ers are therefore\n\n$$\\boxed{4\\text{ and }8}$$\n\nThese total $30$ with the other cards, giving a mean of $5$, and $4$ is the only number that appears twice. The correct pair earns **A1**.","highlights":[{"text":"Work out the two numbers that are hidden.","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:59:28.362Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"61e02b0a-58d0-4cbb-9989-cbb6f1dde9f0","revisionId":"cb047394-2744-4cb4-9b4e-53803680d065","questionNumber":"11","questionType":"LA","specification":"","difficulty":3,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"c1a688dc-c6ba-4ee5-8c01-c2695a3938d1","label":"","content":"The mean of eight numbers is 41. The mean of two of the numbers is 29. Work out the mean of the other six numbers.","markscheme":"- Total sum of 8 numbers: $8 \\times 41 = 328$ M1\n- Total sum of 2 numbers: $2 \\times 29 = 58$\n- Sum of remaining 6: $328 - 58 = 270$ M1\n- Mean of 6: $270 \\div 6 = 45$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates total sum of all 8 numbers (328).","code":"M"},{"id":"p2","marks":1,"description":"Calculates sum of remaining 6 numbers (270).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 45.","code":"A"}],"finalAnswers":["45"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"total_and_subtract","label":"Use totals then subtract","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{total of 8}=\\color{@sky}{8\\times41}=328$"},{"latex":"$$\\text{total of 2}=\\color{@amber}{2\\times29}=58$"}]},"order":1,"title":"Find both totals","description":"To find a total from a mean, multiply the mean by the number of values. Calculate each total. The first calculation earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{sum of remaining 6}=328-58=\\color{@green}{270}$"},{"text":"This earns the second M1 mark."}]},"order":2,"title":"Find remaining total","description":"Remove the two-number total from the eight-number total."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{mean of remaining 6}=270\\div 6=\\color{@teal}{45}$"},{"text":"This earns the A1 mark."}]},"order":3,"title":"State the mean","description":"Share the remaining total equally among the six numbers."}]}],"generatedAt":"2026-07-21T04:10:52.134Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"fe426d45-33bf-4d51-b49c-31d49611a0da","revisionId":"97e4eb74-ac66-49fc-9c4e-d150a8228ce7","questionNumber":"12","questionType":"LA","specification":"","difficulty":3,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"afa0ccfc-2a6f-4f6e-94d2-8a5ea9957747","label":"","content":"Mark ran a mean distance of 13.2 km in five days. The next day Mark ran 20 km. Find the mean distance Mark ran in the six days.","markscheme":"- Total distance for 5 days: $13.2 \\times 5 = 66$ km M1\n- Total distance for 6 days: $66 + 20 = 86$ km M1\n- New mean: $86 \\div 6 = 14.3$ km (to 1 d.p.) A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates total distance for first 5 days (66).","code":"M"},{"id":"p2","marks":1,"description":"Calculates total distance for 6 days (86).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 14.3 (or $14.3\\dot{3}$).","code":"A"}],"finalAnswers":["14.3"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"total_then_divide","label":"Total then divide","steps":[{"type":"text","

Averages

Question 2

Averages Questions

Averages

Question 2

Averages Questions