// Numbas version: exam_results_page_options {"name": "Eirik's copy of Solve equations which include a single root (e.g. \\sqrt{x}=blah)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "
a) Given $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, we raise both sides to the power of $\\var{intpower}$ to get $x$ by itself.
\n$\\sqrt[\\var{intpower}]{x}$ | \n$=$ | \n$\\var{intrhs}$ | \n
\n | \n | \n |
$\\left(\\sqrt[\\var{intpower}]{x}\\right)^{\\var{intpower}}$ | \n$=$ | \n$\\simplify[basic]{({intrhs})^{intpower}}$ | \n
\n | \n | \n |
$x$ | \n$=$ | \n$\\var{intsoln}$ | \n
b) Given $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, we can rearrange the equation to get $y^\\frac{1}{\\var{bpower}}$ by itself and then we can raise both sides to the power of $\\var{bpower}$ to get $y$ by itself.
\n$\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}$ | \n$=$ | \n$\\var{bc}$ | \n
\n | \n | \n |
$\\simplify{{bxcoeff}y^(1/{bpower})}$ | \n$=$ | \n$\\simplify[basic]{{bc}-{bb}}$ | \n
\n | \n | \n |
$\\simplify{{bxcoeff}y^(1/{bpower})}$ | \n$=$ | \n$\\simplify{{bc-bb}}$ | \n
\n | \n | \n |
$y^\\frac{1}{\\var{bpower}}$ | \n$=$ | \n$\\simplify[!basic]{{bc-bb}/{bxcoeff}}$ | \n
\n | \n | \n |
$y^\\frac{1}{\\var{bpower}}$ | \n$=$ | \n$\\simplify{{bc-bb}/{bxcoeff}}$ | \n
\n | \n | \n |
$\\left(y^\\frac{1}{\\var{bpower}}\\right)^{\\var{bpower}}$ | \n$=$ | \n$\\simplify[basic]{({(bc-bb)/bxcoeff})^{bpower}}$ | \n
\n | \n | \n |
$y$ | \n$=$ | \n$\\var{bsoln}$ | \n
c) Given $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, we can rearrange the equation to get $\\simplify{(root(z+{db},{dpower}))}$ by itself, then we can raise both sides to the power of $\\var{dpower}$, and finally rearrange to get $z$ by itself.
\n$\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}$ | \n$=$ | \n$\\var{dc}$ | \n
\n | \n | \n |
$\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$ | \n$=$ | \n$\\simplify[basic]{{dc}*{ddenom}}$ | \n
\n | \n | \n |
$\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$ | \n$=$ | \n$\\var{dc*ddenom}$ | \n
\n | \n | \n |
$\\left(\\sqrt[\\var{dpower}]{\\simplify{z+{db}}}\\right)^\\var{dpower}$ | \n$=$ | \n$\\simplify[basic]{({dc*ddenom})^{dpower}}$ | \n
\n | \n | \n |
$\\simplify{z+{db}}$ | \n$=$ | \n$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}}$ $\\simplify[basic]{({abs(dc*ddenom)})^{dpower}}$ $\\simplify[basic]{({(dc*ddenom)})^{dpower}}$ | \n
\n | \n | \n |
$z$ | \n$=$ | \n$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}-{db}}$ $\\simplify[basic]{({abs(dc*ddenom)})^{dpower}-{db}}$ $\\simplify[basic]{({(dc*ddenom)})^{dpower}-{db}}$ | \n
((bc-bb)/bxcoeff)^(1/bpower)
", "name": "bnice"}, "db": {"definition": "random(-100..100 except -1..1)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "db"}, "bpower": {"definition": "random(2..9)", "templateType": "anything", "group": "b", "description": "", "name": "bpower"}, "intsoln": {"definition": "intrhs^intpower", "templateType": "anything", "group": "a", "description": "", "name": "intsoln"}, "intpower": {"definition": "random(2..9)", "templateType": "anything", "group": "a", "description": "", "name": "intpower"}, "intrhs": {"definition": "switch(intpower=3 or intpower=4, random(2..12), intpower=5 or intpower=6, random(2..5), intpower=7 or intpower=8, random(2..3), 2)\n", "templateType": "anything", "group": "a", "description": "intsoln^intpower
", "name": "intrhs"}, "dpower": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "dpower"}, "ddenom": {"definition": "random(2..15)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "ddenom"}}, "parts": [{"gaps": [{"scripts": {}, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "checkvariablenames": false, "type": "jme", "answer": "{intsoln}", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrangepoints": 5, "showFeedbackIcon": true}], "prompt": "If $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, then $x=$ [[0]].
", "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}}, {"gaps": [{"scripts": {}, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "checkvariablenames": false, "type": "jme", "answer": "{bsoln}", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrangepoints": 5, "showFeedbackIcon": true}], "prompt": "If $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, then $y=$ [[0]].
", "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}}, {"gaps": [{"scripts": {}, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "answersimplification": "basic", "checkvariablenames": false, "type": "jme", "answer": "({dc*ddenom})^({dpower})-{db}", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrangepoints": 5, "showFeedbackIcon": true}], "prompt": "For this question, if the answer was $\\left(\\frac{35}{11}\\right)^{11}-24$, then you could enter (35/11)^(11)-24.
\nIf $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, then $z=$ [[0]].
", "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}}], "name": "Eirik's copy of Solve equations which include a single root (e.g. \\sqrt{x}=blah)", "ungrouped_variables": ["dpower", "dc", "db", "ddenom"], "metadata": {"description": "Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them).
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "statement": "Please complete the following.
", "rulesets": {}, "tags": [], "type": "question", "contributors": [{"name": "Eirik Heen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1225/"}]}]}], "contributors": [{"name": "Eirik Heen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1225/"}]}