// Numbas version: exam_results_page_options
{"name": "Mock exam 1  Simplify algebra equations L1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<h2></h2>\n<p>For the following, leave the numbers as is, do not put into lowest form as these are algebra expressions:</p>\n<p>For example:</p>\n<p>When you simplify the equation and the answer is $3x -6$, leave it as that, do not answer $3(x - 2)$.</p>", "parts": [{"scripts": {}, "prompt": "<p>$\\var{num1p[0]}(\\var{num1p[1]}x + \\var{num1p[2]})&nbsp;\\var{num1n[0]}(\\var{num1p[3]} \\var{num1n[1]}x) + \\var{num1p[4]}$</p>\n<p>[[0]]</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "gaps": [{"checkvariablenames": false, "answer": "{ans11}+{ans12}x", "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answersimplification": "std", "vsetrange": [0, 1], "scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 1, "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "variableReplacements": []}], "variableReplacements": []}, {"scripts": {}, "prompt": "<p>$(\\var{p4[0]}x \\var{n4[0]})(\\var{p4[1]}x +\\var{p4[2]})$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "gaps": [{"checkvariablenames": false, "answer": "{ans43}x^2+{ans42}x+{ans41}", "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answersimplification": "std", "vsetrange": [0, 1], "scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 1, "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "variableReplacements": []}], "variableReplacements": []}, {"scripts": {}, "prompt": "<p>$(\\var{n5[0]}x + \\var{p5[0]})^2$</p>\n<p>[[0]]</p>", "variableReplacementStrategy": "originalfirst", "steps": [{"scripts": {}, "prompt": "<p>Don't forget to fully square out the bracket. $(ax + b)^2 = (ax + b)(ax + b)$</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "type": "information", "showCorrectAnswer": true, "variableReplacements": []}], "stepsPenalty": 0, "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "gaps": [{"checkvariablenames": false, "answer": "{ans53}x^2 +{ans52}x +{ans51}", "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answersimplification": "std", "vsetrange": [0, 1], "scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 1, "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "variableReplacements": []}], "variableReplacements": []}, {"scripts": {}, "prompt": "<p>Express $\\frac{\\var{nm[0]}x}{\\var{dm[0]}} + \\frac{\\var{nm[1]}x}{\\var{dm[1]}}$ as a single fraction.</p>\n<p>[[0]]</p>", "variableReplacementStrategy": "originalfirst", "steps": [{"scripts": {}, "prompt": "<p>First you need to find a common denominator. To do this you need to find the lowest common multiple of the three denominator.</p>\n<p>Watch video for help</p>\n<p><a href=\"https://www.youtube.com/watch?v=1l1XzthGg9Y\">Video</a></p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "type": "information", "showCorrectAnswer": true, "variableReplacements": []}], "stepsPenalty": 0, "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "gaps": [{"checkvariablenames": false, "answer": "({ans2}x)/{ans1}", "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answersimplification": "std", "vsetrange": [0, 1], "scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 1, "type": "jme", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "variableReplacements": []}], "variableReplacements": []}], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["num1p", "num1n", "ans11", "ans12", "p2", "p3", "p4", "p5", "n2", "n3", "n4", "n5", "ans21", "ans22", "div", "d3", "t3", "ans31", "ans32", "ans41", "ans42", "ans43", "ans51", "ans52", "ans53"], "tags": [], "rulesets": {"std": ["all", "!collectNumbers "]}, "variables": {"ans32": {"templateType": "anything", "description": "", "name": "ans32", "group": "Ungrouped variables", "definition": "(p3[0]*d3[1]*d3[2]*t3[0])-(n3[1]*d3[0]*d3[2]*t3[1])-(p3[2]*d3[1]*d3[0]*t3[2])"}, "ans53": {"templateType": "anything", "description": "", "name": "ans53", "group": "Ungrouped variables", "definition": "n5[0]*n5[0]"}, "p5": {"templateType": "anything", "description": "", "name": "p5", "group": "Ungrouped variables", "definition": "shuffle(2..10)[0..9]"}, "ans43": {"templateType": "anything", "description": "", "name": "ans43", "group": "Ungrouped variables", "definition": "p4[0]*p4[1]"}, "n2": {"templateType": "anything", "description": "", "name": "n2", "group": "Ungrouped 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"group": "new", "definition": "((ans1/dm[0])nm[0]) + ((ans1/dm[1])nm[1])"}, "ans11": {"templateType": "anything", "description": "", "name": "ans11", "group": "Ungrouped variables", "definition": "(num1p[0]*num1p[2])+(num1n[0]*num1p[3])+ num1p[4]"}, "p4": {"templateType": "anything", "description": "", "name": "p4", "group": "Ungrouped variables", "definition": "shuffle(2..10)[0..9]"}, "ans21": {"templateType": "anything", "description": "", "name": "ans21", "group": "Ungrouped variables", "definition": "(p2[1]*div[1]*div[2])+(p2[2]*div[0]*div[2])-(p2[4]*div[1]*div[0])"}, "nm": {"templateType": "anything", "description": "", "name": "nm", "group": "new", "definition": "shuffle([2,4,6,8,10])[0..2]"}, "ans52": {"templateType": "anything", "description": "", "name": "ans52", "group": "Ungrouped variables", "definition": "n5[0]*p5[0]*2"}, "n4": {"templateType": "anything", "description": "", "name": "n4", "group": "Ungrouped variables", "definition": "shuffle(-9..-2)[0..8]"}, "ans31": {"templateType": "anything", "description": "", "name": "ans31", "group": "Ungrouped variables", "definition": "(n3[0]*d3[1]*d3[2]*t3[0])-(p3[1]*d3[0]*d3[2]*t3[1])-(p3[3]*d3[1]*d3[0]*t3[2])"}, "n3": {"templateType": "anything", "description": "", "name": "n3", "group": "Ungrouped variables", "definition": "shuffle(-9..-2)[0..8]"}, "ans1": {"templateType": "anything", "description": "", "name": "ans1", "group": "new", "definition": "lcm(dm[0],dm[1])"}, "ans42": {"templateType": "anything", "description": "", "name": "ans42", "group": "Ungrouped variables", "definition": "(p4[0]*p4[2])+(p4[1]*n4[0])"}, "dv2": {"templateType": "anything", "description": "", "name": "dv2", "group": "edt", "definition": "d3[0]*d3[1]*d3[2]"}, "p3": {"templateType": "anything", "description": "", "name": "p3", "group": "Ungrouped variables", "definition": "shuffle(2..10)[0..9]"}, "ans22": {"templateType": "anything", "description": "", "name": "ans22", "group": "Ungrouped variables", "definition": "(p2[0]*div[1]*div[2])+(n2[0]*div[0]*div[2])-(p2[3]*div[1]*div[0])"}, "n5": {"templateType": "anything", "description": "", "name": "n5", "group": "Ungrouped variables", "definition": "shuffle(-9..-2)[0..8]"}, "div": {"templateType": "anything", "description": "", "name": "div", "group": "Ungrouped variables", "definition": "shuffle([3,5,7,9,11])[0..5]"}, "ans51": {"templateType": "anything", "description": "", "name": "ans51", "group": "Ungrouped variables", "definition": "p5[0]*p5[0]"}, "dv1": {"templateType": "anything", "description": "", "name": "dv1", "group": "edt", "definition": "div[0]*div[1]*div[2]"}, "p2": {"templateType": "anything", "description": "", "name": "p2", "group": "Ungrouped variables", "definition": "shuffle(2..10)[0..9]"}, "ans41": {"templateType": "anything", "description": "", "name": "ans41", "group": "Ungrouped variables", "definition": "n4[0]*p4[2]"}}, "extensions": [], "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>", "variable_groups": [{"name": "new", "variables": ["dm", "nm", "ans1", "ans2"]}, {"name": "edt", "variables": ["dv1", "dv2"]}], "name": "Mock exam 1  Simplify algebra equations L1", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Simplifying algebraic expressions</p>"}, "functions": {}, "type": "question", "contributors": [{"name": 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