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{"name": "Harry's copy of CF Maths Portfolio - Differentiation 2 - Basic Polynomial Expressions (with fractional coefficients)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p style=\"text-align: center;\">If $y=ax^n$,</p>\n<p style=\"text-align: center;\">$\\frac{dy}{dx}=anx^{n-1}$ for all rational $n$.</p>\n<p style=\"text-align: left;\">We'll take the following term as an example:</p>\n<p style=\"text-align: left;\">$\\frac{3}{8}x^2$</p>\n<p style=\"text-align: left;\">All we have to do to terms where $x$ is to a power of anything is times the coefficient of $x$ by the original power, and then take one away from the original power.</p>\n<p style=\"text-align: left;\">If you are not familiar with this kind of work, these instructions may sound confusing, but it is much easier once you have seen it in practice.</p>\n<p style=\"text-align: left;\">We take</p>\n<p style=\"text-align: left;\">$\\frac{3}{8}x^2$</p>\n<p style=\"text-align: left;\">and times $\\frac{3}{8}$ by $2$, to get</p>\n<p style=\"text-align: left;\">$(\\frac{3}{8}\\times2)x^2=\\frac{6}{8}x^2=\\frac{3}{4}x^2$.</p>\n<p style=\"text-align: left;\">We then subtract one from the original power, $2$.</p>\n<p style=\"text-align: left;\">This gives us the final answer of</p>\n<p style=\"text-align: left;\"><strong>$\\frac{3}{4}x^1=\\frac{3}{4}x$</strong>.</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">Remember, don't be confused if there is no coefficient. The fact the term is there means the coefficient must be $1$, but we don't tend to write it out as, for example $1x$, we just say $x$.</p>", "type": "question", "statement": "<p><strong>Differentiate the following polynomials.</strong></p>", "rulesets": {}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>More work on differentiation with fractional coefficients.</p>"}, "parts": [{"type": "jme", "marks": "2", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "answersimplification": "all", "expectedvariablenames": [], "answer": "3{ac[0]}/{d[0]}x^2+2{bc[0]}/{d[1]}x+{cc[0]}/{d[2]}", "variableReplacements": [], "scripts": {}, "showpreview": true, "showCorrectAnswer": true, "checkvariablenames": false, "prompt": "<p>$\\simplify{({ac[0]}/{d[0]})x^3+({bc[0]}/{d[1]})x^2+({cc[0]}/{d[2]})x+({dc[0]}/{d[3]})}$</p>"}, {"type": "jme", "marks": "2", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "answersimplification": "all", "expectedvariablenames": [], "answer": "3{ac[1]}/{d[4]}x^2+2{bc[1]}/{d[5]}x+{cc[1]}/{d[6]}", "variableReplacements": [], "scripts": {}, "showpreview": true, "showCorrectAnswer": true, "checkvariablenames": false, "prompt": "<p>$\\simplify{({ac[1]}/{d[4]})x^3+({bc[1]}/{d[5]})x^2+({cc[1]}/{d[6]})x+({dc[1]}/{d[7]})}$</p>"}, {"type": "jme", "marks": "2", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "answersimplification": "all", "expectedvariablenames": [], "answer": "3{ac[2]}/{d[8]}x^2+2{bc[2]}/{d[9]}x+{cc[2]}/{d[10]}", "variableReplacements": [], "scripts": {}, "showpreview": true, "showCorrectAnswer": true, "checkvariablenames": false, "prompt": "<p>$\\simplify{({ac[2]}/{d[8]})x^3+({bc[2]}/{d[9]})x^2+({cc[2]}/{d[10]})x+({dc[2]}/{d[11]})}$</p>"}], "variable_groups": [], "functions": {}, "variables": {"dc": {"name": "dc", "definition": "repeat(random(-30..30),3)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "ac": {"name": "ac", "definition": "repeat(random(-3..3),3)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "cc": {"name": "cc", "definition": "repeat(random(-15..15),3)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "bc": {"name": "bc", "definition": "repeat(random(-10..10),3)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d": {"name": "d", "definition": "repeat(random(1..9),12)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "question_groups": [{"name": "", "questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0}], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Harry's copy of CF Maths Portfolio - Differentiation 2 - Basic Polynomial Expressions (with fractional coefficients)", "preamble": {"css": "", "js": ""}, "extensions": [], "showQuestionGroupNames": false, "ungrouped_variables": ["ac", "bc", "cc", "dc", "d"], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}