// Numbas version: exam_results_page_options
{"name": "MATH6052 - Short Test 4", "metadata": {"description": "", "licence": "None specified"}, "duration": 1500, "percentPass": "40", "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questions": [{"name": "Chain Base Index", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "thing"], "tags": ["cr1", "data analysis", "fitted value", "rebelmaths", "regression", "residual value", "sc", "statistics"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>For the years 2008 to 2013 calculate a chain base index for the {thing[0]}. (round answers to nearest whole number)</p>\n<table border=\"1\" height=\"91\" width=\"573\">\n<tbody>\n<tr><th align=\"left\">Year</th><th>2008</th><th>2009</th><th>2010</th><th>2011</th><th>2012</th><th>2013</th></tr>\n<tr><th align=\"left\">\n<p>The {thing[0]}</p>\n<p>Index Number</p>\n</th>\n<td style=\"text-align: center;\">-</td>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>&nbsp;[[2]]</td>\n<td>[[3]]</td>\n<td>[[4]]</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;Click on Show steps if you want more information. You will not lose any marks by doing so.</p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To calculate the index number for a particular year use the following formula</p>\n<p>$\\frac{\\text{Value for the year}}{\\text{Value for the previous year}}\\times 100$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{b}/{a}*100", "strictPrecision": true, "minValue": "{b}/{a}*100", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{c}/{b}*100", "strictPrecision": true, "minValue": "{c}/{b}*100", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{d}/{c}*100", "strictPrecision": true, "minValue": "{d}/{c}*100", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{f}/{d}*100", "strictPrecision": true, "minValue": "{f}/{d}*100", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{g}/{f}*100", "strictPrecision": true, "minValue": "{g}/{f}*100", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The table below shows the frequency distribution for {thing[0]}.</p>\n<table border=\"1\" height=\"91\" width=\"573\">\n<tbody>\n<tr><th align=\"left\">Year</th><th>2008</th><th>2009</th><th>2010</th><th>2011</th><th>2012</th><th>2013</th></tr>\n<tr><th align=\"left\">{thing[0]}</th>\n<td>{a}</td>\n<td>{b}</td>\n<td>{c}</td>\n<td>&nbsp;{d}</td>\n<td>{f}</td>\n<td>{g}</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "Random(485..550)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "Random(500..600)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "Random(500..600)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "Random(550..600)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "Random(600..650)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "Random(600..650)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "thing": {"definition": "random(['average monthly rent ', 'for residents of a town'],['average weekly salary','for employees of a company'])", "templateType": "anything", "group": "Ungrouped variables", "name": "thing", "description": ""}}, "metadata": {"description": "<p>Chain Base Index Numbers</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Simple interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "metadata": {"description": "<p>Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Suppose you put &pound;{money} into a savings account&nbsp;exactly {years} years ago and you haven't touched the money since. The simple interest rate on the account is {perc2}% per year.</p>", "variables": {"perc2": {"name": "perc2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(0..2.5 #0.05)"}, "money": {"name": "money", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(100..5000 #100)"}, "years": {"name": "years", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..6)"}}, "tags": ["interests", "percentages", "taxonomy"], "ungrouped_variables": ["perc2", "money", "years"], "functions": {}, "preamble": {"js": "", "css": ""}, "advice": "<p>This is <em>simple</em> interest, which means the amount added each year is a percentage of the <strong>original</strong> amount. The amount we add is fixed for all {years} years.</p>\n<p>First,&nbsp;we work out the amount of interest for one year:</p>\n<p>\\begin{align} <br/>\\var{perc2} \\text{% of } \\var{money} &amp;= \\frac{\\var{perc2}}{100} \\times \\var{money} \\\\<br/>&amp;= \\var{perc2/100} \\times \\var{money} \\\\<br/>&amp;= &pound;\\var{dpformat(perc2/100*money,2)} \\text{.}&nbsp;<br/>\\end{align}</p>\n<p>The money has been in the account for {years} years, so we multiply $&pound;\\var{dpformat(perc2/100*money,2)}$ by $\\var{years}$.</p>\n<p>\\[ &pound;\\var{dpformat(perc2/100*money,2)} \\times \\var{years} = &pound;\\var{dpformat(perc2/100*money*years,2)} \\text{.} \\]</p>\n<p>Adding this to the original balance:</p>\n<p>\\[ &pound;\\var{money} + &pound;\\var{dpformat(perc2/100*money*years,2)}&nbsp; = &pound;\\var{dpformat(perc2/100*money*years + money,2)} \\text{.} \\]</p>\n<p>This is the amount we would get if we withdrew the whole savings balance today.</p>", "type": "question", "variable_groups": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "precision": "2", "variableReplacements": [], "mustBeReducedPC": 0, "precisionPartialCredit": 0, "minValue": "(1 + perc2/100*years)*money", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "precisionType": "dp", "scripts": {}, "maxValue": "(1 + perc2/100*years)*money", "showCorrectAnswer": false, "strictPrecision": true, "type": "numberentry", "showPrecisionHint": true, "mustBeReduced": false, "marks": "2", "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision."}], "type": "gapfill", "marks": 0, "prompt": "<p>&nbsp;If you were to withdraw the money from this account now, how much&nbsp;would you have?</p>\n<p>&pound; [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}]}, {"name": "Savings compound interest 2 ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["n", "P", "A", "perc", "int", "ratio", "intplus"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths"], "advice": "<p><span>The compound interest formula is: $\\ A = P(1+i)^n $</span></p>\n<p><strong>Part (a)</strong></p>\n<p><em><strong>P</strong></em> represents the principal sum invested , so in this example it is &euro;$\\var{P}$.</p>\n<p><strong>Part (b)</strong></p>\n<p><span><em><strong>A</strong></em>&nbsp;represents the amount in the&nbsp;<span>deposit account after $\\var{n}$ years, so in this example&nbsp;it is &euro;$\\var{A}$</span>.</span></p>\n<p><strong>Part (c)</strong></p>\n<p><em><strong>n</strong></em>&nbsp;represents the number of compounding periods&nbsp;, so in this example it is $\\var{n}$ years.</p>\n<p><strong>Part(d)</strong></p>\n<p><span>Using the compound interest formula:</span></p>\n<p><span>$A=P(1+i)^n$</span></p>\n<p><span>$\\var{A}=\\var{P}(1+i)^\\var{n}$</span></p>\n<p><span>We need to rearrange the equation to find the value of $i$.</span></p>\n<p><span>$\\frac{\\var{A}}{\\var{P}}=(1+i)^\\var{n}$</span></p>\n<p><span>$\\var{ratio}=(1+i)^\\var{n}$</span></p>\n<p><span>$\\sqrt[\\var{n}]{\\var{ratio}}=1+i$</span></p>\n<p><span>$\\var{intplus}=1+i$</span></p>\n<p>$i=\\var{int}$ so the annual interest rate is $\\var{perc}$%.</p>", "rulesets": {}, "parts": [{"prompt": "<p><span>What is the value of </span><em><strong>P</strong></em><span>?</span></p>\n<p><span>&euro;[[0]]</span></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "P+0.0001", "minValue": "P-0.0001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><span>What is the value of <em><strong>A</strong></em></span><span>?</span></p>\n<p><span>&euro;[[0]]</span></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "A+0.0001", "minValue": "A-0.0001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><span>What is the value of <em><strong>n</strong></em></span><span>?</span></p>\n<p><span></span></p>\n<p><span>[[0]]</span></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "n+0.0001", "minValue": "n-0.0001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>What is the interest rate per annum?</p>\n<p>Please give your answer as a <strong>percentage</strong>&nbsp;correct to 2 decimal places.</p>\n<p></p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "perc+0.02", "minValue": "perc-0.02", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>A lump sum of &euro;$\\var{P}$ is deposited into a savings account that pays compound interest for $\\var{n}$ years. If no withdrawals are made from the account, then the amount that the lump sum will have grown to is &euro;$\\var{A}$.</p>\n<p>The compound interest formula is:</p>\n<p>$\\ A = P(1+i)^n $</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"A": {"definition": "precround(P*(1+int)^n,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "A", "description": ""}, "perc": {"definition": "random(1.5..5.5 #0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "perc", "description": ""}, "ratio": {"definition": "A/P", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio", "description": ""}, "int": {"definition": "perc/100", "templateType": "anything", "group": "Ungrouped variables", "name": "int", "description": ""}, "intplus": {"definition": "ratio^(1/n)", "templateType": "anything", "group": "Ungrouped variables", "name": "intplus", "description": ""}, "n": {"definition": "random(2..6 #1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "P": {"definition": "random(1000..6000 #500)", "templateType": "anything", "group": "Ungrouped variables", "name": "P", "description": ""}}, "metadata": {"description": "<p>Calculate the annual interest rate for a savings account where A, P and n are given.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q1 Calculating weekly Net Tax", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["name", "wage", "cut", "credit", "standard", "higher", "ans"], "tags": ["rebelmaths"], "advice": "<p>{standard}% =&gt; $\\frac{\\var{standard}}{100}$</p>\n<p>{higher}% =&gt; $\\frac{\\var{higher}}{100}$</p>\n<p></p>\n<p><em>Calculate the gross income tax for the week first as follows:</em></p>\n<p>Calculate the standard cut-off point amount first by $\\frac{\\var{standard}}{100} \\times \\var{cut}$</p>\n<p>Then, the income tax at the&nbsp;higher rate by $\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut})$</p>\n<p>Finally, add them to get the gross income tax</p>\n<p>$(\\frac{\\var{standard}}{100} \\times \\var{cut}) + (\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut}))$</p>\n<p><em>&nbsp;</em></p>\n<p><em>Using the gross income tax calculated in above</em></p>\n<p>Subtract the tax credit, $\\var{credit}$, giving the amount of income tax paid.</p>\n<p>$(\\frac{\\var{standard}}{100} \\times \\var{cut}) + (\\frac{\\var{higher}}{100} \\times (\\var{wage} - \\var{cut})) - \\var{credit} = \\var{ans}$</p>\n<p></p>\n<p>Look at this website for worked examples:</p>\n<p><a href=\"http://www.revenue.ie/en/personal/faqs/how-do-i-work-out-my-tax.html\">how to work out my tax</a></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Calculate the amount of income tax he pays each week.</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans}", "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>$\\var{name}$ pays tax at $\\var{standard}$% on the first&nbsp;$\\var{cut}$ of his money, so you need to find&nbsp;$\\var{standard}$% of&nbsp;$\\var{cut}$.</p>\n<p>He pays tax at&nbsp;$\\var{higher}$% on everything above&nbsp;$\\var{cut}$, so you need to find out how much he earns above the cut off&nbsp;$\\var{cut}$ and get&nbsp;$\\var{higher}$% of that.</p>\n<p>Add the two tax bills together to find the gross tax that&nbsp;$\\var{name}$ owes.</p>\n<p>Subtract his tax credits from this.</p>\n<p>The result is the net tax that he has to pay.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>$\\var{name}$ has a weekly wage of &euro;$\\var{wage}$. His standard cut-off point is &euro;$\\var{cut}$, and his tax credit is &euro;$\\var{credit}$ per week. The standard rate of income tax is $\\var{standard}$% and the higher rate is $\\var{higher}$%.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"wage": {"definition": "random(750..950#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "wage", "description": ""}, "cut": {"definition": "random(520..680#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "cut", "description": ""}, "name": {"definition": "random('David','John','Paul','Noel','Steve')", "templateType": "anything", "group": "Ungrouped variables", "name": "name", "description": ""}, "standard": {"definition": "random(20..23)", "templateType": "anything", "group": "Ungrouped variables", "name": "standard", "description": ""}, "credit": {"definition": "random(40..75)", "templateType": "anything", "group": "Ungrouped variables", "name": "credit", "description": ""}, "ans": {"definition": "((({standard}/100)*{cut})+(({higher}/100)*({wage}-{cut})))-{credit}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "higher": {"definition": "random(40..43)", "templateType": "anything", "group": "Ungrouped variables", "name": "higher", "description": ""}}, "metadata": {"description": "<p>Net Tax</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q3 Triangle problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/area-of-a-equilateral-triangle-formula.png", "/srv/numbas/media/question-resources/area-of-a-equilateral-triangle-formula.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"tri": {"definition": "        var c = document.createElement('canvas');\n        $(c).attr('width',200).attr('height',200);\n        var context = c.getContext('2d');\n        \nvar height = 100 * (Math.sqrt(3)/2);\nvar XX = 100\nvar YY = 100\n\n// the triangle\ncontext.beginPath();\ncontext.moveTo(100, 100);\ncontext.lineTo(XX+50, YY+height);\ncontext.lineTo(XX-50, YY+height);\ncontext.closePath();\n \n// the outline\ncontext.lineWidth = 10;\ncontext.strokeStyle = '#666666';\ncontext.stroke();\n \n// the fill color\ncontext.fillStyle = \"#FFCC00\";\ncontext.fill();\n\n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["h", "number"]]}, "tri1": {"definition": "        var c = document.createElement('canvas');\n        $(c).attr('width',500).attr('height',500);\n        var context = c.getContext('2d');\n        \nvar height = 100 * (Math.sqrt(3)/2);\nvar XX = 200\nvar YY = 200\n\n// the triangle\ncontext.beginPath();\ncontext.moveTo(100, 100);\ncontext.lineTo(XX+50, YY+height);\ncontext.lineTo(XX-50, YY+height);\ncontext.closePath();\n \n// the outline\ncontext.lineWidth = 10;\ncontext.strokeStyle = '#666666';\ncontext.stroke();\n \n// the fill color\ncontext.fillStyle = \"#FFCC00\";\ncontext.fill();\n\n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["a", "number"]]}}, "ungrouped_variables": ["side1", "ans1", "lent2", "area2", "ans2"], "tags": ["area", "Area", "area of a triangle", "Area of a triangle", "canvas", "function", "graphic", "rebelmaths", "triangle", "Triangle"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part1</p>\n<p><img src=\"resources/question-resources/area-of-a-equilateral-triangle-formula.png\"/></p>\n<p>where a=length of side</p>\n<p>$\\frac{\\sqrt3}{4} \\times \\var{side1}^2= \\var{ans1}m^2$</p>\n<p><strong>Or another method is:</strong></p>\n<p>A = $\\frac{1}{2}$ab $\\sin(c)$ =&nbsp;$\\frac{1}{2}&nbsp;\\times \\var{side1} \\times \\var{side1} \\times&nbsp;\\sin(60) = \\var{ans1}m^2$</p>\n<p></p>\n<p>Formula for perpendicular height&nbsp;of triangle.</p>\n<p>Area&nbsp;= $\\frac{1}{2}&nbsp;\\times $base$&nbsp;&nbsp;\\times$ perpendicular height</p>\n<p>$2 \\times \\frac{\\var{area2}}{\\var{lent2}} = \\var{ans2}m$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the area of an equilateral triangle which has a side of $\\var{side1}$m.</p>\n<p>{tri(side1)}</p>\n<p>[[0]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Calculate the perpendicular height of a&nbsp;triangle whose&nbsp;base length is&nbsp;$\\var{lent2}$m, if the area of this triangle is&nbsp;$\\var{area2}m^2$</p>\n<p>{tri1(lent2)}</p>\n<p>[[0]]$m$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Correct to <strong>2 decimal place</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "(sqrt(3)/4)*side1^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(2*area2)/lent2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "lent2": {"definition": "random(7..12#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent2", "description": ""}, "area2": {"definition": "random(60..70#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "area2", "description": ""}, "side1": {"definition": "random(12..16#0.25)", "templateType": "anything", "group": "Ungrouped variables", "name": "side1", "description": ""}}, "metadata": {"description": "<p>Areas of triangles</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q2 Rectangle problems", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"rectangle": {"definition": "\n\n      var c = document.createElement('canvas');\n        $(c).attr('width',w+400).attr('height',h+400);\n        var context = c.getContext('2d');\n        \n        //fill in rectangle with a light shade\n        context.fillStyle = '#eee';\n        context.fillRect(50,50,w*10,h*10);\n        \n        //draw outline\n        context.strokeStyle = '#000';\n        context.lineWidth = 3;\n        context.strokeRect(50,50,w*10,h*10);\n        \n        //draw labels\n        context.fillStyle = '#000';\n        context.font = '20px sans-serif';\n        var wstring = 'x'+'m';\n        var tw = context.measureText(wstring).width;\n//        console.log(tw);\n        context.fillText(wstring,60,38);\n        \n        var hstring = h+'m';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(-Math.PI/2);\n        context.fillText(hstring,0,0);\n        \n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["h", "number"], ["w", "number"]]}}, "ungrouped_variables": ["p", "w", "h", "x", "a", "p1", "w1", "h1", "area1"], "tags": ["Area", "area", "canvas", "function", "graphic", "Perimeter", "perimeter", "rebelmaths", "rectangle", "Rectangle"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part 1</p>\n<p>Formula for perimeter of rectangle.</p>\n<p>Perimeter = $2 \\times$ width&nbsp;$+ 2 \\times$ length</p>\n<p>Therefore;</p>\n<p>width = $\\frac{(\\text{perimter} -&nbsp;2 \\times length)}{2}$</p>\n<p>$\\frac{(\\var{p} -&nbsp;2 \\times \\var{h})}{2} = \\var{w}m$</p>\n<p>Formula for area&nbsp;of rectangle.</p>\n<p>Area&nbsp;= width $\\times$ length&nbsp;</p>\n<p>$\\var{w} \\times&nbsp;\\var{h} = \\var{a}m^2$</p>\n<p></p>\n<p>Part 2</p>\n<p>Formula for area&nbsp;of rectangle.</p>\n<p>Area&nbsp;= width $\\times$ length&nbsp;</p>\n<p>$\\frac{\\var{area1}}{\\var{h1} } = \\var{w1}$</p>\n<p>Perimeter = $2 \\times$ width&nbsp;$+ 2 \\times$ length</p>\n<p>$2 \\times \\var{w1} + 2 \\times&nbsp;\\var{h1} = \\var{p1}m$</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>{rectangle(h,w)}</p>\n<p>A&nbsp;rectangle has a perimeter of $\\var{p}m$. If the length is $\\var{h}m$, first calculate its width and then its area.&nbsp;</p>\n<p>width =&nbsp;[[0]]m</p>\n<p>area =&nbsp;[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First write the perimeter in terms of x.</p>\n<p>Solve for x.</p>\n<p>Then calculate the area.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{w}", "strictPrecision": false, "minValue": "{w}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{a}", "strictPrecision": false, "minValue": "{a}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{rectangle(h1,w1)}</p>\n<p>Calculate the&nbsp;perimeter of a&nbsp;rectangle which has a length of&nbsp;$\\var{h1}m$, if the&nbsp;area of this rectangle is $\\var{area1}m^2$. First calculate its width.</p>\n<p>width =&nbsp;[[0]]m</p>\n<p>perimeter =&nbsp;[[1]]$m$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First write the areain terms of x.</p>\n<p>Next, find the length of side x.</p>\n<p>Then find the perimeter.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{w1}", "strictPrecision": false, "minValue": "{w1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{p1}", "strictPrecision": false, "minValue": "{p1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Correct to <strong>2 decimal places</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "h*w", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "p1": {"definition": "2*h1+2*w1", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "w": {"definition": "random(5..h-6#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "h": {"definition": "random(15..34)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "h1": {"definition": "random(20..26 except h)", "templateType": "anything", "group": "Ungrouped variables", "name": "h1", "description": ""}, "p": {"definition": "2*h+2*w", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "w1": {"definition": "random(5..h-6#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "w1", "description": ""}, "x": {"definition": "\"x\"", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "area1": {"definition": "h1*w1", "templateType": "anything", "group": "Ungrouped variables", "name": "area1", "description": ""}}, "metadata": {"description": "<p>Area and Perimeter of Rectangles</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": false, "showfrontpage": true, "showresultspage": "oncompletion", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "warn", "message": "<p>You have 5 minutes remaining, please ensure that all work is submitted before the time runs out.</p>"}}, "feedback": {"showactualmark": false, "showtotalmark": false, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "<p>Please have the formulae and table booklet open in a separate tab on your computer before you begin, you will find this under Course Notes on the MATH6052 Home page on Canvas.</p>", "feedbackmessages": []}, "contributors": [{"name": "Katie Bullen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2255/"}], "extensions": ["stats"], "custom_part_types": [], "resources": [["question-resources/area-of-a-equilateral-triangle-formula.png", "/srv/numbas/media/question-resources/area-of-a-equilateral-triangle-formula.png"]]}