// Numbas version: exam_results_page_options
{"name": "Powers of negative numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["n", "ans1", "ans2", "m", "ans3", "ans4", "p"], "name": "Powers of negative numbers", "tags": ["exponents", "indices", "negative numbers", "Negative Numbers", "negatives", "powers"], "preamble": {"css": "", "js": ""}, "advice": "<p>Notice that we need to distinguish between, say, $-3^2$ and $(-3)^2$. The convention is that when we write $(-3)^2$ we mean the square of $-3$, which is $9$. When we write $-3^2$ we mean minus the square of $3$ or $-9$.</p>\n<p>In part (d), $\\var{m}^3 = \\var{m} \\times \\var{m} \\times \\var{m}$. Multiplying three negative numbers together will give us a negative answer.</p>\n<p>In part (e) the sign of the answer will depend on the power. Multiplying an even number of negative numbers will give us a positive answer; multiplying an odd number of negative numbers will give us a negative answer.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\var{n[0]}^2$ =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$(\\var{n[1]})^2$ =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$-(\\var{n[1]})^2$ =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{-ans2}", "minValue": "{-ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$(\\var{m})^3$ =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$(-1)^\\var{p}$ =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Find the value of the following. You should try to do these without a&nbsp; calculator but also check that you can use your calculator to get the correct answer.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "-n[0]^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "n[1]^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "m^3", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "(-1)^p", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "m": {"definition": "random(-5..-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "n": {"definition": "shuffle(-12..-2)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "p": {"definition": "random(4..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}}, "metadata": {"description": "<p>Distinguishing -(7<sup>2</sup>) and (-7)<sup>2</sup>.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}