2..6
"}, "neg": {"templateType": "anything", "group": "Ungrouped variables", "name": "neg", "definition": "random(-12..-1)", "description": ""}, "primes": {"templateType": "anything", "group": "Ungrouped variables", "name": "primes", "definition": "shuffle([2,3,5,7,11,13,17,19])[0..3] ", "description": ""}, "diffpow1": {"templateType": "anything", "group": "Ungrouped variables", "name": "diffpow1", "definition": "powers1[0][0]-powers1[1][0]", "description": ""}, "powers3": {"templateType": "anything", "group": "Ungrouped variables", "name": "powers3", "definition": "shuffle([[2,\"two\"],[3,\"three\"],[4,\"four\"],[5,\"five\"],[6,\"six\"]])[0..3]", "description": ""}}, "variable_groups": [], "type": "question", "parts": [{"showCorrectAnswer": true, "gaps": [{"checkingtype": "absdiff", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "marks": 1, "showCorrectAnswer": true, "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"}}, "checkvariablenames": false, "type": "jme", "showpreview": true, "answer": "{base1}^{diffpow1}", "variableReplacements": [], "answersimplification": "basic", "expectedvariablenames": [], "checkingaccuracy": "0.0000001", "musthave": {"strings": ["^"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "steps": [{"variableReplacements": [], "prompt": "Write the division as a fraction and cancel common factors.
\nRecall, negative indices mean you divided by more than you had, for example, $\\displaystyle \\frac{1}{12^3}$ can be written as $12^{-3}$.
\n\n
In general, we have $\\displaystyle\\frac{a^b}{a^c}=a^{b-c}$.
", "showCorrectAnswer": true, "scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst"}], "prompt": "$\\var{base1}^\\var{powers1[0][0]}\\div \\var{base1}^\\var{powers1[1][0]}$ = [[0]]
", "scripts": {}, "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "gaps": [{"checkingtype": "absdiff", "vsetrangepoints": 5, "marks": 1, "showCorrectAnswer": true, "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"}}, "checkvariablenames": false, "type": "jme", "showpreview": true, "answer": "{base2}^{diffpow2}", "variableReplacements": [], "answersimplification": "basic", "expectedvariablenames": [], "checkingaccuracy": "0.0000001", "musthave": {"strings": ["^"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "steps": [{"variableReplacements": [], "prompt": "Cancel common factors.
\nRecall, negative indices mean you divided by more than you had, for example, $\\displaystyle \\frac{1}{12^3}$ can be written as $12^{-3}$.
\n\n
In general, we have $\\displaystyle\\frac{a^b}{a^c}=a^{b-c}$.
", "showCorrectAnswer": true, "scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst"}], "prompt": "$\\displaystyle\\frac{\\var{base2}^\\var{powers2[0]}\\times\\var{base2}}{\\var{base2}^\\var{powers2[1]} \\times \\var{base2}^\\var{powers2[2]}}$ = [[0]]
\n\n", "scripts": {}, "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "gaps": [{"checkingtype": "absdiff", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "marks": 1, "showCorrectAnswer": true, "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"}}, "checkvariablenames": false, "type": "jme", "showpreview": true, "answer": "{base2}^{diffpow3}", "variableReplacements": [], "answersimplification": "basic", "expectedvariablenames": [], "checkingaccuracy": "0.0000001", "musthave": {"strings": ["^"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "steps": [{"variableReplacements": [], "prompt": "Since the bases are all the same ($\\var{base2}$) and we are dividing, we can simply subtract the powers.
\n\n
In general, we have $\\displaystyle\\frac{a^b}{a^c}=a^{b-c}$.
", "showCorrectAnswer": true, "scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst"}], "prompt": "Use the same approach you used in the above questions to simplify the following in index form.
\n
$\\displaystyle\\frac{\\var{base2}^\\var{ndec}}{\\var{base2}^\\var{neg}}$ = [[0]]
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 $12^\\frac{2}{3}$.
\n\n", "scripts": {}, "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "gaps": [{"checkingtype": "absdiff", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "marks": 1, "showCorrectAnswer": true, "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"}}, "checkvariablenames": false, "type": "jme", "showpreview": true, "answer": "{base1}^{powers3[1][0]}*{base3}^{diffpow4}", "variableReplacements": [], "answersimplification": "basic", "expectedvariablenames": [], "checkingaccuracy": "0.00001", "musthave": {"strings": ["^"], "message": "Use ^ for powers. Input your answer in index form.
", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "steps": [{"variableReplacements": [], "prompt": "It is important to note that the bases are different! Index laws only can be applied if the bases are the same (or can be made the same). Because of this we deal with the different bases separately.
\n\nNotice the first part of the expression can not be simplified using index laws.
\n$\\var{base3}^\\var{powers3[0][0]}\\times \\var{base1}^\\var{powers3[1][0]}$
\nHowever, with the division we can do some simplification. We can either:
\n$\\var{base3}^\\var{powers3[0][0]}\\times \\var{base1}^\\var{powers3[1][0]} \\div \\var{base3}^\\var{powers3[2][0]}$ = [[0]]
\n\nNote: use * for multiplication.
", "scripts": {}, "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst"}, {"matrix": [0, "1"], "shuffleChoices": false, "choices": ["True
", "False
"], "steps": [{"variableReplacements": [], "prompt": "It is important to note that the bases are different! Index laws only can be applied if the bases are the same (or can be made the same).
", "showCorrectAnswer": true, "scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst"}], "minMarks": 0, "showCorrectAnswer": true, "scripts": {}, "distractors": ["", ""], "maxMarks": 0, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "prompt": "Is the following statement true or false?
\n$\\displaystyle\\frac{\\var{2*base2}}{\\var{base2}^\\var{powers1[0][0]}} = \\var{2}^\\var{-powers1[0][0]}$
", "variableReplacements": [], "displayColumns": 0, "marks": 0, "type": "1_n_2", "displayType": "radiogroup"}, {"matrix": [0, "1"], "shuffleChoices": false, "choices": ["True
", "False
"], "steps": [{"variableReplacements": [], "prompt": "It is important to note that the 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.
", "showCorrectAnswer": true, "scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst"}], "minMarks": 0, "showCorrectAnswer": true, "scripts": {}, "distractors": ["", ""], "maxMarks": 0, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "prompt": "Is the following statement true or false?
\n$\\displaystyle\\frac{\\var{2*base2}}{\\var{base2}^\\var{powers1[0][0]}} = \\var{2}^\\var{1-powers1[0][0]}$
", "variableReplacements": [], "displayColumns": 0, "marks": 0, "type": "1_n_2", "displayType": "radiogroup"}, {"matrix": ["1", "0"], "shuffleChoices": false, "choices": ["True
", "False
"], "steps": [{"variableReplacements": [], "prompt": "It is important to note that the 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.
\n\nNote in this question we can make the bases the same.
\n\\[\\frac{\\var{2*base2}}{\\var{base2}^\\var{powers1[0][0]}} = \\frac{2\\times\\var{base2}}{\\var{base2}^\\var{powers1[0][0]}} = 2\\times\\var{base2}^\\var{1-powers1[0][0]}\\]
", "showCorrectAnswer": true, "scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst"}], "minMarks": 0, "showCorrectAnswer": true, "scripts": {}, "distractors": ["", ""], "maxMarks": 0, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "prompt": "Is the following statement true or false?
\n$\\displaystyle\\frac{\\var{2*base2}}{\\var{base2}^\\var{powers1[0][0]}} = 2\\times\\var{base2}^\\var{1-powers1[0][0]}$
", "variableReplacements": [], "displayColumns": 0, "marks": 0, "type": "1_n_2", "displayType": "radiogroup"}], "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "statement": "Simplify the following without the use of a calculator. Write your answer in index form using ^ to signify powers. Use negative powers if necessary.
", "ungrouped_variables": ["primes", "base1", "powers1", "diffpow1", "base2", "powers2", "diffpow2", "ndec", "neg", "diffpow3", "base3", "powers3", "diffpow4", "minpow4"], "rulesets": {}, "advice": "", "tags": ["Dividing", "dividing", "exponent", "exponents", "index", "index laws", "indices", "power", "powers", "subtracting"], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "notes": "It is possible that the first answer doesn't need a
Before this we need a question about negative indices I think.