2, c = -13$ B1\n- Substitutes into the quadratic formula: $x = \\frac{-(2) \\pm \\sqrt{(2)^2 - 4(3)(-13)}}{2(3)}$ M1\n- Final answers: $1.8$ and $-2.4$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies correct coefficients $a=3, b=2, c=-13$.","code":"B"},{"id":"p2","marks":1,"description":"Correct substitution into the quadratic formula.","code":"M"},{"id":"p3","marks":1,"description":"Final answers of $1.8$ and $-2.4$ (correct to 1dp).","code":"A"}],"finalAnswers":["1.8","-2.4"],"generatedAt":"2026-05-07T02:08:38.200Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"quadratic_formula","label":"Use the quadratic formula","steps":[{"type":"text","order":0,"title":"Identify the coefficients","content":"Write the equation in the standard form $ax^2+bx+c=0$. Comparing with $3x^2+2x-13=0$ gives\n\n$$a=3,\\\\ b=2,\\\\ c=-13.$$\n\nThis identification earns the **B1** mark.","highlights":[{"text":"Solve $3x^2 + 2x - 13 = 0$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"x=\\frac{\\htmlData{anchor=formula}{-b\\pm\\sqrt{b^2-4ac}}}{2a}"},{"latex":"x=\\frac{\\htmlData{anchor=substituted}{-(2)\\pm\\sqrt{(2)^2-4(3)(-13)}}}{2(3)}"},{"latex":"x=\\frac{\\htmlData{anchor=simplified}{-2\\pm\\sqrt{160}}}{6}"}],"connections":[{"to":"substituted","from":"formula","color":"sky","label":"substitute values","style":"solid"},{"to":"simplified","from":"substituted","color":"amber","label":"simplify","style":"solid"}]},"order":1,"title":"Substitute into the formula","description":"Use the quadratic formula. Keep the negative sign attached to c when substituting. Correctly substituting the identified values earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"x=\\frac{\\htmlData{anchor=plusbranch}{-2+\\sqrt{160}}}{6}"},{"latex":"x=\\htmlData{anchor=plusresult}{1.774851\\ldots}"},{"latex":"x=\\frac{\\htmlData{anchor=minusbranch}{-2-\\sqrt{160}}}{6}"},{"latex":"x=\\htmlData{anchor=minusresult}{-2.441518\\ldots}"}],"connections":[{"to":"plusresult","from":"plusbranch","color":"green","label":"evaluate","style":"solid"},{"to":"minusresult","from":"minusbranch","color":"purple","label":"evaluate","style":"solid"}]},"order":2,"title":"Calculate both solutions","description":"The plus-or-minus sign means calculate once using addition and once using subtraction."},{"type":"text","order":3,"title":"Round the solutions","content":"Round each value to **1 decimal place**:\n\n$$x=1.8\\quad\\text{or}\\quad x=-2.4.$$\n\nBoth correct rounded solutions earn the **A1** mark.","highlights":[{"text":"Give your solutions correct to 1 decimal place.","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:02:43.295Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"11b5c907-1548-4529-a9c0-7c54fec41208","revisionId":"a7651bba-7a31-4dba-85d2-055b3fc010d7","questionNumber":"4","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Quadratic Formula","calculatorUse":null,"parts":[{"id":"e7c9d673-3d84-4aca-ba54-b7df9c647b30","label":"0","content":"Solve $5x^2 + x - 11 = 0$\n\nGive your solutions correct to 3 significant figures.","markscheme":"- Identifies $a = 5, b = 1, c = -11$ B1\n- Substitutes into the quadratic formula: $x = \\frac{-(1) \\pm \\sqrt{(1)^2 - 4(5)(-11)}}{2(5)}$ M1\n- Final answers: $1.39$ and $-1.59$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies correct coefficients $a=5, b=1, c=-11$.","code":"B"},{"id":"p2","marks":1,"description":"Correct substitution into the quadratic formula.","code":"M"},{"id":"p3","marks":1,"description":"Final answers of $1.39$ and $-1.59$ (correct to 3sf).","code":"A"}],"finalAnswers":["1.39","-1.59"],"generatedAt":"2026-05-07T02:08:38.200Z","modelVersion":"gemini-3-flash-preview"},"explana

Quadratic Formula Questions

Quadratic Formula Questions

Quadratic Formula Questions

Quadratic Formula Questions