= 12. This earns the B1 mark."}]}],"generatedAt":"2026-07-21T03:57:24.977Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"f4dad6c6-0259-4cd2-ad22-418f1024832a","label":"c","content":"Solve $2a - 5 = 19$","markscheme":"- $2a = 24$ so $a = 12$ B1","marks":1,"order":2,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Final answer 12.","code":"B"}],"finalAnswers":["12"],"generatedAt":"2026-05-07T01:45:46.124Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"one_step_equation","label":"Solve by undoing operations","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=given}{\\color{@sky}{2a - 5 = 19}}$"},{"latex":"$$\\htmlData{anchor=after_add}{\\color{@amber}{2a = 24}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"given"}],"connections":[{"to":"after_add","from":"given","color":"sky","style":"solid"}]},"order":0,"title":"Add 5 to both sides","description":"Add 5 to both sides, keeping the equation balanced."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=after_add}{\\color{@amber}{2a = 24}}$"},{"latex":"$$\\htmlData{anchor=answer}{\\color{@green}{a = 12}}$"}],"connections":[{"to":"answer","from":"after_add","color":"green","style":"solid"}]},"order":1,"title":"Divide by 2","description":"Now divide both sides by 2 to find the value of a. Examiner annotation: 2a = 24, so a = 12, earns B1."}]}],"generatedAt":"2026-07-21T04:05:30.494Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ab354558-dab4-4548-a121-2887019f1c66","revisionId":"64814611-2cad-4193-9d82-a9a37bfd1671","questionNumber":"12","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":2,"sourceTitle":"Solving Equations","calculatorUse":null,"parts":[{"id":"df50a244-e9ab-4299-b033-9a9934df779e","label":"0","content":"Solve $3(b - 5) = 27$","markscheme":"- Expands brackets or divides by 3: $3b - 15 = 27$ or $b - 5 = 9$ M1\n- $b = 14$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly expands brackets to $3b - 15$ or divides both sides by 3.","code":"M"},{"id":"p2","marks":1,"description":"Final answer 14.","code":"A"}],"finalAnswers":["14"],"generatedAt":"2026-05-07T01:45:46.124Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"inverse_operations","label":"Use inverse operations","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"3(b-5)=27"},{"latex":"\\frac{3(b-5)}{3}=\\frac{27}{3}"},{"latex":"b-5=9"}]},"order":0,"title":"Divide both sides","description":"Keep the equation balanced: divide both sides by 3, then simplify. Examiner note: obtaining b minus 5 equals 9 earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"b-5=9"},{"latex":"b-5+5=9+5"},{"latex":"b=14"}]},"order":1,"title":"Find b","description":"Add 5 to both sides so that b is left on its own. Examiner note: b equals 14 earns A1."}]}],"generatedAt":"2026-07-21T04:04:37.937Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"584bdc8e-1e00-49ad-87ad-393ed5c6b683","revisionId":"455c7161-dc3f-4f6a-8e04-761aaac2ff9b","questionNumber":"13","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":4,"sourceTitle":"Solving Equations","calculatorUse":null,"parts":[{"id":"5e65b6d7-a2f2-4104-8cb3-87a66fa24059","label":"a","content":"Solve $\\frac{2x}{3} = 6$","markscheme":"- Multiplies by 3: $2x = 18$ M1\n- $x = 9$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Multiplies both sides by 3 to get $2x = 18$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer 9.","code":"A"}],"finalAnswers":["9"],"generatedAt":"2026-05-07T01:45:46.124Z","modelVersion":"gemini-3-flash-

Solving Equations Questions

Solving Equations Questions

Solving Equations Questions

Solving Equations Questions