Type `2 * pi * 3.2` in the expression box."},"description":"Calculate the circumference using the exact value of pi."}]},{"type":"text","order":3,"title":"Round the final answer","content":"The question asks for the answer correct to **2 decimal places**.\n\nLet's look at the third decimal digit of our value $20.10\\underline{6}1...$\n\nSince this digit ($6$) is $5$ or more, we round up the second decimal place from $0$ to $1$:\n\n$$C \\approx 20.11\\text{ m}$$\n\nThis final rounded value completes the third mark.","highlights":[{"text":"correct to 2 decimal places","location":"specification"}]}]},{"id":"14106c6a-8364-4ced-beac-7a401d9d8959:diameter_formula","label":"Using Diameter Formula","steps":[{"type":"text","order":0,"title":"Calculate the diameter","content":"First, we find the diameter of the circular pond. The diameter ($d$) is twice the length of the radius ($r$).\n\nGiven that the radius is $3.2\\text{ m}$:\n\n$$d = 2 \\times 3.2\\text{ m} = 6.4\\text{ m}$$","highlights":[{"text":"radius of 3.2 m","location":"specification"}]},{"type":"text","order":1,"title":"Apply circumference formula","content":"Next, we use the circumference formula that uses the diameter:\n\n$$C = \\pi d$$\n\nSubstituting our diameter $d = 6.4\\text{ m}$ into the formula gives:\n\n$$C = \\pi \\times 6.4$$\n\nThis earns the first method mark M1."},{"type":"text","order":2,"title":"Calculate the value","content":"Now, we calculate the numerical value of the circumference:\n\n$$C = 6.4\\pi \\approx 20.10619298...\\text{ m}$$\n\nThis calculation earns the second method mark M1.","calculator":[{"gdc":{"expression":"6.4 * \\pi","instructions":"Enter `6.4 * π` on the main run screen and press `EXE`."},"ti84":{"expression":"6.4 * \\pi","instructions":"Type `6.4` followed by `*` and then press `2nd` then `^` (to get $\\pi$). Press `ENTER`."},"desmos":{"expression":"6.4\\pi","instructions":"Type `6.4 * pi` in the input bar to see the decimal result."},"description":"Calculate the circumference on a calculator using the $\\pi$ button."}]},{"type":"text","order":3,"title":"Round to 2 d.p.","content":"Finally, we round our answer to $2$ decimal places as requested:\n\n$$20.10619... \\rightarrow 20.11\\text{ m}$$\n\nSince the third decimal digit ($6$) is $5$ or greater, we round up the second decimal digit ($0$) to $1$.\n\nThis final rounded answer earns the accuracy mark A1.","highlights":[{"text":"correct to 2 decimal places","location":"specification"}]}]}],"generatedAt":"2026-06-12T17:57:27.758Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"bf61ac5d-8ed9-44c8-a085-306f42112edd","revisionId":"fb3dcf8d-9a2d-41f0-82f1-2a9ea2b36bd3","questionNumber":null,"questionType":"LA","specification":"A square garden of side length $12\\text{ m}$ has a circular pond in the center. \nThe pond touches all four sides of the garden boundary.","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"58cf7a31-68dd-4e1a-bfeb-22dd071e3f39","label":"a","content":"Work out the area of the garden that is not covered by the pond.\nGive your answer correct to 1 decimal place.","markscheme":"- Calculates area of garden: $12 \\times 12 = 144$ M1\n- Calculates area of pond: $\\pi \\times 6^2 = 36\\pi \\approx 113.10$ M1\n- Subtracts areas: $144 - 113.10 = 30.9$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the area of the square garden ($12 \\times 12$)","code":"M"},{"id":"p2","marks":1,"description":"Calculates the area of the circular pond using radius 6 ($\\pi \\times 6^2$)","code":"M"},{"id":"p3","marks":1,"description":"Finds the difference and rounds to 1 decimal place","code":"A","acceptable":["30.9"]}],"finalAnswers":["30.9"],"generatedAt":"2026-05-06T13:59:24.474Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"subtract_pond_area","label":"Subtract the pond area","steps":[{"type

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