// Numbas version: exam_results_page_options
{"name": "RAW demo", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "statement": "<p>This question is about manipulating linear and quadratic functions.&nbsp;</p>\n<p>(You could also use this section to provide any formulae the students might want to reference.) </p>\n<p>(Or it could be the main, referenced part of a multi-part question.) </p>\n<hr/>\n<p></p>", "variable_groups": [{"variables": ["x0", "a", "b"], "name": "Part 1"}, {"variables": ["a2", "b2", "c2", "name"], "name": "Part 2"}, {"variables": ["r", "s", "b3", "c3"], "name": "Part 3"}], "ungrouped_variables": [], "variables": {"c3": {"group": "Part 3", "description": "<p>Constant term in part 3.&nbsp;</p>", "definition": "r*s", "name": "c3", "templateType": "anything"}, "s": {"group": "Part 3", "description": "<p>One root of the polynomial in part 3.</p>", "definition": "random(-10..10 except [0,r])", "name": "s", "templateType": "anything"}, "c2": {"group": "Part 2", "description": "", "definition": "random(-5..5 except 0)", "name": "c2", "templateType": "anything"}, "b3": {"group": "Part 3", "description": "<p>Coefficient of x in part 3.</p>", "definition": "-(r+s)", "name": "b3", "templateType": "anything"}, "b": {"group": "Part 1", "description": "", "definition": "random(-5 .. 5#1)", "name": "b", "templateType": "randrange"}, "a2": {"group": "Part 2", "description": "", "definition": "random(-5..5 except 0)", "name": "a2", "templateType": "anything"}, "b2": {"group": "Part 2", "description": "", "definition": "random(-5..5 except 0)", "name": "b2", "templateType": "anything"}, "x0": {"group": "Part 1", "description": "<p>This is the value for x which is substituted in part 1.&nbsp;</p>", "definition": "random(0 .. 5#1)", "name": "x0", "templateType": "randrange"}, "name": {"group": "Part 2", "description": "", "definition": "random(['Matt','Jessica','Luke','Danny'])", "name": "name", "templateType": "anything"}, "a": {"group": "Part 1", "description": "", "definition": "random(-5 .. 5#1)", "name": "a", "templateType": "randrange"}, "r": {"group": "Part 3", "description": "<p>One root of the polynomial in part 3.&nbsp;</p>", "definition": "random(-10..10 except 0)", "name": "r", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A worked example about polynomials.&nbsp;</p>"}, "parts": [{"variableReplacementStrategy": "originalfirst", "showFractionHint": true, "prompt": "<p>Let's look at functions of the form $f(x) = \\simplify{a x + b}$.&nbsp;</p>\n<p>Suppose $f(x) = \\simplify{{a}x+{b}}$.&nbsp;</p>\n<p>Find $f(\\var{x0})$.&nbsp;</p>", "correctAnswerFraction": false, "minValue": "a*x0+b", "type": "numberentry", "useCustomName": false, "customMarkingAlgorithm": "", "variableReplacements": [], "mustBeReduced": false, "marks": 1, "unitTests": [], "customName": "", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "maxValue": "a*x0+b", "showFeedbackIcon": true, "scripts": {}, "allowFractions": false}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>{name}'s favourite quadratic is&nbsp;$g(x) = \\simplify[all,!noleadingminus]{{a2}x^2 + {b2}x + {c2}}$.</p>\n<p>Find $g'(x)$.&nbsp;</p>", "vsetRange": [0, 1], "checkingType": "absdiff", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "scripts": {}, "checkVariableNames": true, "failureRate": 1, "marks": "1", "unitTests": [], "customName": "", "answer": "2*{a2}*x+{b2}", "showCorrectAnswer": true, "vsetRangePoints": 5, "checkingAccuracy": 0.001, "extendBaseMarkingAlgorithm": true, "showPreview": true}, {"variableReplacementStrategy": "originalfirst", "stepsPenalty": "0", "vsetRangePoints": 5, "prompt": "<p>Consider the quadratic $h(x) = \\simplify{x^2 + {b3}x + {c3}}$.</p>\n<p>What is the set of roots of $h(x)$? Use the Numbas syntax&nbsp;<code>set(a,b,c)</code> in your answer.&nbsp;</p>\n<p></p>", "vsetRange": [0, 1], "checkingType": "absdiff", "type": "jme", "useCustomName": false, "customMarkingAlgorithm": "", "valuegenerators": [], "variableReplacements": [], "scripts": {}, "checkVariableNames": false, "steps": [{"variableReplacementStrategy": "originalfirst", "distractors": ["", "", "Check the sign of the coefficient of $x$. ", ""], "prompt": "<p>If the roots of $h(x)$ are $r$ and $s$, then $h(x) = (x-r)(x-s) = x^2 -(r+s)x +rs$.&nbsp;</p>\n<p>What does this tell us about $r$ and $s$?</p>", "displayColumns": 0, "useCustomName": false, "type": "1_n_2", "matrix": ["1", 0, 0, 0], "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "choices": ["$\\simplify{r+s = {-b3}}$ and $\\simplify{r s = {c3}}$.", "$\\simplify{r+s = {-b3}}$ and $\\simplify{r s = {-c3}}$.", "$\\simplify{r+s = {b3}}$ and $\\simplify{r s = {c3}}$.", "$\\simplify{r+s = {b3}}$ and $\\simplify{r s = {-c3}}$."], "maxMarks": 0, "marks": 0, "unitTests": [], "shuffleChoices": true, "customName": "", "showCorrectAnswer": true, "displayType": "radiogroup", "extendBaseMarkingAlgorithm": true, "showCellAnswerState": true, "showFeedbackIcon": true, "minMarks": 0}], "failureRate": 1, "marks": "2", "unitTests": [], "customName": "", "answer": "set({r},{s})", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "showFeedbackIcon": true, "showPreview": true}], "advice": "<p>When evaluating a function $f(x)$ at a point $x=\\var{x0}$, simply substitute $x$ in the expression with the value $\\var{x0}$.</p>\n<p>When differentiating a polynomial with respect to $x$,&nbsp;take each term $a_n x^n$ and multiply its coefficient by $n$ before reducing its power by 1, giving $n a_n x^{n-1}$.&nbsp;</p>\n<p>To find the roots of a quadratic, you&nbsp;might be able to do it by sight by noting that the sum of the two roots should be the negative of the coefficient of $x$, while the product of the two roots should be the constant term. This is explained in more detail in the expanded part above.&nbsp;</p>\n<p>Otherwise, you can always find the root(s) of a general quadratic $a x^2 + b x + c = 0$ by using the quadratic formula:&nbsp;</p>\n<p style=\"text-align: left;\">\\[r = \\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}\\]</p>", "functions": {}, "rulesets": {}, "extensions": [], "name": "RAW demo", "contributors": [{"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}]}]}], "contributors": [{"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}]}