// Numbas version: exam_results_page_options
{"name": "Substituting values into algebraic expressions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Substituting values into algebraic expressions", "tags": [], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Given $a=\\var{aval}$, $b=\\var{bval}$ and $c=\\var{cval}$, the value of $b^2-4ac$ is&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "disans", "minValue": "disans", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>Be mindful of the order of operations and negatives when evaluating expressions.</em></p>\n<p><em></em></p>\n<p>Substituting $a=\\var{aval}$, $b=\\var{bval}$ and $c=\\var{cval}$ into $b^2-4ac$ gives</p>\n<p>\\[(\\var{bval})^2-4(\\var{aval})(\\var{cval})=\\simplify[basic]{{bval^2}-4{aval}{cval}}=\\simplify[basic]{{bval^2}+{-4*aval*cval}}=\\var{disans}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>If $x=\\var{xval}$ and $y=\\var{yval}$ then $\\simplify{(x-{x0})^2+(y-{y0})^2}$ =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "cirans", "minValue": "cirans", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>Be mindful of the order of operations and negatives when evaluating expressions.</em></p>\n<p></p>\n<p>Substituting $x=\\var{xval}$ and $y=\\var{yval}$ into $\\simplify{(x-{x0})^2+(y-{y0})^2}$ &nbsp;gives</p>\n<p>\\[\\simplify[basic]{({xval}-{x0})^2+({yval}-{y0})^2}=(\\var{xval-x0})^2+(\\var{yval-y0})^2=\\var{(xval-x0)^2}+\\var{(yval-y0)^2}=\\var{cirans}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "statement": "", "variable_groups": [{"variables": ["x0", "y0", "xval", "yval", "cirans"], "name": "Circle"}, {"variables": ["aval", "bval", "cval", "disans"], "name": "Discriminant"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"disans": {"definition": "bval^2-4*aval*cval", "templateType": "anything", "group": "Discriminant", "name": "disans", "description": ""}, "yval": {"definition": "random(-7..7 except [0,xval,y0])", "templateType": "anything", "group": "Circle", "name": "yval", "description": ""}, "aval": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Discriminant", "name": "aval", "description": ""}, "cirans": {"definition": "(xval-x0)^2+(yval-y0)^2", "templateType": "anything", "group": "Circle", "name": "cirans", "description": ""}, "y0": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Circle", "name": "y0", "description": ""}, "xval": {"definition": "random(-7..7 except [0,x0])", "templateType": "anything", "group": "Circle", "name": "xval", "description": ""}, "x0": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Circle", "name": "x0", "description": ""}, "bval": {"definition": "random(-12..12)", "templateType": "anything", "group": "Discriminant", "name": "bval", "description": ""}, "cval": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Discriminant", "name": "cval", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}