**2 decimal places**. The third decimal place in each value determines the rounding, giving\n\n$$x=-0.70\\quad\\text{or}\\quad x=-4.30$$\n\nThese correctly rounded solutions earn the **A1** mark.","highlights":[{"text":"Give your solutions correct to 2 decimal places.","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:38:43.247Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":35,"sampleSize":26}},{"id":"903ccfdb-5fe3-4972-aa9a-f2fd08a058ff","revisionId":"d8cbb132-679f-4138-9337-d3d5bf8affc3","questionNumber":"2","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Quadratic Formula","calculatorUse":null,"parts":[{"id":"92797741-dd5c-4143-82ae-72ae934abdb5","label":"0","content":"Solve $2x^2 + 13x + 7 = 0$\n\nGive your solutions correct to 2 decimal places.","markscheme":"- Identifies $a = 2, b = 13, c = 7$ B1\n- Substitutes into the quadratic formula: $x = \\frac{-(13) \\pm \\sqrt{(13)^2 - 4(2)(7)}}{2(2)}$ M1\n- Final answers: $-0.59$ or $-5.91$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies correct coefficients $a=2, b=13, c=7$.","code":"B"},{"id":"p2","marks":1,"description":"Correct substitution into the quadratic formula.","code":"M"},{"id":"p3","marks":1,"description":"Final answers of $-0.59$ and $-5.91$ (correct to 2dp).","code":"A"}],"finalAnswers":["-0.59","-5.91"],"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":"Compare the equation with $ax^2+bx+c=0$. Therefore, $a=2$, $b=13$ and $c=7$. This identification earns the B1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=general}{x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}}"},{"latex":"\\htmlData{anchor=substituted}{x=\\frac{-(13)\\pm\\sqrt{(13)^2-4(2)(7)}}{2(2)}}"},{"latex":"(13)^2-4(2)(7)=169-56=113"},{"latex":"x=\\frac{-13\\pm\\sqrt{113}}{4}"}],"connections":[{"to":"substituted","from":"general","color":"sky","label":"substitute coefficients","style":"solid"}]},"order":1,"title":"Substitute into formula","description":"Use the quadratic formula. Substituting the coefficients into the quadratic formula earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"x=\\frac{-13+\\sqrt{113}}{4}"},{"latex":"x=-0.592463\\ldots"},{"latex":"x=\\frac{-13-\\sqrt{113}}{4}"},{"latex":"x=-5.907536\\ldots"},{"latex":"\\boxed{x=-0.59\\text{ or }x=-5.91}"}]},"order":2,"title":"Evaluate both solutions","description":"Use the plus and minus signs separately, then round each answer to 2 decimal places. Both values, correctly rounded to 2 decimal places, earn the A1 mark."}]}],"generatedAt":"2026-07-21T04:09:12.463Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"05c0dded-85da-4c32-b30e-5d095716d018","revisionId":"bbd73c1e-6e0a-4edf-acd0-4b528af31ae5","questionNumber":"3","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Quadratic Formula","calculatorUse":null,"parts":[{"id":"21a63685-77b6-49c9-8624-2ae51698b591","label":"0","content":"Solve $3x^2 + 2x - 13 = 0$\n\nGive your solutions correct to 1 decimal place.","markscheme":"- Identifies $a = 3, b = 2, c = -13$ 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

Quadratic Formula Questions

Quadratic Formula Questions

Quadratic Formula Questions

Quadratic Formula Questions