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":14,"initialQuestionWindow":[{"id":"e8ee2fa4-e18b-4386-aecb-928227c7ce01","revisionId":"3966ea2d-7f5a-48d1-bb62-9b203ec14ad4","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"096a99df-a127-4a47-a99c-a5928472711f","label":"a","content":"Solve $x^2 - 2x - 15 < 0$","markscheme":"- Factorises the quadratic: $(x - 5)(x + 3) < 0$ M1\n- Identifies critical values: $x = 5$ and $x = -3$ M1\n- States correct inequality: $-3 < x < 5$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Attempt to factorise the quadratic into two brackets.","code":"M"},{"id":"p2","marks":1,"description":"Identify the critical values (roots) correctly.","code":"M"},{"id":"p3","marks":1,"description":"Provide the final answer as a single continuous inequality.","code":"A"}],"finalAnswers":["-3 < x < 5"],"generatedAt":"2026-08-10T10:52:25.163Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"f312d9c1-4c1a-4911-afd1-f4be69313e64","revisionId":"a7eaa352-0a23-466c-8c24-493ac5c8c158","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"3e0e55a2-1c5a-4320-85d3-797fe7cbb3e0","label":"a","content":"Work out the integer values that satisfy: $2x^2 - 18x + 30 < 0$","markscheme":"- Simplifies to $x^2 - 9x + 15 < 0$ M1\n- Uses quadratic formula to find critical values: $x = \\frac{-(-9) \\pm \\sqrt{(-9)^2 - 4(1)(15)}}{2(1)}$ M1\n- Finds decimal critical values: $x \\approx 6.79$ and $x \\approx 2.21$ A1\n- Identifies integers between values: 3, 4, 5, and 6 A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Simplifies the quadratic by dividing by 2 or identifies correct coefficients for the quadratic formula from the original equation.","code":"M"},{"id":"p2","marks":1,"description":"Correct substitution into the quadratic formula to find critical values.","code":"M"},{"id":"p3","marks":1,"description":"Finds critical values as decimals (approx. 2.21 and 6.79).","code":"A"},{"id":"p4","marks":1,"description":"Correctly identifies the integers in the range.","code":"A"}],"finalAnswers":["3, 4, 5, 6"],"generatedAt":"2026-08-10T10:54:13.223Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"48aea5f5-39df-483b-b2bc-7e605c4cdcf6","revisionId":"582fb3bb-2374-4dfa-abda-1ff4e104ed38","questionNumber":"2","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Quadratic Inequalities","calculatorUse":null,"parts":[{"id":"7db8a3b2-c722-4b54-8eda-0f0ad565a17e","label":"0","content":"Solve $x^2 - x - 20 < 0$","markscheme":"- Factorises the quadratic: $(x + 4)(x - 5) < 0$ M1\n- Identifies critical values: $x = -4$ and $x = 5$ M1\n- States correct inequality: $-4 < x < 5$ A1\n\n![](https://assets.mathsgenie.co.uk/booklet/90b58dca801fe650b9160c2ff26efdeb9f8aa7e3ae6d43fc0c0801fda7fb3ba8.jpg)","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Factorises the quadratic expression into $(x+4)(x-5)$.","code":"M"},{"id":"p2","marks":1,"description":"Identifies the critical values as $-4$ and $5$.","code":"M"},{"id":"p3","marks":1,"description":"Gives the final answer as $-4 < x < 5$.","code":"A"}],"finalAnswers":["-4 < x < 5"],"generatedAt":"2026-08-10T10:26:15.961Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions

Quadratic Inequalities Questions