},{"color":"amber","style":"text-color","anchor":"vol2"}],"connections":[{"to":"mass2","from":"mass1","color":"sky","label":"mass","style":"solid"},{"to":"vol2","from":"vol1","color":"amber","label":"volume","style":"solid"}]},"order":1,"title":"Set up the proportion","description":"Density tells us the relationship between mass and volume. A density of $0.9\\text{ g/cm}^3$ means that $0.9\\text{ g}$ of wood has a volume of exactly $1\\text{ cm}^3$. We can set up a proportion comparing the ratio of mass to volume."},{"type":"text","order":2,"title":"Write the proportion equation","content":"Since mass and volume are directly proportional, we can write the ratio of mass to volume as:\n\n$$\\frac{\\text{mass}_1}{\\text{volume}_1} = \\frac{\\text{mass}_2}{\\text{volume}_2}$$\n\nSubstituting our values in, we get:\n\n$$\\frac{0.9}{1} = \\frac{162}{V}$$\n\nSimplifying the left-hand side, we have:\n\n$$0.9 = \\frac{162}{V}$$"},{"type":"text","order":3,"title":"Solve for the volume","content":"To solve for $V$, we rearrange the equation by multiplying both sides by $V$ and then dividing by $0.9$:\n\n$$\\begin{aligned} 0.9 \\times V &= 162 \\\\[1em] V &= \\frac{162}{0.9} \\end{aligned}$$\n\nTo make this division easier without a calculator, we can multiply both the numerator and denominator by $10$:\n\n$$V = \\frac{1620}{9}$$\n\nNow, divide $1620$ by $9$:\n\n$$V = 180\\text{ cm}^3$$","calculator":[{"gdc":{"expression":"162 / 0.9","instructions":"Enter 162 ÷ 0.9 and hit EXE."},"ti84":{"expression":"162 / 0.9","instructions":"Type 162 / 0.9 and press ENTER."},"desmos":{"expression":"162 / 0.9","instructions":"Type 162/0.9 into the input bar."},"description":"Verify the division calculation using a scientific or graphing calculator."}]},{"type":"text","order":4,"title":"State the final answer","content":"The volume of the wooden block is **$180\\text{ cm}^3$**.\n\n### Markscheme Breakdown\n- **M1**: Correct method shown by setting up the division: $\\frac{162}{0.9}$\n- **A1**: Correct final value of $180$"}]}],"generatedAt":"2026-06-12T13:25:51.226Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"4a7dda08-176c-41b8-ac25-8080d53a2814","revisionId":"43eb2079-a33a-497c-b465-3211f0f97929","questionNumber":null,"questionType":"LA","specification":"Sam rowed 1.5 km in 6 minutes and 50 seconds.\n\nHe assumes he can row 5 km at the same speed.","difficulty":4,"difficultyBand":"hard","totalMarks":6,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"b1c6428f-5414-4a4b-968e-18cc3cfbc943","label":"a","content":"Work out how long it would take Sam to row 5 km.\n\nGive your answer in minutes and seconds to the nearest second.","markscheme":"- Time in minutes: $6 + \\frac{50}{60} = 6.833...$ M1\n- Speed: $\\frac{1.5}{6.833...} = 0.21951...$ km/min M1\n- Time for 5 km: $\\frac{5}{0.21951...} = 22.777...$ minutes M1\n- $0.777... \\times 60 = 46.666...$ seconds M1\n- Final answer 22 mins 47 secs A1","marks":5,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Method to convert 6 minutes 50 seconds to minutes (6.833...) or seconds.","code":"M"},{"id":"p2","marks":1,"description":"Method to find speed or a relevant distance/time multiplier.","code":"M"},{"id":"p3","marks":1,"description":"Method to find total time for 5 km (e.g. $22.77...$ mins).","code":"M"},{"id":"p4","marks":1,"description":"Final answer of 22 minutes 47 seconds to the nearest second.","code":"A"}],"finalAnswers":["22 mins 47 secs","22 minutes 47 seconds"],"generatedAt":"2026-05-06T14:06:28.905Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"speed_in_km_per_minute","label":"Find speed in km per minute","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$t=6+\\color{@sky}{\\htmlData{anchor=seconds}{\\dfrac{50}{60}}}$"},{"latex":"$$t=\\color{@sky}{\\htmlData{anchor=time}{6.833\\ldots}}\\text{ minutes}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"seconds"},{"col

Speed and Density

Question 20

Speed and Density Questions

Speed and Density

Question 20

Speed and Density Questions