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