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Undo the operations around $a$ in reverse order.","highlights":[{"text":"Make $a$ the subject","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$s=\\color{@orange}{\\htmlData{anchor=ut_start}{ut}}+\\dfrac{1}{2}at^2$"},{"latex":"$$s-\\color{@orange}{\\htmlData{anchor=ut_end}{ut}}=\\dfrac{1}{2}at^2$"}],"highlights":[{"color":"orange","style":"text-color","anchor":"ut_start"},{"color":"orange","style":"text-color","anchor":"ut_end"}]},"order":1,"title":"Subtract the first term","description":"Subtract $ut$ from both sides. This keeps the equation balanced and earns the method mark M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$s-ut=\\dfrac{1}{2}at^2$"},{"latex":"$$\\color{@purple}{\\htmlData{anchor=numerator_mid}{2(s-ut)}}=a\\color{@sky}{\\htmlData{anchor=t_squared_mid}{t^2}}$"},{"latex":"$$\\color{@green}{a}=\\dfrac{\\color{@purple}{\\htmlData{anchor=numerator_final}{2(s-ut)}}}{\\color{@sky}{\\htmlData{anchor=t_squared_final}{t^2}}}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"numerator_mid"},{"color":"purple","style":"text-color","anchor":"numerator_final"},{"color":"sky","style":"text-color","anchor":"t_squared_mid"},{"color":"sky","style":"text-color","anchor":"t_squared_final"}]},"order":2,"title":"Isolate the subject","description":"Multiply both sides by $2$, then divide both sides by $t^2$. Writing the final formula correctly earns A1."}]}],"generatedAt":"2026-07-20T16:43:41.447Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":82},"walkthroughVideo":null},{"id":"ddfb58b2-0ae1-442b-a426-76015be5284f","revisionId":"9a5c8239-cb22-48e1-b564-6fe564a1dc78","questionNumber":"6","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","totalMarks":2,"sourceTitle":"Rearranging Harder Formulae","calculatorUse":null,"isCalculation":false,"parts":[{"id":"f53faf0b-8b63-4b21-9fc8-3fc9571241ad","label":"0","content":"Make $v$ the subject of the formula $T = \\frac{1}{2}mv^2$","markscheme":"- Multiply by 2 and divide by $m$: $\\frac{2T}{m} = v^2$ M1\n- Square root: $v = \\sqrt{\\frac{2T}{m}}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Isolates $v^2$ by multiplying by 2 and dividing by $m$.","code":"M"},{"id":"p2","marks":1,"description":"Square roots the expression to find $v$.","code":"A"}],"finalAnswers":["v = \\sqrt{\\frac{2T}{m}}"],"generatedAt":"2026-05-07T02:09:01.541Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":86},"walkthroughVideo":null},{"id":"0d84ec73-daad-4d69-85c5-1c042c944964","revisionId":"e4bc48a0-1a97-437d-a8a4-648e1f042d36","questionNumber":"7","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Rearranging Harder Formulae","calculatorUse":null,"isCalculation":false,"parts":[{"id":"2f8b310d-54af-4d60-aa5e-8aa053d39456","label":"0","content":"Make $x$ the subject of the formula $2x + a = b(x - 2)$","markscheme":"- Expand brackets: $2x + a = bx - 2b$ M1\n- Rearrange to get $x$ terms on one side: $a + 2b = bx - 2x$ M1\n- Factorise $x$ and divide: $x = \\frac{a + 2b}{b - 2}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Expands the bracket $b(x - 2)$.","code":"M"},{"id":"p2","marks":1,"description":"Rearranges terms so that all terms containing $x$ are on one side and others on the other.","code":"M"},{"id":"p3","marks":1,"description":"Factorises $x$ and divides to reach the final answer $x = \\frac{a + 2b}{b - 2}$.","code":"A"}],"finalAnswers":["x = \\frac{a + 2b}{b - 2}"],"generatedAt":"2026-05-07T02:09:01.541Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":86},"walkthroughVideo":null}],"subjectCode":"igcse_maths__cie","summaries":[{"id":"2221441c-51c6-4cfd-93ef-53180ca8ac25","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"12ad6831-a4eb-48e4-b127-d2dda549930e","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"8e9b6070-da7d-4c7d-a510-9a8450b986cd","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"c7909575-fb91-43f8-8546-2b607d2c86aa","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"677e251b-a63e-4950-b2ba-89b1e78838a9","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"ddfb58b2-0ae1-442b-a426-76015be5284f","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"0d84ec73-daad-4d69-85c5-1c042c944964","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"eb2afcdb-1c77-41d5-8538-845fe750eb12","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"755c4481-3ea7-44ff-9272-f4357df6e354","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"f6801ff0-5743-4c8c-b825-57d53a40fe4f","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"1ce4d46d-9bd2-4a8c-92f3-7f6bfc30bef8","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"e33c522c-f4e0-4a9f-9178-2bb9f609023d","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"4cbe4739-918d-4f11-9d03-99fb594d5d29","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false}],"title":"Rearranging Harder Formulae","topicId":"007629bb-592b-47e0-8265-34ce43031d53","topicSidebar":"$L3c","topicSlug":"grade-7-7-7-rearranging-harder-formulae","topicTitle":"Rearranging Harder Formulae"}]}],"$L3d","$L3e"]}]

Rearranging Harder Formulae

Question 2

Rearranging Harder Formulae Questions

Rearranging Harder Formulae

Question 2

Rearranging Harder Formulae Questions