// Numbas version: exam_results_page_options
{"name": "Rachel's copy of Algebra and  parenthesis 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Simplify algebra expressions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Rachel's copy of Algebra and  parenthesis 1", "variables": {"a3": {"name": "a3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "b5": {"name": "b5", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "b4": {"name": "b4", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "a1": {"name": "a1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except [0, 1, -1])"}, "a4": {"name": "a4", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..15)"}, "c2": {"name": "c2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..10)"}, "d3": {"name": "d3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..10)"}, "a2": {"name": "a2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..10)"}, "b1": {"name": "b1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except [0, 1, -1])"}, "c3": {"name": "c3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(5..15)"}, "b6": {"name": "b6", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "d2": {"name": "d2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..10)"}, "d4": {"name": "d4", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "c4": {"name": "c4", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "c1": {"name": "c1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except[0, 1, -1])"}, "b2": {"name": "b2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "b3": {"name": "b3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..10)"}, "d1": {"name": "d1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..10)"}, "c5": {"name": "c5", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(5..10)"}}, "rulesets": {"std": ["all", "!collectNumbers "]}, "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "functions": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "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>", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "scripts": {}, "type": "information"}], "prompt": "<p>Simplify:</p>\n<p>$\\var{a1}a-\\var{a2}b+\\var{a3}a+\\var{a4}b =$</p>\n<p>[[0]]</p>", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "expectedvariablenames": [], "answersimplification": "std", "type": "jme", "checkingtype": "absdiff", "answer": "{a1+a3}a+{a4-a2}b", "showpreview": true, "vsetrangepoints": 5, "checkingaccuracy": 0.001, "marks": 1, "showCorrectAnswer": true, "maxlength": {"partialCredit": 0, "message": "<p>Du har ikke trukket sammen alle mulige ledd</p>", "length": "10"}, "vsetrange": [0, 1]}], "marks": 0, "variableReplacements": [], "scripts": {}, "stepsPenalty": 0, "type": "gapfill"}, {"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "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>", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "scripts": {}, "type": "information"}], "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>", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "expectedvariablenames": [], "answersimplification": "std", "type": "jme", "checkingtype": "absdiff", "answer": "{b1+b4}a^2+{b2-b5}a+{b3-b6}", "showpreview": true, "vsetrangepoints": 5, "checkingaccuracy": 0.001, "marks": 1, "showCorrectAnswer": true, "maxlength": {"partialCredit": 0, "message": "<p>Du har ikke trukket sammen alle mulige ledd</p>", "length": "21"}, "vsetrange": [0, 1]}], "marks": 0, "variableReplacements": [], "scripts": {}, "stepsPenalty": 0, "type": "gapfill"}, {"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "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>", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "scripts": {}, "type": "information"}], "prompt": "<p>Simplify (removing the brackets):</p>\n<p>$(\\var{d1}a+\\var{d2}b)-(\\var{d3}a-\\var{d4}b) =$</p>\n<p>[[0]]</p>", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "expectedvariablenames": [], "answersimplification": "std", "type": "jme", "checkingtype": "absdiff", "answer": "{d1-d3}a+{d2+d4}b", "notallowed": {"partialCredit": 0, "showStrings": false, "message": "", "strings": ["("]}, "showpreview": true, "vsetrangepoints": 5, "checkingaccuracy": 0.001, "marks": 1, "showCorrectAnswer": true, "maxlength": {"partialCredit": 0, "message": "<p>Du har ikke trukket sammen alle mulige ledd</p>", "length": "15"}, "vsetrange": [0, 1]}], "marks": 0, "variableReplacements": [], "scripts": {}, "stepsPenalty": 0, "type": "gapfill"}], "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>", "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b1", "b2", "b3", "b4", "b5", "b6", "c1", "c2", "c3", "c4", "c5", "d1", "d2", "d3", "d4"], "variable_groups": [], "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>", "type": "question", "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}