tions","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":9,"initialQuestionWindow":[{"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},{"id":"b77033cf-d912-4f57-92b2-f8dcb3b4cc5c","revisionId":"82bd4867-b175-4877-9514-7067ea0ffa43","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"9f4a0595-b12a-47f2-9d05-5e5f6c534493","label":"","content":"Solve $y^2 < 64$","markscheme":"- Rearranges to $y^2 - 64 < 0$ M1\n- Factorises using difference of two squares: $(y+8)(y-8) < 0$ M1\n- Identifies critical values: $y = -8$ and $y = 8$ M1\n- States correct inequality: $-8 < y < 8$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Rearranges the inequality to the standard quadratic form $y^2 - 64 < 0$.","code":"M"},{"id":"p2","marks":1,"description":"Factorises the quadratic expression using the difference of two squares.","code":"M"},{"id":"p3","marks":1,"description":"Identifies the critical values as $y = -8$ and $y = 8$.","code":"M"},{"id":"p4","marks":1,"description":"States the final solution as a single inequality range $-8 < y < 8$.","code":"A"}],"finalAnswers":["-8 < y < 8"],"generatedAt":"2026-08-10T10:52:35.243Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3d","subjectCode":"gcse_maths","summaries":

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions