7-4ce3-ace1-4c5e45b597ae","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"7f7ff8e9-e2b3-44f2-9d18-bd1f6dd12912","label":"","content":"Solve $w^2 \\leq 144$","markscheme":"- Rearranges to $w^2 - 144 \\leq 0$ M1\n- Factorises using difference of two squares: $(w+12)(w-12) \\leq 0$ M1\n- Identifies critical values: $w = -12$ and $w = 12$ M1\n- States correct inequality: $-12 \\leq w \\leq 12$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Rearranges the inequality to the standard quadratic form $w^2 - 144 \\leq 0$.","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 $w = -12$ and $w = 12$.","code":"M"},{"id":"p4","marks":1,"description":"States the final solution as a single inequality range $-12 \\leq w \\leq 12$.","code":"A"}],"finalAnswers":["-12 \\leq w \\leq 12"],"generatedAt":"2026-08-10T10:52:36.684Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"7c998476-0abe-45db-9254-a834130cfa1d","revisionId":"0aff041a-83b2-41af-b665-32b156cf3bed","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"a63149b1-9d6d-4048-9685-d704633b3acc","label":"a","content":"Solve $x^2 > 21 - 4x$","markscheme":"- Rearranges to $x^2 + 4x - 21 > 0$ M1\n- Factorises the quadratic: $(x + 7)(x - 3) > 0$ M1\n- Identifies critical values: $x = -7$ and $x = 3$ M1\n- States correct inequality: $x < -7$ or $x > 3$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Rearranges to $x^2 + 4x - 21 > 0$","code":"M"},{"id":"p2","marks":1,"description":"Factorises the quadratic correctly into two brackets","code":"M"},{"id":"p3","marks":1,"description":"Identifies critical values: $x = -7$ and $x = 3$","code":"M"},{"id":"p4","marks":1,"description":"States correct final inequality solution using 'or'","code":"A"}],"finalAnswers":["x < -7 \\text{ or } x > 3"],"generatedAt":"2026-08-10T10:52:53.773Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"92469713-1a42-4129-9bfe-12fa55557953","revisionId":"b88777ff-bce7-40d6-88da-f8322969afaa","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"9cb19fc3-5b7e-4976-abc5-7661eb35d38b","label":"a","content":"Solve $y^2 + y - 12 < 0$","markscheme":"- Factorises the quadratic: $(y + 4)(y - 3) < 0$ M1\n- Identifies critical values: $y = -4$ and $y = 3$ M1\n- States correct inequality: $-4 < y < 3$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Factorise the quadratic expression correctly.","code":"M"},{"id":"p2","marks":1,"description":"Find the correct roots of the quadratic equation.","code":"M"},{"id":"p3","marks":1,"description":"State the correct inequality range for y.","code":"A"}],"finalAnswers":["-4 < y < 3"],"generatedAt":"2026-08-10T10:52:27.660Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3f","subjectCode":"gcse_maths","summaries":[{"id":"fc3aa417-4bcf-44e4-8ec3-2f239ef63a3a","difficultyBand":"hard","calculatorUse":null},{"id":"061c58ee-41ed-4950-85b2-d8dd2ceb52f7","difficultyBand":"hard","calculatorUse":null},{"id":"07242bfc-6245-4217-9291-c9e0761c355c",

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions