7efe-4cf4-8cc1-02e68fdbf90d","label":"a","content":"Draw an ordered stem and leaf diagram to show this information. You must include a key.","markscheme":"- Correct stems 4, 5, 6, 7, 8 B1\n- All leaves correct and ordered B1\n- Correct key, e.g., $4|2 = 42$ points B1\n\n| Stem | Leaf |\n| :--- | :--- |\n| 4 | 2 5 8 9 |\n| 5 | 2 3 5 8 8 9 |\n| 6 | 0 1 2 3 6 7 |\n| 7 | 1 4 7 |\n| 8 | 2 5 |","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct stems: 4, 5, 6, 7, 8","code":"B"},{"id":"p2","marks":1,"description":"All leaves correct and in ascending order","code":"B"},{"id":"p3","marks":1,"description":"Correct key provided (e.g., 4|2 = 42)","code":"B"}],"finalAnswers":[],"generatedAt":"2026-05-06T13:59:10.999Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"ordered_stem_and_leaf","label":"Build an ordered stem-and-leaf diagram","steps":[{"type":"text","order":0,"title":"Write the stems","content":"Use each score's tens digit as its stem. The scores run from $42$ to $85$, so write the stems vertically as $4$, $5$, $6$, $7$ and $8$.\n\nUsing all five correct stems earns the first B1 mark.","highlights":[{"text":"scores achieved by 21 competitors","location":"specification"}]},{"type":"text","order":1,"title":"Place and order leaves","content":"Use each score's units digit as its leaf beside the matching tens stem, then sort the leaves from smallest to largest within each row.\n\n| Stem | Leaf |\n| :---: | :--- |\n| $4$ | $2\\quad 5\\quad 8\\quad 9$ |\n| $5$ | $2\\quad 3\\quad 5\\quad 8\\quad 8\\quad 9$ |\n| $6$ | $0\\quad 1\\quad 2\\quad 3\\quad 6\\quad 7$ |\n| $7$ | $1\\quad 4\\quad 7$ |\n| $8$ | $2\\quad 5$ |\n\nKeep repeated scores as repeated leaves, so the two scores of $58$ give two leaves of $8$. All $21$ leaves are correct and in ascending order, earning the second B1 mark.","highlights":[{"text":"Draw an ordered stem and leaf diagram","location":"specification"}]},{"type":"text","order":2,"title":"Add the key","content":"Finish with a key that explains the place value:\n\n$$4\\mid 2=42\\text{ points}$$\n\nThis correct key earns the final B1 mark.","highlights":[{"text":"You must include a key.","location":"specification"}]}]}],"generatedAt":"2026-07-19T19:28:27.221Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"8971a2cd-4de3-4b48-a520-297da234832b","label":"b","content":"One of the competitors is selected at random. Find the probability that their score was lower than 60.","markscheme":"- Identifies 10 competitors with scores lower than 60 M1\n- Final answer $\\frac{10}{21}$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of identifying 10 values from the data/diagram","code":"M"},{"id":"p2","marks":1,"description":"Final probability as 10/21","code":"A"}],"finalAnswers":["10/21"],"generatedAt":"2026-05-06T13:59:10.999Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"count_favourable_outcomes","label":"Count favourable outcomes","steps":[{"type":"text","order":0,"title":"Interpret the condition","content":"“Lower than” means strictly less than, so include scores below $60$ but do **not** include a score of exactly $60$.","highlights":[{"text":"lower than 60","location":"specification"}]},{"type":"text","order":1,"title":"Count qualifying scores","content":"The scores below $60$ are\n\n$$42,\\ 55,\\ 48,\\ 59,\\ 53,\\ 58,\\ 45,\\ 52,\\ 49,\\ 58.$$\n\nThere are $10$ such competitors. Identifying this count earns **M1**."},{"type":"text","order":2,"title":"Form the probability","content":"Use\n\n$$\\text{probability}=\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}.$$\n\nThere are $10$ favourable competitors out of all $21$ competitors, so\n\n$$\\boxed{\\frac{10}{21}}.$$\n\nThis correct final answer earns **A1**. The fraction is already in its simplest form."}]}],"generatedAt":"2026-07-19T19:29:08.828Z","modelVersio

Stem and Leaf Questions

Stem and Leaf Questions

Stem and Leaf Questions

Stem and Leaf Questions