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M1\n- Factorise as $(x+5)(x-2)\\leq0$, identifying the critical values $-5$ and $2$. M1\n- State $-5\\leq x\\leq2$. A1\n\n![A sketch of a quadratic curve on coordinate axes for the inequality x(x + 3) ≤ 10.](https://assets.mathsgenie.co.uk/question-variant-figures/v1/a21782fb4d9da2cc1daab3c52bb3b3c8.svg)","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Expand and rearrange the inequality.","code":"M","acceptable":["$$x^2+3x-10\\leq0$"]},{"id":"p2","marks":1,"description":"Factorise and identify both critical values.","code":"M","acceptable":["$$(x+5)(x-2)\\leq0$; critical values $-5$ and $2$"]},{"id":"p3","marks":1,"description":"State the solution interval, including its endpoints.","code":"A","acceptable":["$$-5\\leq x\\leq2$"]}],"finalAnswers":["$$-5\\leq x\\leq2$"],"generatedAt":"2026-09-24T09:29:50.433Z","modelVersion":"gpt-6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"f23dcedf-2a4c-4de0-847d-e018d9bab020","revisionId":"d14f058d-c559-48f8-a410-cd272fa088a0","questionNumber":"3","questionType":"LA","specification":"","difficultyBand":"easy","tier":null,"totalMarks":4,"sourceTitle":"3.5 Quadratic Inequalities","calculatorUse":null,"isCalculation":true,"parts":[{"id":"1b672fde-51f2-4651-ba1b-571b8bb1e0bd","label":"","content":"Solve the simultaneous equations\n\n$$x + y = 3$$\n\n$$x^2 + 2y^2 - 8x = 6$$","markscheme":"- Rearrange the linear equation to $y=3-x$ and substitute into the quadratic equation. M1\n- Simplify to obtain $3x^2-20x+12=0$. A1\n- Factorise and solve to obtain $x=\\frac{2}{3}$ or $x=6$. M1\n- Find the corresponding values of $y$, giving $(x,y)=\\left(\\frac{2}{3},\\frac{7}{3}\\right)$ or $(6,-3)$. 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Quadratic Inequalities","topicId":"b71eaaab-1c2a-1513-4c9c-786f6ed06f91","topicSidebar":"$L3b","topicSlug":"as-pure-mathematics-3-5-quadratic-inequalities","topicTitle":"3.5 Quadratic Inequalities"}]}],"$L3c","$L3d"]}]

3.5 Quadratic Inequalities

Question 9

3.5 Quadratic Inequalities Questions

3.5 Quadratic Inequalities

Question 9

3.5 Quadratic Inequalities Questions