b63cfaca-de48-4e62-ab11-886c7ef673da","revisionId":"ff057153-7ef0-4b77-a122-a2ad92bd26af","questionNumber":null,"questionType":"LA","specification":"The diagram shows a six sided shape formed from two rectangles. All measurements are given in centimetres.\n\n![A diagram of a six-sided shape formed by two adjacent rectangles. The left rectangle has a width of x-5 and a height of 2x. The right rectangle has a width of 4 and a height of 10-x. They share a common vertical side.](https://assets.mathsgenie.co.uk/questions/8b71c22c-00cf-4d07-b249-754748a4da00.png)\n\nThe area of the shape is $35\\text{cm}^2$","difficulty":3,"difficultyBand":"medium","totalMarks":5,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"6c0ea4c9-f54b-40dd-8eea-cd1454342e0d","label":"a","content":"Show that $2x^2 - 14x + 5 = 0$","markscheme":"- Sets up area equation: $2x(x-5) + 4(10-x) = 35$ M1\n- Expands and simplifies: $2x^2 - 10x + 40 - 4x = 35 \\Rightarrow 2x^2 - 14x + 40 = 35 \\Rightarrow 2x^2 - 14x + 5 = 0$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Sets up the area sum equation correctly.","code":"M"},{"id":"p2","marks":1,"description":"Reduces the equation to the required quadratic form.","code":"A"}],"finalAnswers":["2x^2 - 14x + 5 = 0"],"generatedAt":"2026-05-06T14:02:25.104Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"add_rectangle_areas","label":"Add the rectangle areas","steps":[{"type":"text","order":0,"title":"Split the shape","content":"Treat the shape as the two non-overlapping rectangles shown. Use $\\text{area}=\\text{width}\\times\\text{height}$ for each rectangle, then add their areas because together they make the whole shape.","highlights":[{"text":"six sided shape formed from two rectangles","location":"specification"},{"text":"The area of the shape is $35\\text{cm}^2$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A_{\\text{left}}=\\color{@sky}{2x(x-5)}$"},{"latex":"$$A_{\\text{right}}=\\color{@orange}{4(10-x)}$"},{"latex":"$$\\color{@sky}{2x(x-5)}+\\color{@orange}{4(10-x)}=35$"}]},"order":1,"title":"Form the area equation","description":"The left rectangle has width x − 5 and height 2x; the right has width 4 and height 10 − x. Add their areas and equate the total to 35. This earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=before_expand}{2x(x-5)+4(10-x)=35}$"},{"latex":"$$\\htmlData{anchor=after_expand}{2x^2-10x+40-4x=35}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"before_expand"},{"color":"purple","style":"text-color","anchor":"after_expand"}]},"order":2,"title":"Expand both brackets","description":"Multiply each term inside a bracket by the factor outside. In particular, 4 multiplies both 10 and −x."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$2x^2+40+\\color{@sky}{(-10x-4x)}=35$"},{"latex":"$$2x^2+40\\color{@sky}{-14x}=35$"},{"latex":"$$2x^2-14x+\\color{@orange}{(40-35)}=0$"},{"latex":"$$2x^2-14x+\\color{@green}{5}=0$"}]},"order":3,"title":"Collect and rearrange","description":"First collect the x-terms. Then subtract 35 from both sides and simplify the constants. Reaching the required equation correctly earns A1."}]}],"generatedAt":"2026-07-19T16:39:09.955Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"25240fb2-6335-4df6-937c-61db00c69987","label":"b","content":"Find the value of $x$. Give your answer to 3 significant figures.","markscheme":"- Substitutes $a = 2, b = -14, c = 5$ into formula: $x = \\frac{-(-14) \\pm \\sqrt{(-14)^2 - 4(2)(5)}}{2(2)}$ M1\n- Finds $x = 6.62$ or $x = 0.378$ A1\n- Rejects $x = 0.378$ as $(x-5)$ would be negative, so $x = 6.62$ B1","marks":3,"order":1,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct use of quadratic formula with current coefficients.","code":"M"},{"id":"p2","marks":1,"description":"Finds both numerical solutions to 3 significant fig

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