88d-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":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"2ac31615-8ec8-4d9b-a8c6-ce4dfbe21f41","revisionId":"f27990b8-76f7-4fcf-8fb2-2768223b438f","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"5ada6099-4b78-4efd-a965-76e4624f436c","label":"a","content":"Solve $x^2 > 4x + 12$","markscheme":"- Rearranges to $x^2 - 4x - 12 > 0$ M1\n- Factorises the quadratic: $(x - 6)(x + 2) > 0$ M1\n- Identifies critical values: $x = 6$ and $x = -2$ M1\n- States correct inequality: $x < -2$ or $x > 6$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Rearrange the inequality to form a quadratic expression compared to zero.","code":"M"},{"id":"p2","marks":1,"description":"Factorise the quadratic expression correctly.","code":"M"},{"id":"p3","marks":1,"description":"Identify the two critical values from the factors.","code":"M"},{"id":"p4","marks":1,"description":"State the correct solution set for the inequality.","code":"A"}],"finalAnswers":["x < -2 \\text{ or } x > 6"],"generatedAt":"2026-08-10T10:53:15.398Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"42f00b86-1efb-4e4d-a655-a663b407a1dc","revisionId":"41f78f8e-210f-4c6a-8307-1dada01694f4","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"919df38c-e435-4e2b-bab3-2a7954075015","label":"a","content":"Solve $x^2 - 144 > 0$","markscheme":"- Factorises using difference of two squares: $(x+12)(x-12) > 0$ M1\n- Identifies critical values: $x = -12$ and $x = 12$ M1\n- States correct inequality: $x < -12$ or $x > 12$ A2","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Factorises the quadratic using the difference of two squares method.","code":"M"},{"id":"p2","marks":1,"description":"Identifies both critical values correctly.","code":"M"},{"id":"p3","marks":2,"description":"States the final disjoint inequality correctly ($x < -12$ or $x > 12$). Award 1 mark for identifying the correct region with an error in notation or inequality signs.","code":"A"}],"finalAnswers":["x < -12 \\text{ or } x > 12"],"generatedAt":"2026-08-10T10:54:01.044Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3d","subjectCode":"gcse_maths","summaries":[{"id"

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions