ons","basePath":"/gcse/maths/edexcel/grade-8-9-8-6-quadratic-inequalities/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":8,"initialQuestionWindow":[{"id":"6091b885-6d9b-4411-a40d-5593888c5233","revisionId":"abc85dfa-4a75-4f50-b3b5-21c79bf7a7b9","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e511ea62-bc36-4f2d-a895-60f1070452a3","label":"a","content":"Solve $3x^2 - 13x - 10 < 0$","markscheme":"- Factorises the quadratic: $(3x + 2)(x - 5) < 0$ M2\n- Identifies critical values: $x = -\\frac{2}{3}$ and $x = 5$ M1\n- States correct inequality: $-\\frac{2}{3} < x < 5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":2,"description":"Factorises the quadratic correctly into two linear brackets.","code":"M"},{"id":"p2","marks":1,"description":"Identifies both critical values from their factors.","code":"M"},{"id":"p3","marks":1,"description":"States the correct inequality range based on the critical values.","code":"A"}],"finalAnswers":["-\\frac{2}{3} < x < 5","-0.67 < x < 5"],"generatedAt":"2026-08-10T10:53:47.702Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"828522ce-e3a4-46fd-8201-d419b288be1f","revisionId":"4b851715-0fd4-463f-b7e7-c96922ecd058","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"589a900e-9953-4c7a-997a-34f3e67bc41c","label":"a","content":"Solve $x^2 - 10x + 21 \\le 0$","markscheme":"- Factorises the quadratic: $(x - 7)(x - 3) \\le 0$ M1\n- Identifies critical values: $x = 7$ and $x = 3$ M1\n- States correct inequality: $3 \\le x \\le 7$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Factorises the quadratic expression into two linear brackets.","code":"M"},{"id":"p2","marks":1,"description":"Identifies the correct critical values from their factors.","code":"M"},{"id":"p3","marks":1,"description":"States the correct inequality for the region between the critical values including endpoints.","code":"A"}],"finalAnswers":["3 \\le x \\le 7"],"generatedAt":"2026-08-10T10:52:48.594Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"8d160c7d-161a-4da0-8a48-75fa72fb8d2e","revisionId":"6cb43e7c-f98f-4d44-aa22-280b05e853a1","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"f33be95f-fd29-41bb-be5b-37afd12da39d","label":"a","content":"Solve $x^2 + 4x - 21 < 0$","markscheme":"- Factorises the quadratic: $(x + 7)(x - 3) < 0$ M1\n- Identifies critical values: $x = -7$ and $x = 3$ M1\n- States correct inequality: $-7 < x < 3$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Factorises the quadratic into $(x + 7)(x - 3)$. Accept any method to solve the equation for the first mark.","code":"M"},{"id":"p2","marks":1,"description":"Identifies critical values of $x = -7$ and $x = 3$.","code":"M"},{"id":"p3","marks":1,"description":"States correct inequality: $-7 < x < 3$.","code":"A"}],"finalAnswers":["-7 < x < 3"],"generatedAt":"2026-08-10T10:53:18.982Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3e","subjectCode":"gcse_maths","summaries":[{"id":"fc3aa417-4bcf-44e4-8ec3-2f239ef63a3a","difficultyBand":null,"calculatorUse":null},{"id":"061c58ee-41ed-4950-85b2-d8dd2ceb52f7","difficult

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions