// Numbas version: exam_results_page_options
{"name": "Simplify algebra equations L1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "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"], "name": "Simplify algebra equations L1", "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": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{ans11}+{ans12}x", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$(\\var{p4[0]}x \\var{n4[0]})(\\var{p4[1]}x +\\var{p4[2]})$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{ans43}x^2+{ans42}x+{ans41}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$(\\var{n5[0]}x + \\var{p5[0]})^2$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Don't forget to fully square out the bracket. $(ax + b)^2 = (ax + b)(ax + b)$</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": "{ans53}x^2 +{ans52}x +{ans51}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "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": "({ans2}x)/{ans1}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<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>", "variable_groups": [{"variables": ["dm", "nm", "ans1", "ans2"], "name": "new"}, {"variables": ["dv1", "dv2"], "name": "edt"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "lcm(dm[0],dm[1])", "templateType": "anything", "group": "new", "name": "ans1", "description": ""}, "ans2": {"definition": "((ans1/dm[0])nm[0]) + ((ans1/dm[1])nm[1])", "templateType": "anything", "group": "new", "name": "ans2", "description": ""}, "t3": {"definition": "shuffle([2,3,4,5])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "t3", "description": ""}, "d3": {"definition": "shuffle([7,11,13])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "ans21": {"definition": "(p2[1]*div[1]*div[2])+(p2[2]*div[0]*div[2])-(p2[4]*div[1]*div[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "nm": {"definition": "shuffle([2,4,6,8,10])[0..2]", "templateType": "anything", "group": "new", "name": "nm", "description": ""}, "num1n": {"definition": "shuffle(-9..-2)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1n", "description": ""}, "ans41": {"definition": "n4[0]*p4[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans43": {"definition": "p4[0]*p4[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans43", "description": ""}, "ans42": {"definition": "(p4[0]*p4[2])+(p4[1]*n4[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num1p": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1p", "description": ""}, "dv1": {"definition": "div[0]*div[1]*div[2]", "templateType": "anything", "group": "edt", "name": "dv1", "description": ""}, "dv2": {"definition": "d3[0]*d3[1]*d3[2]", "templateType": "anything", "group": "edt", "name": "dv2", "description": ""}, "dm": {"definition": "shuffle([3,5,7,11])[0..2]", "templateType": "anything", "group": "new", "name": "dm", "description": ""}, "ans12": {"definition": "(num1p[0]*num1p[1])+(num1n[0]*num1n[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "(num1p[0]*num1p[2])+(num1n[0]*num1p[3])+ num1p[4]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"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])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"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])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans22": {"definition": "(p2[0]*div[1]*div[2])+(n2[0]*div[0]*div[2])-(p2[3]*div[1]*div[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "div": {"definition": "shuffle([3,5,7,9,11])[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "div", "description": ""}, "p2": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "p4": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p4", "description": ""}, "p5": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p5", "description": ""}, "ans52": {"definition": "n5[0]*p5[0]*2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans52", "description": ""}, "ans53": {"definition": "n5[0]*n5[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans53", "description": ""}, "ans51": {"definition": "p5[0]*p5[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}, "n2": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "n5": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n5", "description": ""}}, "metadata": {"description": "<p>Simplifying algebraic expressions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}