// Numbas version: finer_feedback_settings
{"name": "HELM Book 1.2.4 exercises", "metadata": {"description": "<p>HELM Book 1.2.4 exercises</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "1.2.4.1 Rewrite an expression using a positive index", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.</p>\n<p>The variable a and the index k are randomised.</p>\n<p>Part of HELM Book 1.2</p>\n<p></p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write $\\displaystyle{\\var{expr}}$ using a positive index.</p>", "advice": "<p><span data-jme-visible=\"isFrac=1\">\\[\\var{expr}=\\frac{1}{\\var{v}^{\\var{idx}}}\\]</span></p>\n<p><span data-jme-visible=\"isFrac=0\">\\[\\var{expr}=\\var{v}^{\\var{idx}}\\]</span><span data-jme-visible=\"isFrac=0\"></span></p>\n<p><span data-jme-visible=\"(isfrac=0) and (idx=1)\">\\[=\\var{v}\\]</span></p>\n<p><span data-jme-visible=\"(isFrac=1) and (idx=1)\">\\[=\\frac{1}{\\var{v}}\\]</span></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"expr": {"name": "expr", "group": "Ungrouped variables", "definition": "if(isFrac,\n  expression(letter + \"^-\" + idx),\n  expression(\"1/\" + letter + \"^-\" + idx)\n)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "if(isFrac,\n  expression(\"1/\" + letter + \"^\" + idx),\n  expression(letter + \"^\" + idx)\n)", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "letter": {"name": "letter", "group": "Ungrouped variables", "definition": "random(random(alphabet),random(2..20))", "description": "", "templateType": "anything", "can_override": false}, "alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','v','w','x','y','z']", "description": "", "templateType": "anything", "can_override": false}, "isFrac": {"name": "isFrac", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>Is the answer a fraction?</p>", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(type(letter)=\"string\",\n  expression(letter),\n  expression(string(letter))\n)", "description": "<p>The expression version of the variable so that it displays correctly in the advice.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet", "letter", "idx", "isFrac", "expr", "ans", "v"], "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": "{ans}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": ["0.4", "0.8"], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "1.2.4.2 Simplify an expression using only positive indices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised and can be positive or negative numbers.</p>\n<p>Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify $\\displaystyle{\\var{q2_expr}}$. Do not use any negative indices in your answer.</p>", "advice": "<p>First simplify the numerator using the first law of indices.</p>\n<p>\\[\\var{q2_expr}=\\frac{\\var{v}^{(\\var{q2_idx1})+(\\var{q2_idx2})}}{\\var{v}^{(\\var{q2_idx3})}}=\\frac{\\var{v}^{(\\var{q2_idx1+q2_idx2})}}{\\var{v}^{(\\var{q2_idx3})}}\\]</p>\n<p>Then use the second law.</p>\n<p>\\[=\\var{v}^{(\\var{q2_idx1+q2_idx2})-(\\var{q2_idx3})}=\\var{v}^{\\var{q2_idx1+q2_idx2-q2_idx3}}\\]</p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)=0\">\\[=1\\]</span></p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)=1\">\\[=\\var{v}\\]</span></p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)&lt;0\">Finally, convert to a positive index.</span></p>\n<p><span data-jme-visible=\"(q2_idx1+q2_idx2-q2_idx3)&lt;0\">\\[=\\frac{1}{\\var{v}^{\\var{-1*(q2_idx1+q2_idx2-q2_idx3)}}}\\]</span></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q2_expr": {"name": "q2_expr", "group": "Ungrouped variables", "definition": "expression( \n  \"(\" + q2_letter + \"^\" + q2_idx1 + \"*\" + q2_letter + \"^\" + q2_idx2 + \")\" +\n  \"/\" + q2_letter + \"^\" + q2_idx3 )", "description": "", "templateType": "anything", "can_override": false}, "q2_ans": {"name": "q2_ans", "group": "Ungrouped variables", "definition": "simplify(if(q2_idx > 0,\n  expression(q2_letter+\"^\"+q2_idx),\n  expression(\"1/\"+q2_letter+\"^\"+q2_negidx)\n),[\"basic\",\"unitPower\",\"zeroPower\",\"simplifyFractions\"])", "description": "", "templateType": "anything", "can_override": false}, "alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','v','w','x','y','z']", "description": "", "templateType": "anything", "can_override": false}, "q2_letter": {"name": "q2_letter", "group": "Ungrouped variables", "definition": "random(random(alphabet),random(2..20))", "description": "", "templateType": "anything", "can_override": false}, "q2_idx": {"name": "q2_idx", "group": "Ungrouped variables", "definition": "q2_idx1+q2_idx2-q2_idx3", "description": "", "templateType": "anything", "can_override": false}, "q2_negidx": {"name": "q2_negidx", "group": "Ungrouped variables", "definition": "-q2_idx", "description": "", "templateType": "anything", "can_override": false}, "q2_idx1": {"name": "q2_idx1", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything", "can_override": false}, "q2_idx2": {"name": "q2_idx2", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything", "can_override": false}, "q2_idx3": {"name": "q2_idx3", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(type(q2_letter)=\"string\",\n  expression(q2_letter),\n  expression(string(q2_letter))\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet", "q2_letter", "q2_expr", "q2_ans", "q2_idx", "q2_negidx", "q2_idx1", "q2_idx2", "q2_idx3", "v"], "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, "stepsPenalty": 0, "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": "<p>First simplify the numerator using the first law of indices.</p>"}, {"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": "<p>Then use the second law.</p>"}, {"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": "<p>Finally, convert to a positive index, if needed.</p>"}], "answer": "{q2_ans}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": ["0.7", "0.8"], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": true, "caseSensitive": false, "notallowed": {"strings": ["-"], "showStrings": false, "partialCredit": 0, "message": ""}, "mustmatchpattern": {"pattern": "$v^$n`? `| 1/$v^$n`? `| $n^$n`? `| 1/$n^$n`? `| 1", "partialCredit": 0, "message": "You need to give the answer as a single variable to a positive power.", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "1.2.4.3 Rewrite expression without using indices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.</p>\n<p>Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write $\\var{q3_expr}$ as a fraction with no indices.</p>", "advice": "<p>\\[\\var{q3_expr}=\\frac{1}{10^{\\var{q3_idx}}}=\\frac{1}{\\var{10^q3_idx}}\\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q3_expr": {"name": "q3_expr", "group": "Ungrouped variables", "definition": "expression(\"10^-\"+q3_idx)", "description": "", "templateType": "anything", "can_override": false}, "q3_ans": {"name": "q3_ans", "group": "Ungrouped variables", "definition": "rational(1/(10^(q3_idx)))", "description": "", "templateType": "anything", "can_override": false}, "q3_idx": {"name": "q3_idx", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["q3_expr", "q3_ans", "q3_idx"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{q3_ans}", "maxValue": "{q3_ans}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": "", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>Work through these practice questions. You are encouraged to try each question multiple times as the expressions in each question will change each time you try it.&nbsp;</p>\n<p>(Note: To enter an answer of $\\dfrac{1}{m^5}$, type <code>1/m^(5)</code> )</p>", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "extensions": [], "custom_part_types": [], "resources": []}