// Numbas version: exam_results_page_options
{"name": "Negatives: powers of negative numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"type": "question", "functions": {}, "name": "Negatives: powers of negative numbers", "variable_groups": [], "tags": ["exponents", "indices", "negative numbers", "Negative Numbers", "negatives", "powers"], "variables": {"ans1": {"definition": "-n[0]^2", "name": "ans1", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ans4": {"definition": "(-1)^p", "name": "ans4", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "n": {"definition": "shuffle(-12..-2)[0..2]", "name": "n", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ans3": {"definition": "m^3", "name": "ans3", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"definition": "random(-5..-1)", "name": "m", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "p": {"definition": "random(4..12)", "name": "p", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ans2": {"definition": "n[1]^2", "name": "ans2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "showQuestionGroupNames": false, "preamble": {"js": "", "css": ""}, "question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "ungrouped_variables": ["n", "ans1", "ans2", "m", "ans3", "ans4", "p"], "advice": "", "parts": [{"prompt": "<p>$\\var{n[0]}^2$ =&nbsp;[[0]]</p>", "showCorrectAnswer": true, "steps": [{"prompt": "<p>Here the square is acting only on the number and not on the negative sign. So you square the number first and then take the negative.</p>\n<p>\\[-6^2\\ne (-6)^2\\]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "information", "variableReplacements": [], "marks": 0}], "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans1}", "showPrecisionHint": false, "marks": 1}], "scripts": {}, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$(\\var{n[1]})^2$ =&nbsp;[[0]]</p>", "showCorrectAnswer": true, "steps": [{"prompt": "<p>Here we have the square acting on a negative number. When two negatives are multiplied together the result is a positive number.&nbsp;</p>\n<p>This means when a negative number is squared the result is positive.</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "information", "variableReplacements": [], "marks": 0}], "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans2}", "showPrecisionHint": false, "marks": 1}], "scripts": {}, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$-(\\var{n[1]})^2$ =&nbsp;[[0]]</p>", "showCorrectAnswer": true, "steps": [{"prompt": "<p>Deal with the squaring of the negative number first (which results in a positive) and then deal with the negative outside the brackets.&nbsp;</p>\n<p>\\[-(-2)^2\\ne 2^2\\]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "information", "variableReplacements": [], "marks": 0}], "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "minValue": "{-ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{-ans2}", "showPrecisionHint": false, "marks": 1}], "scripts": {}, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$(\\var{m})^3$ =&nbsp;[[0]]</p>", "showCorrectAnswer": true, "steps": [{"prompt": "<p>Suppose you had $(-10)^3$. Recall this is the same as $(-10)\\times(-10)\\times(-10)$. Here we have three negative symbols, <g class=\"gr_ gr_314 gr-alert gr_spell ContextualSpelling\" id=\"314\" data-gr-id=\"314\">two</g> give a positive and the remaining negative makes the result negative, that is,</p>\n<p>\\[(-10)^3=-1000\\]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "information", "variableReplacements": [], "marks": 0}], "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans3}", "showPrecisionHint": false, "marks": 1}], "scripts": {}, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$(-1)^\\var{p}$ =&nbsp;[[0]]</p>", "showCorrectAnswer": true, "steps": [{"prompt": "<p>Any even power of a negative number will have an even number of negatives multiplied together. This will then result in a positive number.</p>\n<p></p>\n<p>Any odd power of a negative number will have an odd number of negatives multiplied together. This will then result in a negative number.</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "information", "variableReplacements": [], "marks": 0}], "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans4}", "showPrecisionHint": false, "marks": 1}], "scripts": {}, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "marks": 0}], "metadata": {"notes": "<p>need to put steps in to explain the answers, maybe then have a combined ridiculous question.</p>", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Complete the following without the use of a calculator:</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}