// Numbas version: exam_results_page_options
{"name": "Simplify algebra equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "rulesets": {"std": ["all", "!collectNumbers "]}, "parts": [{"type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answer": "{ans11}+{ans12}x", "marks": 1, "type": "jme", "answersimplification": "std", "expectedvariablenames": [], "vsetrange": [0, 1], "vsetrangepoints": 5, "variableReplacements": [], "checkingaccuracy": 0.001}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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": []}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answer": "{ans43}x^2+{ans42}x+{ans41}", "marks": 1, "type": "jme", "answersimplification": "std", "expectedvariablenames": [], "vsetrange": [0, 1], "vsetrangepoints": 5, "variableReplacements": [], "checkingaccuracy": 0.001}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>$(\\var{p4[0]}x \\var{n4[0]})(\\var{p4[1]}x +\\var{p4[2]})$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": []}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answer": "{ans53}x^2 +{ans52}x +{ans51}", "marks": 1, "type": "jme", "answersimplification": "std", "expectedvariablenames": [], "vsetrange": [0, 1], "vsetrangepoints": 5, "variableReplacements": [], "checkingaccuracy": 0.001}], "stepsPenalty": 0, "steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>Don't forget to fully square out the bracket. $(ax + b)^2 = (ax + b)(ax + b)$</p>", "variableReplacements": []}], "marks": 0, "showCorrectAnswer": true, "prompt": "<p>$(\\var{n5[0]}x + \\var{p5[0]})^2$</p>\n<p>[[0]]</p>", "variableReplacements": [], "scripts": {}}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answer": "({ans2}x)/{ans1}", "marks": 1, "type": "jme", "answersimplification": "std", "expectedvariablenames": [], "vsetrange": [0, 1], "vsetrangepoints": 5, "variableReplacements": [], "checkingaccuracy": 0.001}], "stepsPenalty": 0, "steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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": []}], "marks": 0, "showCorrectAnswer": true, "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": [], "scripts": {}}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answer": "({ans21}+{ans22}x)/({dv1})", "marks": 1, "type": "jme", "answersimplification": "std", "expectedvariablenames": [], "vsetrange": [0, 1], "vsetrangepoints": 5, "variableReplacements": [], "checkingaccuracy": 0.001}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>$\\frac{\\var{p2[0]}x+ \\var{p2[1]}}{\\var{div[0]}}+\\frac{\\var{p2[2]} \\var{n2[0]}x}{\\var{div[1]}}-\\frac{\\var{p2[3]}x+ \\var{p2[4]}}{\\var{div[2]}}$</p>\n<p>[[0]]</p>", "variableReplacements": []}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "answer": "({ans31}+{ans32}x)/({dv2})", "marks": 1, "type": "jme", "answersimplification": "std", "expectedvariablenames": [], "vsetrange": [0, 1], "vsetrangepoints": 5, "variableReplacements": [], "checkingaccuracy": 0.001}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>$\\frac{\\var{t3[0]}}{\\var{d3[0]}}(\\var{p3[0]}x \\var{n3[0]})-\\frac{\\var{t3[1]}}{\\var{d3[1]}}(\\var{p3[1]} \\var{n3[1]}x)-\\frac{\\var{t3[2]}}{\\var{d3[2]}}(\\var{p3[2]}x + \\var{p3[3]})$&nbsp;</p>\n<p>&nbsp;[[0]]</p>\n<p></p>", 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"definition": "shuffle(-9..-2)[0..8]", "group": "Ungrouped variables"}, "ans2": {"description": "", "templateType": "anything", "name": "ans2", "definition": "((ans1/dm[0])nm[0]) + ((ans1/dm[1])nm[1])", "group": "new"}, "p5": {"description": "", "templateType": "anything", "name": "p5", "definition": "shuffle(2..10)[0..9]", "group": "Ungrouped variables"}, "dv1": {"description": "", "templateType": "anything", "name": "dv1", "definition": "div[0]*div[1]*div[2]", "group": "edt"}, "ans43": {"description": "", "templateType": "anything", "name": "ans43", "definition": "p4[0]*p4[1]", "group": "Ungrouped variables"}, "ans1": {"description": "", "templateType": "anything", "name": "ans1", "definition": "lcm(dm[0],dm[1])", "group": "new"}, "div": {"description": "", "templateType": "anything", "name": "div", "definition": "shuffle([3,5,7,9,11])[0..5]", "group": "Ungrouped variables"}, "p2": {"description": "", "templateType": "anything", "name": "p2", "definition": "shuffle(2..10)[0..9]", "group": "Ungrouped variables"}, "ans21": {"description": "", "templateType": "anything", "name": "ans21", "definition": "(p2[1]*div[1]*div[2])+(p2[2]*div[0]*div[2])-(p2[4]*div[1]*div[0])", "group": "Ungrouped variables"}, "num1n": {"description": "", "templateType": "anything", "name": "num1n", "definition": "shuffle(-9..-2)[0..2]", "group": "Ungrouped variables"}, "ans53": {"description": "", "templateType": "anything", "name": "ans53", "definition": "n5[0]*n5[0]", "group": "Ungrouped variables"}, "dm": {"description": "", "templateType": "anything", "name": "dm", "definition": "shuffle([3,5,7,11])[0..2]", "group": "new"}, "p3": {"description": "", "templateType": "anything", "name": "p3", "definition": "shuffle(2..10)[0..9]", "group": "Ungrouped variables"}, "ans41": {"description": "", "templateType": "anything", "name": "ans41", "definition": "n4[0]*p4[2]", "group": "Ungrouped variables"}, "ans51": {"description": "", "templateType": "anything", "name": "ans51", "definition": "p5[0]*p5[0]", "group": "Ungrouped variables"}, "ans22": {"description": "", "templateType": "anything", "name": "ans22", "definition": "(p2[0]*div[1]*div[2])+(n2[0]*div[0]*div[2])-(p2[3]*div[1]*div[0])", "group": "Ungrouped variables"}, "n4": {"description": "", "templateType": "anything", "name": "n4", "definition": "shuffle(-9..-2)[0..8]", "group": "Ungrouped variables"}, "ans31": {"description": "", "templateType": "anything", "name": "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])", "group": "Ungrouped variables"}, "ans32": {"description": "", "templateType": "anything", "name": "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])", "group": "Ungrouped variables"}, "n2": {"description": "", "templateType": "anything", "name": "n2", "definition": "shuffle(-9..-2)[0..8]", "group": "Ungrouped variables"}, "ans42": {"description": "", "templateType": "anything", "name": "ans42", "definition": "(p4[0]*p4[2])+(p4[1]*n4[0])", "group": "Ungrouped variables"}, "ans52": {"description": "", "templateType": "anything", "name": "ans52", "definition": "n5[0]*p5[0]*2", "group": "Ungrouped variables"}, "p4": {"description": "", "templateType": "anything", "name": "p4", "definition": "shuffle(2..10)[0..9]", "group": "Ungrouped variables"}, "nm": {"description": "", "templateType": "anything", "name": "nm", "definition": "shuffle([2,4,6,8,10])[0..2]", "group": "new"}, "t3": {"description": "", "templateType": "anything", "name": "t3", "definition": "shuffle([2,3,4,5])[0..3]", "group": "Ungrouped variables"}, "n5": {"description": "", "templateType": "anything", "name": "n5", "definition": "shuffle(-9..-2)[0..8]", "group": "Ungrouped variables"}, "dv2": {"description": "", "templateType": "anything", "name": "dv2", "definition": "d3[0]*d3[1]*d3[2]", "group": "edt"}, "ans11": {"description": "", "templateType": "anything", "name": "ans11", "definition": "(num1p[0]*num1p[2])+(num1n[0]*num1p[3])+ num1p[4]", "group": "Ungrouped variables"}, "num1p": {"description": "", "templateType": "anything", "name": "num1p", "definition": "shuffle(2..10)[0..9]", "group": "Ungrouped variables"}}, "functions": {}, "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>", "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "teame"], "name": "Simplify algebra equations", "showQuestionGroupNames": false, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": [], "name": ""}], "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 $x - 2$.</p>", "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/"}]}