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1.2.4 Quadratic functions A Level Maths exam-style questions with worked solutions on MathsGenie.\",\"learningResourceType\":\"Practice questions\",\"educationalLevel\":\"A Level\",\"about\":{\"@type\":\"Thing\",\"name\":\"1.2.4 Quadratic functions\"},\"url\":\"https://mathsgenie.co.uk/a-level/maths/ocr/quadratic-functions/questions/q4\",\"inLanguage\":\"en-GB\",\"provider\":{\"@id\":\"https://mathsgenie.co.uk/#organization\"}}"}}],["$","div",null,{"className":"min-h-0 w-full flex-1 overflow-hidden bg-background","children":["$","$L3b",null,{"backHref":"/a-level/maths/ocr/questions","basePath":"/a-level/maths/ocr/quadratic-functions/questions","formulaUrl":null,"initialIndex":3,"initialQuestionWindow":[{"id":"338f82cc-6fd1-4c8d-ada8-9d958e2e4322","revisionId":"225fb88e-03ec-4e3d-bc7e-a2e77f88e6aa","questionNumber":null,"questionType":"LA","specification":"A curve has equation\n$y = x^2 + (k - 1)x + 9$\nwhere $k$ is a constant.\n\nThe line with equation $y = 3x$ is a tangent to the curve.","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":5,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"52fc45c6-535a-402c-bcb1-8b39cc55d80c","label":null,"content":"Find the possible values of $k$.","markscheme":"- Equates the curve and the line: $x^2 + (k - 1)x + 9 = 3x$ M1\n- Rearranges to $x^2 + (k - 4)x + 9 = 0$ A1\n- States that a tangent requires $b^2 - 4ac = 0$ M1\n- $(k - 4)^2 - 36 = 0$, so $k - 4 = \\pm 6$ A1\n- $k = 10$ and $k = -2$ A1\n\nBoth values required for the final mark.","marks":5,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"4cca4bcd-9a7f-4cad-b8c6-b202d063fe5f","revisionId":"b0fb780d-c802-40b5-8747-8ac54fc7b4a5","questionNumber":null,"questionType":"LA","specification":"The equation\n$ax^2 + 6x + 5 = 0$\nwhere $a$ is a constant, has two distinct real roots.","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"2055018f-491b-4765-96e4-852c8ab84a1a","label":null,"content":"Find the set of possible values for $a$.","markscheme":"- Uses $b^2 - 4ac > 0$ to give $36 - 20a > 0$ M1\n- Rearranges to $36 > 20a$ M1\n- $a < \\dfrac{9}{5}$ A1\n- States $a \\neq 0$, since the equation must be quadratic B1\n\nFinal answer $\\{a : a < 0\\} \\cup \\left\\{a : 0 < a < \\frac95\\right\\}$. Accept $a < 1.8$, $a \\neq 0$. Common error: dividing by $-20$ without reversing the inequality.","marks":4,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"643fead4-0d49-45ec-a84c-99c29d13cadb","revisionId":"97f85a0a-0e96-4c10-9e4f-b2f506504d03","questionNumber":null,"questionType":"LA","specification":"The equation\n$x^2 + kx + 2 = 0$\nwhere $k$ is a constant, has no real roots.","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"0137857f-12d3-4333-b902-ac98b669901c","label":null,"content":"Find the set of possible values for $k$, giving your answer in set notation.","markscheme":"- Uses the condition for no real roots, $b^2 - 4ac < 0$ M1\n- $k^2 - 8 < 0$ A1\n- Critical values $k = -2\\sqrt{2}$ and $k = 2\\sqrt{2}$ A1\n- $\\left\\{k : -2\\sqrt{2} < k < 2\\sqrt{2}\\right\\}$ A1\n\nAccept $\\pm\\sqrt{8}$ for the critical values. The final mark requires correct set-builder notation with a single interval; award A0 for a union of two sets here, since the solution is the region between the critical values.","marks":4,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"a_level_maths__ocr","summaries":[{"id":"30889776-8de9-40e5-a129-1287df6acee3","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"MC","isCalculation":true},{"id":"338f82cc-6fd1-4c8d-ada8-9d958e2e4322","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"3d6cd9b7-d1fe-4684-a858-afd2567070ba","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4cca4bcd-9a7f-4cad-b8c6-b202d063fe5f","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"643fead4-0d49-45ec-a84c-99c29d13cadb","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"ccec71ea-f803-4432-a38b-9fc74a03a5df","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"f7ab325e-1f11-4d9f-8ad5-b1aabfc7c243","difficultyBand":"hard","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"ff1d2f18-261a-4412-bf63-0db59a3f68db","difficultyBand":"hard","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true}],"title":"1.2.4 Quadratic functions","topicId":"419fdf61-4e02-4a7d-b6c8-1b2bf3db974e","topicSidebar":"$L3c","topicSlug":"quadratic-functions","topicTitle":"1.2.4 Quadratic functions"}]}],"$L3d","$L3e"]}]

1.2.4 Quadratic functions

Question 2

1.2.4 Quadratic functions Questions

1.2.4 Quadratic functions

Question 2

1.2.4 Quadratic functions Questions