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formula.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $\\frac{1}{2}$ or $0.5$.","code":"A"}],"finalAnswers":["1/2","0.5"],"generatedAt":"2026-05-07T01:56:01.132Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"gradient_formula","label":"Use the gradient formula","steps":[{"type":"text","order":0,"title":"Identify the coordinates","content":"The two points are $(-3,4)$ and $(5,8)$. Write each as $(x,y)$, so the changes can be found in the same order: second point minus first point.","highlights":[{"text":"passes through $(-3, 4)$ and $(5, 8)$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"m=\\frac{y_2-y_1}{x_2-x_1}"},{"text":"Use the second point minus the first point in both the numerator and denominator."},{"latex":"m=\\frac{8-4}{5-(-3)}"}]},"order":1,"title":"Substitute into the formula","description":"Gradient means vertical change divided by horizontal change. Substituting the coordinates correctly earns the method mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"m=\\frac{8-4}{5-(-3)}"},{"latex":"m=\\frac{4}{8}"},{"text":"Divide the numerator and denominator by 4."},{"latex":"\\boxed{m=\\frac{1}{2}}"}]},"order":2,"title":"Simplify the fraction","description":"Calculate the two differences, then simplify the fraction. The final boxed answer earns the accuracy mark."}]}],"generatedAt":"2026-07-21T03:59:46.990Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":69},"walkthroughVideo":null},{"id":"e46b2f61-2614-4a13-b2ab-b93d514b48e1","revisionId":"a1ab6523-2e14-4239-b796-79fee8595d6d","questionNumber":"10","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Gradient of a Line","calculatorUse":null,"isCalculation":true,"parts":[{"id":"0ac8bfd4-77c7-476d-b00f-e074b781f99b","label":"","content":"Find the gradient of the line that passes through $(3, 7)$ and $(1, 10)$.","markscheme":"- Use of $m = \\frac{y_2 - y_1}{x_2 - x_1}$, e.g., $\\frac{10 - 7}{1 - 3}$ M1\n- Final answer -1.5 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correct substitution into the gradient formula.","code":"M"},{"id":"p2","marks":1,"description":"Final answer -1.5 or $-\\frac{3}{2}$.","code":"A"}],"finalAnswers":["-1.5","-3/2"],"generatedAt":"2026-05-07T01:56:01.132Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"gradient_formula","label":"Use the gradient formula","steps":[{"type":"text","order":0,"title":"Set up the changes","content":"From $(3,7)$ to $(1,10)$, the vertical change is $10-7=3$ and the horizontal change is $1-3=-2$.\n\nUse the gradient formula:\n$$m=\\frac{\\text{change in }y}{\\text{change in }x}=\\frac{10-7}{1-3}=\\frac{3}{-2}$$\nWriting this formula with the coordinate differences earns **M1**.","highlights":[{"text":"passes through $(3, 7)$ and $(1, 10)$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"m=\\htmlData{anchor=wholefraction}{\\color{@sky}{\\frac{3}{-2}}}"},{"latex":"m=\\htmlData{anchor=finalgradient}{\\color{@green}{-1.5}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"finalgradient"}],"connections":[{"to":"finalgradient","from":"wholefraction","color":"green","label":"divide"}]},"order":1,"title":"Divide the changes","description":"Divide the vertical change by the horizontal change. The negative horizontal change makes the gradient negative. m = -1.5 is the final answer, earning A1."}]}],"generatedAt":"2026-07-21T04:13:09.475Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":79},"walkthroughVideo":null}],"subjectCode":"igcse_maths","summaries":[{"id":"fa899f43-fbad-4cab-8973-1dff524a1446","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"e12c08b9-3d80-4812-8a9f-6cdfd38bc4f8","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"13b8ee25-ef17-486c-a8d5-93f42f684e03","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"e46b2f61-2614-4a13-b2ab-b93d514b48e1","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"5f640781-d36e-49c8-a664-b54d4c48225f","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"4278ac65-1e23-4cb5-b08f-63b259fad0ba","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"44ebcf99-99bf-4dc4-a2ee-b45efe585521","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b3db6a40-ab0e-417a-86a8-c1ca17f2308a","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"81c967ca-65d8-4392-b326-d3ba29f864e0","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c7aa15f4-8747-41e0-8a4a-5006ad3fd6a2","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6212a79a-763d-49b1-852f-34a1bfe25b8b","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"05d65941-8bd3-4400-b588-9daad5244073","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true}],"title":"Gradient of a Line","topicId":"49af1960-7f5b-407b-8bc0-7c9b35604868","topicSidebar":"$L3b","topicSlug":"grade-6-6-7-gradient-of-a-line","topicTitle":"Gradient of a Line"}]}],"$L3c","$L3d"]}]