0$ cm) M1\n- Explains that the ratio of extension to force is constant (equal to $3.0\\text{ cm/N}$) or that the relationship would produce a straight-line graph passing through the origin $(0,0)$ A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"check_proportionality","label":"Check for proportionality","steps":[{"type":"text","order":1,"title":"State the judgement","content":"The student's conclusion is **correct**: the data fully support that extension is directly proportional to applied force. This earns the **B1** mark.","highlights":[{"text":"*\"The extension of the spring is directly proportional to the force applied.\"*","location":"specification"}]},{"type":"text","order":2,"title":"Give data evidence","content":"For example, when the force doubles from $1.0\\ \\text{N}$ to $2.0\\ \\text{N}$, the extension also doubles from $3.0\\ \\text{cm}$ to $6.0\\ \\text{cm}$. This numerical comparison earns the **M1** mark.","highlights":[{"text":"| 1.0 | 3.0 |","location":"specification"},{"text":"| 2.0 | 6.0 |","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{\\htmlData{anchor=extension-one}{3.0\\text{ cm}}}{1.0\\text{ N}}=\\htmlData{anchor=ratio-one}{3.0\\text{ cm/N}}"},{"latex":"\\frac{\\htmlData{anchor=extension-two}{6.0\\text{ cm}}}{2.0\\text{ N}}=\\htmlData{anchor=ratio-two}{3.0\\text{ cm/N}}"},{"latex":"\\frac{\\text{extension}}{\\text{force}}=\\htmlData{anchor=constant-ratio}{3.0\\text{ cm/N}}\\quad\\text{for every row}"}],"highlights":[{"color":"green","style":"box","anchor":"constant-ratio"}],"connections":[{"to":"ratio-two","from":"ratio-one","color":"green","label":"same value"}]},"order":3,"title":"Check the ratio","description":"For direct proportionality, dividing extension by force must give the same value each time. Both calculations give 3.0 cm/N, and checking the remaining rows gives the same ratio. Therefore the extension is directly proportional to force. This earns A1."}]}],"generatedAt":"2026-07-22T11:57:09.824Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ba94ddaa-f4ab-4f64-9ff2-f3c374c3e28c","revisionId":"bf2d2031-89f0-45e5-88fb-5da9a415dc8c","questionNumber":null,"questionType":"LA","specification":"A student concludes that the extension of a spring is directly proportional to the force applied to it.\n\n![A line graph showing the relationship between Force and Extension. The x-axis is labeled 'Force in N' and ranges from 0.0 to 6.0. The y-axis is labeled 'Extension in mm' and ranges from 0.0 to 25.0. A straight line is drawn through the origin (0, 0) and two data points marked with 'x' at (1.0, 3.5) and (2.0, 7.0).](https://assets.mathsgenie.co.uk/aqa-qb/9f40a0a2-0c48-4d6e-8263-9421967f449f.png)\n\n| Force in N | Extension in mm |\n|---|---|\n| 0.0 | 0.0 |\n| 1.0 | 3.5 |\n| 2.0 | 7.0 |","difficulty":5,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"d32be6bf-7c7d-41ef-ae82-ddd23b0c8157","label":null,"content":"Explain what the student must do to test this conclusion in more detail.","markscheme":"- Suggests collecting more data points over a wider range of forces (e.g. up to $5.0$ N or $6.0$ N) and/or using smaller, regular intervals (e.g. every $0.5$ N) M1\n- Suggests plotting these new data points on the graph to check if they continue to lie on a straight line M1\n- Confirms that the line of best fit continues to pass through the origin $(0,0)$, or calculates the ratio of extension to force for each point to verify that it remains constant A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"extend_the_test","label":"Extend the test","steps":[{"type":"text","order":0,"title":"Take more readings","content":"The conclusion is based on only two non-zero force readings, so test many more forces over a wider range, for example up to $6.0\\ \\mathrm{N}$. Use smaller regular interva

Force (N)	Extension (cm)
0.5	1.5
1.0	3.0
1.5	4.5
2.0	6.0
2.5	7.5
3.0	9.0

Force (N)	Extension (cm)
0.5	1.5
1.0	3.0
1.5	4.5
2.0	6.0
2.5	7.5
3.0	9.0

Forces and springs

Question 23

Forces and springs Questions

Forces and springs

Question 23

Forces and springs Questions