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":2,"initialQuestionWindow":[{"id":"061c58ee-41ed-4950-85b2-d8dd2ceb52f7","revisionId":"90f1a2ae-1067-4a7e-86d2-cad4b5a161ee","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"0fe2bce1-0d0c-48c7-9477-41e54fc1499d","label":"a","content":"Solve $x^2 - 11x + 24 < 0$","markscheme":"- Factorises the quadratic: $(x - 3)(x - 8) < 0$ M1\n- Identifies critical values: $x = 3$ and $x = 8$ M1\n- States correct inequality: $3 < x < 8$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Attempt to factorise the quadratic expression.","code":"M"},{"id":"p2","marks":1,"description":"Identify the critical values of the inequality.","code":"M"},{"id":"p3","marks":1,"description":"State the correct final inequality in terms of x.","code":"A"}],"finalAnswers":["3 < x < 8"],"generatedAt":"2026-08-10T10:54:26.940Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"07242bfc-6245-4217-9291-c9e0761c355c","revisionId":"0983e350-5061-46cd-8b54-7bbe53f26404","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"59a982a8-01a7-4040-8749-a5385c61c91a","label":"a","content":"Solve $10x^2 - 11x - 6 \\ge 0$","markscheme":"- Factorises the quadratic: $(5x + 2)(2x - 3) \\ge 0$ M2\n- Identifies critical values: $x = -0.4$ and $x = 1.5$ M1\n- States correct inequality: $x \\le -0.4$ or $x \\ge 1.5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":2,"description":"Factorises the quadratic correctly or uses an equivalent method to find roots.","code":"M","acceptable":["(5x + 2)(2x - 3)"]},{"id":"p2","marks":1,"description":"Identifies critical values: $x = -0.4$ and $x = 1.5$","code":"M","acceptable":["x = -2/5 and x = 3/2"]},{"id":"p3","marks":1,"description":"States correct inequality: $x \\le -0.4$ or $x \\ge 1.5$","code":"A","acceptable":["x \\le -2/5 \\cup x \\ge 3/2"]}],"finalAnswers":["x \\le -0.4 \\text{ or } x \\ge 1.5"],"generatedAt":"2026-08-10T10:53:24.533Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"229d7324-23a9-4f66-a6be-b17f400cbe4c","revisionId":"c76ac388-d790-488d-9276-abcbab44a88e","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"94924b8a-2ae2-49c9-8546-9e38e8f21e83","label":"a","content":"Work out the integer values that satisfy: $x^2 - 6x + 7 < 0$","markscheme":"- Uses quadratic formula to find critical values: $x = \\frac{-(-6) \\pm \\sqrt{(-6)^2 - 4(1)(7)}}{2(1)}$ M1\n- Finds decimal critical values: $x \\approx 1.59$ and $x \\approx 4.41$ A2\n- Identifies integers between values: 2, 3, and 4 A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Correct substitution into the quadratic formula or completing the square to find roots.","code":"M"},{"id":"p2","marks":1,"description":"At least one critical value found correctly as a decimal (1.59 or 4.41).","code":"A"},{"id":"p3","marks":1,"description":"Both critical values found correctly as decimals (1.59 and 4.41).","code":"A"},{"id":"p4","marks":1,"description":"Identifies the correct set of integers: 2, 3, 4.","code":"A"}],"finalAnswers":["2, 3, 4"],"generatedAt":"2026-08-10T10:52:55.919Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanat

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions