Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd).
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Please complete the following.
", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"bsoln": {"name": "bsoln", "group": "b", "definition": "switch(bpower=3, random(-10..10 except -1..1), bpower=5, random(-4..4 except -1..1), bpower=7, random(-3..3 except -1..1), 2)", "description": "", "templateType": "anything", "can_override": false}, "intrhs": {"name": "intrhs", "group": "a", "definition": "intsoln^intpower\n", "description": "", "templateType": "anything", "can_override": false}, "powers": {"name": "powers", "group": "a", "definition": "shuffle([3,5,7,9])", "description": "", "templateType": "anything", "can_override": false}, "ddenom": {"name": "ddenom", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "can_override": false}, "cxcoeff": {"name": "cxcoeff", "group": "c", "definition": "random(-12..12 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "bc": {"name": "bc", "group": "b", "definition": "bsoln^bpower*bxcoeff+bb", "description": "", "templateType": "anything", "can_override": false}, "bpower": {"name": "bpower", "group": "b", "definition": "powers[1]", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "b", "definition": "random(1..100)", "description": "", "templateType": "anything", "can_override": false}, "dc": {"name": "dc", "group": "Ungrouped variables", "definition": "random(2..100 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "intpower": {"name": "intpower", "group": "a", "definition": "powers[0]", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "c", "definition": "if(cxcoeff>0,cb+random(10..50),cb-random(10..50))", "description": "This is to force the root to be taken of a positive power since the student input of negative ^ fraction leads to a complex number and I don't want the students to input using the root syntax
", "templateType": "anything", "can_override": false}, "brhs": {"name": "brhs", "group": "b", "definition": "(bc-bb)/bxcoeff", "description": "", "templateType": "anything", "can_override": false}, "bxcoeff": {"name": "bxcoeff", "group": "b", "definition": "random(-3..3 except 0..1)", "description": "", "templateType": "anything", "can_override": false}, "intsoln": {"name": "intsoln", "group": "a", "definition": "switch(intpower=3, random(2..12), intpower=5, random(2..5), intpower=7, random(2..3), 2)", "description": "", "templateType": "anything", "can_override": false}, "cpower": {"name": "cpower", "group": "c", "definition": "powers[2]", "description": "", "templateType": "anything", "can_override": false}, "db": {"name": "db", "group": "Ungrouped variables", "definition": "random(-100..100 except -1..1)", "description": "", "templateType": "anything", "can_override": false}, "cb": {"name": "cb", "group": "c", "definition": "random(-100..100)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dc", "db", "ddenom"], "variable_groups": [{"name": "a", "variables": ["intpower", "intrhs", "intsoln", "powers"]}, {"name": "b", "variables": ["bpower", "bsoln", "bxcoeff", "bb", "bc", "brhs"]}, {"name": "c", "variables": ["cpower", "cxcoeff", "cb", "cc"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "If $x^\\var{intpower}=\\var{intrhs}$, then $x=$ [[0]]. (This answer should be a whole number, use a calculator if necessary)
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Given $x^\\var{intpower}=\\var{intrhs}$, we can take the $\\var{intpower}$nd rd th root of both sides.
\n| $x^\\var{intpower}$ | \n$=$ | \n$\\var{intrhs}$ | \n
| \n | \n | \n |
| $\\sqrt[\\var{intpower}]{x^\\var{intpower}}$ | \n$=$ | \n$\\sqrt[\\var{intpower}]{\\var{intrhs}}$ | \n
| \n | \n | \n |
| $x$ | \n$=$ | \n$\\var{intsoln}$ | \n
If $\\simplify{{bxcoeff}y^{bpower}+{bb}}=\\var{bc}$, then $y=$ [[0]]. (This answer should be a whole number, use a calculator if necessary)
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Given $\\simplify{{bxcoeff}y^{bpower}+{bb}}=\\var{bc}$, we can rearrange the equation to get $y^\\var{bpower}$ by itself and then we can take the $\\var{bpower}$nd rd th root of both sides to get $y$ by itself.
\n| $\\simplify{{bxcoeff}y^{bpower}+{bb}}$ | \n$=$ | \n$\\var{bc}$ | \n
| \n | \n | \n |
| $\\simplify{{bxcoeff}y^{bpower}}$ | \n$=$ | \n$\\simplify[basic]{{bc}-{bb}}$ | \n
| \n | \n | \n |
| $\\simplify{{bxcoeff}y^{bpower}}$ | \n$=$ | \n$\\simplify{{bc-bb}}$ | \n
| \n | \n | \n |
| $y^\\var{bpower}$ | \n$=$ | \n$\\simplify[!basic]{{bc-bb}/{bxcoeff}}$ | \n
| \n | \n | \n |
| $y^\\var{bpower}$ | \n$=$ | \n$\\simplify{{bc-bb}/{bxcoeff}}$ | \n
| \n | \n | \n |
| $\\sqrt[\\var{bpower}]{y^\\var{bpower}}$ | \n$=$ | \n$\\sqrt[\\var{bpower}]{\\var{brhs}}$ | \n
| \n | \n | \n |
| $y$ | \n$=$ | \n$\\var{bsoln}$ | \n
For this question input the exact value by using a fractional power to indicate a root. For example, if the answer was $\\sqrt[3]{\\frac{35}{11}}$, then enter (35/11)^(1/3).
\nIf $\\simplify{{cxcoeff}z^{cpower}+{cb}}=\\var{cc}$, then $z=$ [[0]].
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Given $\\simplify{{cxcoeff}z^{cpower}+{cb}}=\\var{cc}$, we can rearrange the equation to get $z^\\var{cpower}$ by itself and then we can take the $\\var{cpower}$nd rd th root of both sides to get $z$ by itself.
\n| $\\simplify{{cxcoeff}z^{cpower}+{cb}}$ | \n$=$ | \n$\\var{cc}$ | \n
| \n | \n | \n |
| $\\simplify{{cxcoeff}z^{cpower}}$ | \n$=$ | \n$\\simplify[basic]{{cc}-{cb}}$ | \n
| \n | \n | \n |
| $\\simplify{{cxcoeff}z^{cpower}}$ | \n$=$ | \n$\\simplify{{cc-cb}}$ | \n
| \n | \n | \n |
| $z^\\var{cpower}$ | \n$=$ | \n$\\simplify[!basic]{{cc-cb}/{cxcoeff}}$ | \n
| \n | \n | \n |
| $z^\\var{cpower}$ | \n$=$ | \n$\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}$ | \n
| \n | \n | \n |
| $\\sqrt[\\var{cpower}]{z^\\var{cpower}}$ | \n$=$ | \n$\\sqrt[\\var{cpower}]{\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}}}$ | \n
| \n | \n | \n |
| $z$ | \n$=$ | \n$\\simplify[fractionNumbers]{{(cc-cb)/cxcoeff}^{1/{cpower}}}$ | \n
For this question input the exact value by using a fractional power to indicate a root. For example, if the answer was $\\sqrt[3]{\\frac{35}{11}}$, then enter (35/11)^(1/3).
\nIf $\\displaystyle{\\simplify{((z+{db})^{bpower})/({ddenom})}}=\\var{dc}$, then $z=$ [[0]].
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Given $\\displaystyle{\\simplify{((z+{db})^{bpower})/({ddenom})}}=\\var{dc}$, we can rearrange the equation to get $\\simplify{(z+{db})^{bpower}}$ by itself, then we can take the $\\var{bpower}$nd rd th root of both sides, and then rearrange to get $z$ by itself.
\n| $\\displaystyle{\\simplify{((z+{db})^{bpower})/({ddenom})}}$ | \n$=$ | \n$\\var{dc}$ | \n
| \n | \n | \n |
| $\\simplify{(z+{db})^{bpower}}$ | \n$=$ | \n$\\simplify[basic]{{dc}*{ddenom}}$ | \n
| \n | \n | \n |
| $\\simplify{(z+{db})^{bpower}}$ | \n$=$ | \n$\\var{dc*ddenom}$ | \n
| \n | \n | \n |
| $\\sqrt[\\var{bpower}]{\\simplify{(z+{db})^{bpower}}}$ | \n$=$ | \n$\\sqrt[\\var{bpower}]{\\var{dc*ddenom}}$ | \n
| \n | \n | \n |
| $\\simplify{z+{db}}$ | \n$=$ | \n$\\sqrt[\\var{bpower}]{\\var{dc*ddenom}}$ | \n
| \n | \n | \n |
| $z$ | \n$=$ | \n$\\simplify{root({dc*ddenom},{bpower})-{db}}$ | \n
| \n | \n | \n |
| $z$ | \n$=$ | \n$\\simplify{{dc*ddenom}^(1/{bpower})-{db}}$ | \n