// Numbas version: exam_results_page_options
{"name": "Ida's copy of Indices: adding powers (algebraic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"showQuestionGroupNames": false, "type": "question", "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "preamble": {"css": "", "js": ""}, "name": "Ida's copy of Indices: adding powers (algebraic)", "functions": {}, "tags": ["adding", "exponent", "exponents", "index", "index laws", "indices", "multiplying", "power", "powers"], "question_groups": [{"name": "", "questions": [], "pickQuestions": 0, "pickingStrategy": "all-ordered"}], "variables": {"powers3": {"description": "", "definition": "shuffle([[2,\"two\"],[3,\"three\"],[4,\"four\"],[5,\"five\"],[6,\"six\"]])[0..2]", "group": "Ungrouped variables", "templateType": "anything", "name": "powers3"}, "dec": {"description": "", "definition": "random(0.1..0.9#0.1)", "group": "Ungrouped variables", "templateType": "anything", "name": "dec"}, "sumpow2": {"description": "", "definition": "wild[0]+1", "group": "Ungrouped variables", "templateType": "anything", "name": "sumpow2"}, "den": {"description": "", "definition": "random([10,20,25])", "group": "Ungrouped variables", "templateType": "anything", "name": "den"}, "powers1": {"description": "<p>2..6</p>", "definition": "shuffle([[2,\"two\"],[3,\"three\"],[4,\"four\"],[5,\"five\"],[6,\"six\"]])[0..3]", "group": "Ungrouped variables", "templateType": "anything", "name": "powers1"}, "neg": {"description": "", "definition": "random(-12..-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "neg"}, "wild": {"description": "", "definition": "random([[2,\"two\"],[3,\"three\"],[4,\"four\"],[5,\"five\"],[6,\"six\"]])", "group": "Ungrouped variables", "templateType": "anything", "name": "wild"}, "sumpow3": {"description": "", "definition": "dec+neg+num/den", "group": "Ungrouped variables", "templateType": "anything", "name": "sumpow3"}, "sumpow1": {"description": "", "definition": "powers1[0][0]+powers1[1][0]+powers1[2][0]", "group": "Ungrouped variables", "templateType": "anything", "name": "sumpow1"}, "num": {"description": "", "definition": "random(1..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "num"}, "powers2": {"description": "", "definition": "shuffle([[0,\"zero\"],[1,\"one\"],wild])", "group": "Ungrouped variables", "templateType": "anything", "name": "powers2"}, "sumpow4": {"description": "", "definition": "powers3[0][0]+powers3[1][0]", "group": "Ungrouped variables", "templateType": "anything", "name": "sumpow4"}}, "variablesTest": {"maxRuns": 100, "condition": "\n"}, "statement": "<p>Simplify the following without the use of a calculator. Write your answer in index form using ^ to signify powers.</p>", "advice": "", "ungrouped_variables": ["powers1", "wild", "powers2", "sumpow1", "sumpow2", "dec", "neg", "num", "den", "sumpow3", "powers3", "sumpow4"], "parts": [{"steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Recall:</p>\n<ul>\n<li>$w^\\var{powers1[0][0]}$ means $\\var{powers1[0][1]}$ $w$s all multiplied together.&nbsp;</li>\n<li>$w^\\var{powers1[1][0]}$ means $\\var{powers1[1][1]}$ $w$s all multiplied together.&nbsp;</li>\n<li>$w^\\var{powers1[2][0]}$ means $\\var{powers1[2][1]}$ $w$s all multiplied together.&nbsp;</li>\n</ul>\n<p>So in total how many $w$s are there multiplied together?&nbsp;</p>\n<p>Well, $\\var{powers1[0][0]}+\\var{powers1[1][0]}+\\var{powers1[2][0]}=\\var{sumpow1}$. And so our answer is $w^\\var{sumpow1}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Note, in general $a^ba^c=a^{b+c}$.</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "type": "gapfill", "gaps": [{"type": "jme", "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "showpreview": true, "variableReplacements": [], "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": "0.001", "marks": 1, "checkingtype": "absdiff", "showCorrectAnswer": true, "answersimplification": "basic", "notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^0"], "showStrings": false}, "vsetrangepoints": 5, "answer": "w^{sumpow1}", "checkvariablenames": false, "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^"], "showStrings": false}, "expectedvariablenames": []}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>$ w ^\\var{powers1[0][0]}\\times w ^\\var{powers1[1][0]} \\times w ^\\var{powers1[2][0]}$ =&nbsp;[[0]]</p>", "variableReplacements": [], "stepsPenalty": "1", "scripts": {}, "showCorrectAnswer": true, "marks": 0}, {"steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Recall:</p>\n<ul>\n<li>$x^0$ means no $x$s all multiplied together. (As you know, $x^0=1$).</li>\n<li>$x^1$ means just one $x$. (As you know, $x^1=x$)</li>\n<li>$x^\\var{wild[0]}$ means $\\var{wild[1]}$ $x$s all multiplied together.&nbsp;</li>\n</ul>\n<p>So in total how many $x$s are there multiplied together?&nbsp;</p>\n<p>Well, $0+1+\\var{wild[0]}=\\var{sumpow2}$. And so our answer is $x^\\var{sumpow2}$.</p>\n<p></p>\n<hr/>\n<p>Note, in general $a^ba^c=a^{b+c}$, $a^0=1$ and $a^1=a$.</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "type": "gapfill", "gaps": [{"type": "jme", "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "showpreview": true, "variableReplacements": [], "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": 0.001, "marks": 1, "checkingtype": "absdiff", "showCorrectAnswer": true, "answersimplification": "!otherNumbers", "notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^0"], "showStrings": false}, "vsetrangepoints": 5, "answer": "x^{sumpow2}", "checkvariablenames": false, "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^"], "showStrings": false}, "expectedvariablenames": []}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>$x^\\var{powers2[0][0]}\\times x^\\var{powers2[1][0]} \\times x^\\var{powers2[2][0]}$ =&nbsp;[[0]]</p>\n<p></p>\n<p></p>", "variableReplacements": [], "stepsPenalty": "1", "scripts": {}, "showCorrectAnswer": true, "marks": 0}, {"steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Since the bases are all the same ($a$) and we are multiplying, we can simply add the powers.&nbsp;</p>\n<p>You could convert the fraction to a decimal and then add them all. Or you could add them all as fractions.&nbsp;</p>\n<p></p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "type": "gapfill", "gaps": [{"type": "jme", "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "showpreview": true, "variableReplacements": [], "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": 0.001, "marks": 1, "checkingtype": "absdiff", "showCorrectAnswer": true, "answersimplification": "basic", "notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^0"], "showStrings": false}, "vsetrangepoints": 5, "answer": "a^{sumpow3}", "checkvariablenames": false, "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^"], "showStrings": false}, "expectedvariablenames": []}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Use the same approach you used in the above questions to simplify the following in index form.</p>\n<p><br/>$\\displaystyle a^\\var{dec}\\times a^\\var{neg} \\times a^{\\var{num}/\\var{den}}$ =&nbsp;[[0]]</p>\n<p></p>\n<p>Note: If you want to use a fraction as a power you should use brackets to surround your power, for example, type 12^(2/3) for $12^\\frac{2}{3}$.</p>\n<p></p>\n<p></p>", "variableReplacements": [], "stepsPenalty": "1", "scripts": {}, "showCorrectAnswer": true, "marks": 0}, {"steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "prompt": "<p>It is important to note that the&nbsp;bases are different! We can only add the powers if the bases are the same.&nbsp;</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Recall:</p>\n<ul>\n<li>$z^\\var{powers3[0][0]}$ means $\\var{powers3[0][1]}$ $z$s all multiplied together.&nbsp;</li>\n<li>$z^\\var{powers3[1][0]}$ means $\\var{powers3[1][1]}$ $z$s all multiplied together.&nbsp;</li>\n<li>$y^\\var{wild[0]}$ means $\\var{wild[1]}$ $y$s all multiplied together.&nbsp;</li>\n</ul>\n<p>So in total what do we have?</p>\n<p>&nbsp;$y^\\var{wild[0]}z^\\var{sumpow4}$.<br/><br/></p>\n<p></p>\n<hr/>\n<p></p>\n<p>Note we would type {base1}^{wild[0]}*{base3}^{sumpow4}.</p>\n<p></p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "type": "gapfill", "gaps": [{"type": "jme", "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "showpreview": true, "variableReplacements": [], "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ?? * ?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": 0.001, "marks": 1, "checkingtype": "absdiff", "showCorrectAnswer": true, "answersimplification": "basic", "notallowed": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^0"], "showStrings": false}, "vsetrangepoints": 5, "answer": "y^{wild[0]}*z^{sumpow4}", "checkvariablenames": false, "musthave": {"message": "<p>Use ^ for powers. Input your answer in index form.</p>", "partialCredit": 0, "strings": ["^"], "showStrings": false}, "expectedvariablenames": []}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>$z^\\var{powers3[0][0]}\\times y^\\var{wild[0]} \\times z^\\var{powers3[1][0]}$ =&nbsp;[[0]]</p>\n<p></p>\n<p>Note: use * for multiplication.</p>", "variableReplacements": [], "stepsPenalty": "1", "scripts": {}, "showCorrectAnswer": true, "marks": 0}, {"type": "1_n_2", "displayType": "radiogroup", "choices": ["<p>True</p>", "<p>False</p>"], "prompt": "<p>Is the following statement true or false?</p>\n<p>$m\\times p^\\var{powers1[0][0]} = (mp)^\\var{powers1[0][0]}$</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "prompt": "<p>It is important to note that the&nbsp;bases are different! Index laws only can be applied if the bases are the same (or can be made the same).</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "matrix": [0, "1"], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "minMarks": 0, "distractors": ["", ""], "marks": 0, "stepsPenalty": "1", "displayColumns": 0, "shuffleChoices": false}, {"type": "1_n_2", "displayType": "radiogroup", "choices": ["<p>True</p>", "<p>False</p>"], "prompt": "<p>Is the following statement true or false?</p>\n<p>$q\\times u^\\var{powers1[0][0]} = (qu)^\\var{powers1[0][0]+1}$</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "prompt": "<p>It is important to note that the&nbsp;bases are different! Index laws only can be applied if the bases are the same (or can be made the same). We can only add the powers if the bases are the same.&nbsp;</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "matrix": [0, "1"], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "minMarks": 0, "distractors": ["", ""], "marks": 0, "stepsPenalty": "1", "displayColumns": 0, "shuffleChoices": false}], "rulesets": {}, "variable_groups": [], "contributors": [{"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}]}], "contributors": [{"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}