"},{"latex":"\\htmlData{anchor=final}{5p^{-1}}"}],"connections":[{"to":"middle","from":"start","color":"sky","style":"dashed"},{"to":"final","from":"middle","color":"orange","style":"solid"}]},"order":1,"title":"Apply the index law","description":"Divide the numerical coefficients, then subtract the exponent in the denominator from the exponent in the numerator. Getting either the coefficient 5 or p to the power of negative 1 earns M1. Combining them as 5p to the power of negative 1 earns A1."}]}],"generatedAt":"2026-07-21T04:04:44.799Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":79,"sampleSize":43}},{"id":"e881f4ba-85b0-4bd3-ae05-abb7e653e219","revisionId":"39458a7b-3692-4762-b5db-f628471e72a5","questionNumber":"4","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Indices","calculatorUse":null,"parts":[{"id":"b91813a0-cba2-4fe7-a603-51575bfc9064","label":"a","content":"Simplify $(t^3)^4$","markscheme":"- Final answer $t^{12}$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Final answer $t^{12}$.","code":"B"}],"finalAnswers":["t^{12}"],"generatedAt":"2026-05-07T01:51:00.219Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"power_of_a_power","label":"Power of a power","steps":[{"type":"text","order":0,"title":"Use the power rule","content":"The expression is a **power raised to another power**. Multiply the exponents: $(t^a)^b=t^{ab}$.","highlights":[{"text":"Simplify $(t^3)^4$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\left(t^3\\right)^4=t^{\\htmlData{anchor=product}{\\color{@sky}{3\\times4}}}"},{"latex":"t^{\\htmlData{anchor=answer}{\\color{@green}{12}}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"product","color":"green","label":"multiply"}]},"order":1,"title":"Multiply the exponents","description":"Keep the base t and multiply the two exponents. B1: multiply the exponents to obtain t to the power of 12."}]}],"generatedAt":"2026-07-21T02:51:52.181Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"47b4d0d3-c347-4549-b521-cee2f45225c0","label":"b","content":"Simplify $12m^2n^6 \\div 3mn^4$","markscheme":"- Award method mark for two correct terms out of three (e.g., $4m$ or $n^2$) M1\n- Final answer $4mn^2$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly simplifies two of the three components (coefficient, $m$, or $n$).","code":"M"},{"id":"p2","marks":1,"description":"F

Indices Questions

Indices Questions

Indices Questions

Indices Questions