// Numbas version: exam_results_page_options
{"name": "Distributive law: expanding one set of brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Distributive law: expanding one set of brackets", "tags": ["Algebra", "algebra", "distributive law", "Expanding", "expanding", "expanding brackets"], "metadata": {"description": "<p>Things like \"expand 4(5a-3)\"</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets. Also, recall that a negative multiplied by a negative is a positive.</p>\n<p><em>$\\begin{align*}\\simplify{{nmult}({nxcoeff}a+{nconstant})}&amp;=\\simplify[expandBrackets]{{nmult}({nxcoeff}a+{nconstant})}\\\\&amp;=\\simplify[!noLeadingMinus]{{nmult*nxcoeff}a+{nmult*nconstant}}\\end{align*}$ </em></p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"nconstant": {"name": "nconstant", "group": "part b", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "nxcoeff": {"name": "nxcoeff", "group": "part b", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "nmult": {"name": "nmult", "group": "part b", "definition": "random(-12..-2)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "x", "y"], "variable_groups": [{"name": "part b", "variables": ["nmult", "nxcoeff", "nconstant"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>The expression $\\simplify{{nmult}({nxcoeff}a+{nconstant})}$ is factorised (written as a product). We can expand the expression (so it is written as a sum) to get&nbsp;</p>\n<p>[[0]]$a$ +&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{nmult*nxcoeff}", "maxValue": "{nmult*nxcoeff}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{nmult*nconstant}", "maxValue": "{nmult*nconstant}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}