5f1","revisionId":"ce7f07ca-1355-4e06-b9ef-36c6298abe8e","questionNumber":null,"questionType":"LA","specification":"$$XYZ$ is a straight line.\n\n![A straight line segment with points X, Y, and Z marked. X is on the left, Y is in the middle, and Z is on the right. There are small vertical tick marks above each letter.](https://assets.mathsgenie.co.uk/questions/1c1c8690-0151-4eff-b93e-51014e00f26e.png)","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"fbdba614-572a-49c0-8bb0-60960a4cb7ad","label":"a","content":"The length of $YZ$ is three times the length of $XY$.\n\n$YZ = 45$ metres.\nWork out the length $XZ$.","markscheme":"- Calculate $XY$: $45 \\div 3 = 15$ M1\n- Calculate $XZ$ method: $45 + 15$ M1\n- Final length $XZ$: $60$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Evidence of dividing 45 by 3 to find XY.","code":"M"},{"id":"p2","marks":1,"description":"Evidence of adding the two segment lengths (45 + 15).","code":"M"},{"id":"p3","marks":1,"description":"Correct final length of 60 metres.","code":"A"}],"finalAnswers":["60","60 m"],"generatedAt":"2026-05-06T14:05:33.325Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"divide_then_add","label":"Divide, then add","steps":[{"type":"text","order":0,"title":"Interpret the comparison","content":"$$YZ$ consists of three equal lengths, each the same length as $XY$.","highlights":[{"text":"The length of $YZ$ is three times the length of $XY$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$XY=\\htmlData{anchor=known_division}{\\color{@sky}{45\\div3}}$"},{"latex":"$$XY=\\htmlData{anchor=short_length}{\\color{@green}{15}}$"}],"highlights":[{"color":"sky","anchor":"known_division"},{"color":"green","anchor":"short_length"}],"connections":[{"to":"short_length","from":"known_division","color":"sky","label":"calculate"}]},"order":1,"title":"Find the shorter length","description":"Dividing the known length by three finds XY. Writing this calculation earns the first method mark; lengths are measured in metres."},{"type":"text","order":2,"title":"Form the whole length","content":"Because $Y$ lies between $X$ and $Z$ on the straight line, the whole length is the sum of the two adjacent sections:\n\n$$XZ=XY+YZ$$","highlights":[{"text":"$$XYZ$ is a straight line.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$XZ=\\htmlData{anchor=section_sum}{\\color{@sky}{15+45}}$"},{"latex":"$$XZ=\\htmlData{anchor=whole_length}{\\color{@green}{60\\text{ metres}}}$"}],"highlights":[{"color":"sky","anchor":"section_sum"},{"color":"green","anchor":"whole_length"}],"connections":[{"to":"whole_length","from":"section_sum","color":"sky","label":"add"}]},"order":3,"title":"Calculate the whole length","description":"Add the two adjacent sections to get the whole length. Writing 15 + 45 earns the second method mark, and the correct final answer, 60 metres, earns the accuracy mark."}]}],"generatedAt":"2026-07-19T07:02:02.198Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"e2ec14a5-d809-46a2-a4ae-57c1b85830ec","revisionId":"880fad73-99b8-427d-badb-a041f6d014c9","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"65b314cb-c3d9-4a0a-81ad-7e2e05c45b67","label":"a","content":"A builder makes a concrete mix using sand, cement, and gravel.\n\nThe masses of sand, cement, and gravel used are in the ratio $2 : 3 : 10$ respectively.\n\nThe mass of gravel used is $32\\text{ kg}$ more than the mass of sand used.\n\nWork out the total mass of the concrete mix.","markscheme":"- Difference in ratio parts (Gravel - Sand): $10 - 2 = 8$ M1\n- Value of one part: $32 \\div 8 = 4$ M1\n- Total mass: $(2 + 3 + 10) \\times 4

Ratio

Question 30

Ratio Questions

Ratio

Question 30

Ratio Questions