content":"Simplify $8g + 6h - 3g + h$","markscheme":"- Simplifies $g$ terms to $5g$ or $h$ terms to $7h$ M1\n- Final answer $5g + 7h$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Simplifies one set of terms correctly (either $5g$ or $7h$).","code":"M"},{"id":"p2","marks":1,"description":"Final answer $5g + 7h$.","code":"A"}],"finalAnswers":["5g + 7h"],"generatedAt":"2026-05-06T15:39:12.821Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"collect_like_terms","label":"Collect like terms","steps":[{"type":"text","order":0,"title":"Identify like terms","content":"Terms are **like terms** when they have the same letter. Here, $8g$ and $-3g$ are like terms, while $6h$ and $h$ are like terms.\n\nKeep the $g$ terms separate from the $h$ terms; they cannot be combined with each other.","highlights":[{"text":"Simplify $8g + 6h - 3g + h$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=grouped}{\\color{@sky}{(8g-3g)+(6h+h)}}"},{"latex":"\\htmlData{anchor=answer}{\\color{@green}{5g+7h}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"grouped"},{"color":"green","style":"text-color","anchor":"answer"}],"connections":[{"to":"answer","from":"grouped","color":"green","label":"add coefficients","style":"solid"}]},"order":1,"title":"Collect each letter","description":"Simplifying either the g terms to 5g or the h terms to 7h earns M1; the completed answer 5g + 7h earns A1."}]}],"generatedAt":"2026-07-21T03:54:43.051Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":80,"sampleSize":56}},{"id":"c6cd2ccd-4664-4b91-b75a-96a3806476b6","revisionId":"f032c578-be59-4e8a-8ffc-113b4d32e6de","questionNumber":"8","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Simplifying Algebra","calculatorUse":null,"parts":[{"id":"140afec0-7740-4758-923b-55f9f1f9181c","label":"a","content":"Simplify $3 \\times b \\times 9$","markscheme":"- Final answer $27b$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Final answer $27b$.","code":"B"}],"finalAnswers":["27b"],"generatedAt":"2026-05-06T15:39:12.821Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"multiply_coefficients","label":"Multiply the coefficients","steps":[{"type":"text","order":0,"title":"Group the numbers","content":"Multiplication can be done in any order, so multiply the two numbers first and keep $b$ as a factor:\n\n$$3\\times b\\times 9=(3\\times9)b.$$","highlights":[{"text":"Simplify $3 \\times b \\times 9$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=product}{\\color{@sky}{3\\times9}}=27"},{"latex":"(3\\times9)b=\\htmlData{anchor=answer}{27b}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"product","color":"sky","label":"use the product","style":"solid"}]},"order":1,"title":"Write the simplified term","description":"Multiply the numerical coefficients, then write the letter beside the result. This earns the B1 mark for the correct simplified answer, $27b$."}]}],"generatedAt":"2026-07-21T03:55:16.280Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"e58600df-16b0-439e-b323-609d4b9bd257","label":"b","content":"Simplify $2x - 3y - 6x - 4y$","markscheme":"- Simplifies $x$ terms to $-4x$ or $y$ terms to $-7y$ M1\n- Final answer $-4x - 7y$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Simplifies one set of terms correctly (either $-4x$ or $-7y$).","code":"M"},{"id":"p2","marks":1,"description":"Final answer $-4x - 7y$.","code":"A"}],"finalAnswers":["-4x - 7y"],"generatedAt":"2026-05-06T15:39:12.821Z","modelVersion":"gemini-3-flash-preview"},

Simplifying Algebra Questions

Simplifying Algebra Questions

Simplifying Algebra Questions

Simplifying Algebra Questions