// Numbas version: finer_feedback_settings {"name": "36. Multiplying Algebraic Terms", "metadata": {"description": "

Single term expressions various degrees of difficulty simplifying

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Simplifying coefficients and establishing the standardized order of writing expressions.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Simplify the following expression.

{MultiplicationToSimplify}

", "advice": "

To simplify multiplication we need to multiply all numbers together and collect any of the same variables together.

{Advice}

Use this link to find some resources which will help you revise this topic.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"LetterList": {"name": "LetterList", "group": "Ungrouped variables", "definition": "[\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"]", "description": "", "templateType": "anything", "can_override": false}, "Letter1": {"name": "Letter1", "group": "Ungrouped variables", "definition": "random(LetterList)", "description": "", "templateType": "anything", "can_override": false}, "Letter2": {"name": "Letter2", "group": "Ungrouped variables", "definition": "random(LetterList except Letter1)", "description": "", "templateType": "anything", "can_override": false}, "Number1": {"name": "Number1", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "Number2": {"name": "Number2", "group": "Ungrouped variables", "definition": "random(2..12 except Number1)", "description": "", "templateType": "anything", "can_override": false}, "TermChoice": {"name": "TermChoice", "group": "Ungrouped variables", "definition": "random([Letter1, Letter2, string(Number1), string(Number2)] except random(Letter1, Letter2, string(Number1), string(Number2)),[Letter1,Letter1,string(Number1)])", "description": "", "templateType": "anything", "can_override": false}, "TermOrder": {"name": "TermOrder", "group": "Ungrouped variables", "definition": "(([x,y,random(0..2 except [x,y])] for: y of: [random(0..2 except x)]) for: x of: [random(0..2)])[0][0]", "description": "", "templateType": "anything", "can_override": false}, "MultiplicationToSimplify": {"name": "MultiplicationToSimplify", "group": "Ungrouped variables", "definition": "\"

$\\\\var{Termchoice[TermOrder[0]]}\\\\times\\\\var{Termchoice[TermOrder[1]]}\\\\times\\\\var{Termchoice[TermOrder[2]]}$

\"", "description": "", "templateType": "long string", "can_override": false}, "Answer": {"name": "Answer", "group": "Ungrouped variables", "definition": "simplify(expression(Termchoice[TermOrder[0]]+\"*\"+Termchoice[TermOrder[1]]+\"*\"+Termchoice[TermOrder[2]]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "IsLetterTwice": {"name": "IsLetterTwice", "group": "Ungrouped variables", "definition": "TermChoice[0]=Letter1 && TermChoice[1]=Letter1", "description": "", "templateType": "anything", "can_override": false}, "IsNumberTwice": {"name": "IsNumberTwice", "group": "Ungrouped variables", "definition": "TermChoice[1]=string(Number1)", "description": "", "templateType": "anything", "can_override": false}, "AdviceIfLetterTwice": {"name": "AdviceIfLetterTwice", "group": "Ungrouped variables", "definition": "\"

Since we have two variables that are the same we can simplify by multiplying them together to get $\\\\var{Letter1}^2$. This gives us a final answer of \\\\[\\\\var{Answer}.\\\\]

\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceIfNumberTwice": {"name": "AdviceIfNumberTwice", "group": "Ungrouped variables", "definition": "\"

Since we have 2 different numbers we simplify by first multiplying these together to get $\\\\var{Number1}\\\\times\\\\var{Number2}=\\\\var{Number1*Number2}$. This gives us a final answer of \\\\[\\\\var{Answer}.\\\\]

\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceOtherwise": {"name": "AdviceOtherwise", "group": "Ungrouped variables", "definition": "\"

Since there are no repeated variables and we only have one number then we just write them all next to each other with the number in the front to get \\\\[\\\\var{Answer}.\\\\]

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Simplifying single term expressions involving more than one letter.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Simplify the following expression.

{MultiplicationToSimplify}

", "advice": "

To simplify multiplication we need to multiply all numbers together and collect any of the same variables together. Remember that $\\var{Coefficient1}\\var{Letter1}$ just means $\\var{Coefficient1}\\times\\var{Letter1}$.

First we will collect and multiply all of the numbers together. We have to multiply $\\simplify[UnitFactor,alwaysTimes]{{NumbersToMultiply[TermOrder[0]]}*{NumbersToMultiply[TermOrder[1]]}*{NumbersToMultiply[TermOrder[2]]}}$ together which gives us a coefficient of $\\var{AnswerCoefficient}$.

{Advice}

Use this link to find some resources which will help you revise this topic.

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$\\\\var{Termchoice[TermOrder[0]]}\\\\times\\\\var{Termchoice[TermOrder[1]]}\\\\times\\\\var{Termchoice[TermOrder[2]]}$

\"", "description": "", "templateType": "long string", "can_override": false}, "Answer": {"name": "Answer", "group": "Ungrouped variables", "definition": "simplify(expression(Termchoice[TermOrder[0]]+\"*\"+Termchoice[TermOrder[1]]+\"*\"+Termchoice[TermOrder[2]]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "IsLetterTwice": {"name": "IsLetterTwice", "group": "Ungrouped variables", "definition": "TermChoice[0]=Coefficient1+Letter1 && TermChoice[1]=Coefficient2+Letter1", "description": "", "templateType": "anything", "can_override": false}, "IsNumberTwice": {"name": "IsNumberTwice", "group": "Ungrouped variables", "definition": "TermChoice[1]=string(Number1)", "description": "", "templateType": "anything", "can_override": false}, "AdviceIfLetterTwice": {"name": "AdviceIfLetterTwice", "group": "Ungrouped variables", "definition": "\"

Since we have two variables that are the same we can simplify by multiplying them together to get $\\\\var{Letter1}^2$. This gives us a final answer of \\\\[\\\\var{Answer}.\\\\]

\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceIfNumberTwice": {"name": "AdviceIfNumberTwice", "group": "Ungrouped variables", "definition": "\"

Since we only have one variable we just multiply this by the coefficient we have already worked out to get a final answer of \\\\[\\\\var{Answer}.\\\\]

\"", "description": "", "templateType": "long string", "can_override": false}, "Advice": {"name": "Advice", "group": "Ungrouped variables", "definition": "if(IsLetterTwice, AdviceIfLetterTwice, if(IsNumberTwice, AdviceIfNumberTwice, AdviceOtherwise))", "description": "", "templateType": "anything", "can_override": false}, "Coefficient1": {"name": "Coefficient1", "group": "Ungrouped variables", "definition": "string(random(2..8))", "description": "", "templateType": "anything", "can_override": false}, "Coefficient2": {"name": "Coefficient2", "group": "Ungrouped variables", "definition": "string(random(2..5))", "description": "", "templateType": "anything", "can_override": false}, "NumbersToMultiply": {"name": "NumbersToMultiply", "group": "Ungrouped variables", "definition": "if(IsNumberTwice, [int(dec(Coefficient1)),Number1,Number2], if(IsLetterTwice, [int(dec(Coefficient1)),int(dec(Coefficient2)),Number1], if(IsTwoLettersWithCoeff, [int(dec(Coefficient1)),int(dec(Coefficient2)),int(dec(TermChoice[2]))], [int(dec(Coefficient1)),Number1,1])))", "description": "", "templateType": "anything", "can_override": false}, "AnswerCoefficient": {"name": "AnswerCoefficient", "group": "Ungrouped variables", "definition": "NumbersToMultiply[0]*NumbersToMultiply[1]*NumbersToMultiply[2]", "description": "", "templateType": "anything", "can_override": false}, "IsTwoLettersWithCoeff": {"name": "IsTwoLettersWithCoeff", "group": "Ungrouped variables", "definition": "TermChoice[0]=Coefficient1+Letter1 && TermChoice[1]=Coefficient2+Letter2", "description": "", "templateType": "anything", "can_override": false}, "AdviceOtherwise": {"name": "AdviceOtherwise", "group": "Ungrouped variables", "definition": "\"

Since our two variables are different we can\\'t simplify those any further so we just multiply them by our coefficient to get a final answer of \\\\[\\\\var{Answer}.\\\\]

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Simplifying single term expressions involving indices.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Simplify the following expression.

{MultiplicationToSimplify}

", "advice": "

To simplify $\\var{expression(Termchoice[0]+\"*\"+Termchoice[1])}$ we need to multiply the coefficients together and multiply $\\var{expression(LetterPower1)}$ with $\\var{expression(LetterPower2)}$ because they are powers of the same variable. Multiplying the coefficients together gives us

\\[\\var{Coefficient1}\\times\\var{Coefficient2}=\\simplify[all]{{expression(Coefficient1+\"*\"+Coefficient2)}}.\\]

To multiply $\\var{expression(LetterPower1)}$ with $\\var{expression(LetterPower2)}$ we add the powers together to give us $\\simplify[all]{{expression(LetterPower1+\"*\"+LetterPower2)}}$. Putting these together we get a final simplified answer of

\\[\\var{Answer}.\\]

Use this link to find some resources which will help you revise this topic.

$\\\\var{expression(Termchoice[0]+\\\"*\\\"+Termchoice[1])}$

\"", "description": "", "templateType": "long string", "can_override": false}, "Answer": {"name": "Answer", "group": "Ungrouped variables", "definition": "simplify(expression(Termchoice[0]+\"*\"+Termchoice[1]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "Coefficient1": {"name": "Coefficient1", "group": "Ungrouped variables", "definition": "string(random(2..8))", "description": "", "templateType": "anything", "can_override": false}, "Coefficient2": {"name": "Coefficient2", "group": "Ungrouped variables", "definition": "string(random(2..8))", "description": "", "templateType": "anything", "can_override": false}, "Power1": {"name": "Power1", "group": "Ungrouped variables", "definition": "string(random(1..3))", "description": "", "templateType": "anything", "can_override": false}, "Power2": {"name": "Power2", "group": "Ungrouped variables", "definition": "string(random(1..3))", "description": "", "templateType": "anything", "can_override": false}, "LetterPower1": {"name": "LetterPower1", "group": "Ungrouped variables", "definition": "if(Power1=\"1\",Letter1,Letter1+\"^\"+Power1)", "description": "", "templateType": "anything", "can_override": false}, "LetterPower2": {"name": "LetterPower2", "group": "Ungrouped variables", "definition": "if(Power2=\"1\",Letter1,Letter1+\"^\"+Power2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "not(Power1=\"1\" && Power2=\"1\")", "maxRuns": 100}, "ungrouped_variables": ["LetterList", "Letter1", "Coefficient1", "Coefficient2", "Power1", "Power2", "LetterPower1", "LetterPower2", "TermChoice", "MultiplicationToSimplify", "Answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{Answer}", "answerSimplification": "!all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n*$v^$n", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": false, "typeendtoleave": false, "startpassword": "", "autoSubmit": false, "allowAttemptDownload": false, "downloadEncryptionKey": "", "showresultspage": "oncompletion"}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showpartfeedbackmessageswhen": "always", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": true, "intro": "", "end_message": "", "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": true, "reviewshowfeedback": true, "showactualmark": true, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "extensions": [], "custom_part_types": [], "resources": []}