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4900 = 62500$ M1\n- $L = \\sqrt{62500} = 250\\text{ cm}$ or $2.5\\text{ m}$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts units to be consistent.","code":"B","acceptable":["$$2.4\\text{ m}=240\\text{ cm}$"]},{"id":"p2","marks":1,"description":"Applies Pythagoras using consistent units.","code":"M","acceptable":["$$240^2+70^2=L^2$"]},{"id":"p3","marks":1,"description":"Correctly evaluates the sum of the squares.","code":"M","acceptable":["$$L^2=57600+4900=62500$"]},{"id":"p4","marks":1,"description":"Finds the exact length of the ladder.","code":"A","acceptable":["$$L=\\sqrt{62500}=250\\text{ cm}$","$$L=2.5\\text{ m}$"]}],"finalAnswers":["$$250\\text{ cm}$","$$2.5\\text{ m}$"],"generatedAt":"2026-09-22T15:37:57.428Z","modelVersion":"gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"5e7b5350-5f43-418d-a3a6-500b3d92b4ac","revisionId":"e88780ae-ce50-4e3f-a1b7-bc77e46ff95a","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"5d22a65b-b237-4da0-a7b3-4a82e5f65f48","label":null,"content":"A ladder reaches 1.6 m up a vertical wall. \nThe base of the ladder is 60 cm from the base of the wall on a horizontal ground.\n\nFind the length of the ladder.","markscheme":"- Converts units to be consistent (e.g., 1.6 m to 160 cm or 60 cm to 0.6 m) B1\n- Applies Pythagoras: $160^2+60^2=L^2$ M1\n- $L^2=25600+3600=29200$ M1\n- $L=\\sqrt{29200}\\approx170\\text{ cm}$ or $1.7\\text{ m}$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts units to be consistent.","code":"B","acceptable":["$$1.6\\text{ m}=160\\text{ cm}$","$$60\\text{ cm}=0.6\\text{ m}$"]},{"id":"p2","marks":1,"description":"Applies Pythagoras using consistent units.","code":"M","acceptable":["$$160^2+60^2=L^2$","$$1.6^2+0.6^2=L^2$"]},{"id":"p3","marks":1,"description":"Correctly evaluates the sum of the squares.","code":"M","acceptable":["$$L^2=25600+3600=29200$","$$L^2=2.56+0.36=2.92$"]},{"id":"p4","marks":1,"description":"Finds the length of the ladder.","code":"A","acceptable":["$$L=\\sqrt{29200}\\approx170\\text{ cm}$","$$L=\\sqrt{2.92}\\approx1.7\\text{ m}$"]}],"finalAnswers":["$$1.7$ m"],"generatedAt":"2026-09-22T15:37:57.693Z","modelVersion":"gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"b8f1c698-606f-4ae9-aa4d-1e6d35d5cb0c","revisionId":"7b5da242-b1af-47c9-9ac1-313b6e508b81","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"eb934e25-b596-4c3b-b993-76c529aadac4","label":null,"content":"A ship leaves point A and sails for 2.1 km due North. \nThe ship then sails for 2.8 km due East to reach point B.\n\nCalculate the shortest distance between point A and point B. \nGive your answer correct to 1 decimal place.","markscheme":"- Applies Pythagoras: $2.1^2 + 2.8^2 = d^2$ M1\n- $d^2 = 4.41 + 7.84 = 12.25$ M1\n- $d = \\sqrt{12.25} = 3.5$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Applies Pythagoras to the two perpendicular distances.","code":"M","acceptable":["Applies Pythagoras: $2.1^2 + 2.8^2 = d^2$","$$d^2 = 2.1^2 + 2.8^2$"]},{"id":"p2","marks":1,"description":"Correctly evaluates and adds the squares.","code":"M","acceptable":["$$d^2 = 4.41 + 7.84 = 12.25$","$$d^2 = 12.25$"]},{"id":"p3","marks":1,"description":"Finds the shortest distance and gives it correct to 1 decimal place.","code":"A","acceptable":["$$d = \\sqrt{12.25} = 3.5$","$$3.5$","$$3.5\\text{ km}$"]}],"finalAnswers":["3.5 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Pythagoras

Question 8

Pythagoras Questions

Pythagoras

Question 8

Pythagoras Questions