// Numbas version: exam_results_page_options
{"name": "Algebra and  parenthesis 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b1", "b2", "b3", "b4", "b5", "b6", "c1", "c2", "c3", "c4", "c5", "d1", "d2", "d3", "d4"], "name": "Algebra and  parenthesis 1", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><img src=\"http://2.bp.blogspot.com/-cth6k3e3jwQ/VQXfSRgqJHI/AAAAAAAABMI/wxS9Is8HCU8/s1600/bodmas.png\" width=\"326\" height=\"261\"/></p>\n<p>Remove the brackets and gather the x terms together and also the number terms together.</p>\n<p>When in fraction form, get the lowest common multiple (LCM), and multiply the top line by how many times the&nbsp;divisor goes into the LCM.</p>\n<p>Rule for multiping out brackets:</p>\n<p>(a$x$ - b)(c$x$ + d) = (a * c)$x^2$ + ((a * d) + ((-b) *c)))$x$ + ((-b) * d)</p>\n<p>Rule for squaring&nbsp;brackets:</p>\n<p>(-a$x$ + b)$^2$ = (-a * -a)$x^2$ + (2 * (-a) *b)$x$ + (b * b)</p>", "rulesets": {"std": ["all", "!collectNumbers "]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Simplify</p>\n<p>$\\var{a1}a-\\var{a2}b+\\var{a3}a+\\var{a4}b =$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Simplify the parts with the same variable, for example&nbsp;$7a-3a = 4a$, while&nbsp;$2b$ and $3a$ have different variables and can not simplify further.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{a1+a3}a+{a4-a2}b", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "maxlength": {"length": "10", "message": "<p>Du har ikke trukket sammen alle mulige ledd</p>", "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Simplify</p>\n<p>$\\var{b1}a^2+\\var{b2}a+\\var{b3}+\\var{b4}a^2-\\var{b5}a-\\var{b6}=$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Simplify the parts with the same variable, for example $2a^2+3a^2 = 5a^2$, while $2a^2$&nbsp;and $3a$ have different variables and can not simplify further.</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{b1+b4}a^2+{b2-b5}a+{b3-b6}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "maxlength": {"length": "21", "message": "<p>Du har ikke trukket sammen alle mulige ledd</p>", "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Dissolve the parenthesis and simplify</p>\n<p>$(\\var{d1}a+\\var{d2}b)-(\\var{d3}a-\\var{d4}b) =$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Remember: when dissolving a parenthesis with a minus sign next to it, all of the signs inside the parenthesis has to be inverted.</p>\n<p>Example:</p>\n<p>$2a-(a-3b)=2a-a+3b=a+3b$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "", "showStrings": false, "strings": ["("], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{d1-d3}a+{d2+d4}b", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "maxlength": {"length": "15", "message": "<p>Du har ikke trukket sammen alle mulige ledd</p>", "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>You may write your expression in the text box. Remember to write for example a^3 to get&nbsp;$a^3$ and&nbsp;2a-3b to get&nbsp;$2a-3b$.</p>\n<p>Next to the text box, you will get an image of how NUMBAS reads your input. Make sure this is what you intended to answer!</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b4": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "d4": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "d1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "b6": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b6", "description": ""}, "a1": {"definition": "random(-5..5 except [0, 1, -1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b5": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "a3": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "random(3..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "random(5..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(-3..3 except[0, 1, -1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "c4": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "d2": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "c5": {"definition": "random(5..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "b1": {"definition": "random(-7..8 except [0, 1, -1])", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}}, "metadata": {"description": "<p>Simplify algebra expressions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Robert F\u00f8rland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/827/"}]}]}], "contributors": [{"name": "Robert F\u00f8rland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/827/"}]}