// Numbas version: finer_feedback_settings
{"percentPass": 0, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Use formulae for the area and volume of geometric shapes", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/icecrea_QqVaCIf.svg", "/srv/numbas/media/question-resources/icecrea_QqVaCIf.svg"], ["question-resources/frisbee_variable_TESZa4J.svg", "/srv/numbas/media/question-resources/frisbee_variable_TESZa4J.svg"], ["question-resources/tennis-ball_with_variable_MBOLQeM.svg", "/srv/numbas/media/question-resources/tennis-ball_with_variable_MBOLQeM.svg"]], "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": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}], "tags": ["Area", "area", "area of a circle", "area of a trapezium", "area of a triangle", "Area of a triangle", "Circle", "circle", "cone", "Cone", "geometry", "taxonomy", "trapezium", "triangle", "Triangle", "volume", "Volume", "volume of a cone", "volume of a sphere"], "metadata": {"description": "<p>Substitute values into&nbsp;formulae&nbsp;for the area or volume of various geometric objects.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Answer the following questions by substituting the correct&nbsp;values into the given equations.</p>", "advice": "<p>When inserting numbers into your calculator, make sure that you place brackets correctly.</p>\n<h4>a)&nbsp;</h4>\n<p>We can see from the diagram that the radius of the frisbee is $\\var{mccall[2]}$ $\\mathrm{cm}$. <br/>Replacing the letter $r$ in the formula for the area of a circle with $\\var{mccall[2]}$ gives,</p>\n<p>\\begin{align}<br/>\\mathrm{Area} &amp;= \\pi r^2 \\\\<br/>&amp;= \\pi\\times(\\var{mccall[2]})^2 \\\\<br/>&amp;= \\var{dpformat((mccall[2])^2, 2)}\\pi\\, \\mathrm{cm}^2&nbsp;\\\\<br/>&amp;= \\var{dpformat(pi *(mccall[2])^2, 2)}\\, \\mathrm{cm}^2 \\quad \\text{to 2 d.p.} &nbsp;<br/>\\end{align}</p>\n<h4>b)&nbsp;</h4>\n<p>We can see from the diagram that the triangle has two sides with lengths $\\var{length_cdp2}$ $\\mathrm{cm}$, $\\var{length_bdp2}$ $\\mathrm{cm}$ and an angle $\\var{c_thetadp2}\\mathrm{&deg;}$ .<br/>Replacing the letters $a$, $b$ and $C$ in the formula for the area of a triangle with $\\var{length_cdp2}$, $\\var{length_bdp2}$ and $\\var{c_thetadp2}$ respectively gives,</p>\n<p></p>\n<p>\\begin{align}<br/>\\mathrm{Area} &amp;= \\frac{1}{2}ab\\sin{C} \\\\<br/>&amp;= \\frac{1}{2} \\times \\var{length_cdp2} \\times \\var{length_bdp2} \\times \\sin(\\var{c_thetadp2}) \\\\<br/>&amp;= \\var{dpformat(0.5*(length_cdp2)*(length_bdp2)*sin(c_thetadp2* pi/180), 5)}\\, \\mathrm{cm}^2 &nbsp;\\\\<br/>&amp;= \\var{dpformat(0.5*(length_cdp2)*(length_bdp2)*sin(c_thetadp2 * pi/180), 2)}\\, \\mathrm{cm}^2 \\quad&nbsp;\\text{to 2 d.p.}<br/>\\end{align}</p>\n<p></p>\n<h4>c)&nbsp;</h4>\n<p>We can see from the diagram that the radius of the cone is $\\var{r}$ $\\mathrm{cm}$ and the height is $\\var{h}$ $\\mathrm{cm}$.<br/>Replacing the letters $r$ and $h$ in the formula for the volume of a cone with $\\var{r}$ $\\mathrm{cm}$ and $\\var{h}$ $\\mathrm{cm}$ respectively gives,</p>\n<p>\\begin{align}<br/>\\mathrm{Volume} &amp;= \\frac{h}{3} \\pi r^2 \\\\<br/>&amp;= \\frac{(\\var{h})}{3} \\times \\pi \\times (\\var{r})^2 \\\\<br/>&amp;= \\var{dpformat((pi)*(h/3)*(r)^2 , 5)}\\, \\mathrm{cm}^3 \\\\<br/>&amp;=\\var{dpformat(h/3 * pi * (r)^2, 1)}\\, \\mathrm{cm}^3 \\quad&nbsp;\\text{to 1 d.p.} \\\\<br/>\\end{align}</p>\n<p><em><small></small></em></p>\n<h4>d)</h4>\n<p>We can see from the diagram that the radius of the tennis ball is $\\var{mccall[1]}$ $\\mathrm{cm}$.<br/>Replacing the letter $r$ in the formula for the volume of a sphere with $\\var{mccall[1]}$ gives,</p>\n<p>\\begin{align}<br/>\\mathrm{Volume} &amp;= \\frac{4}{3} \\pi r^3 \\\\<br/>&amp;= \\frac{(4)}{(3)} \\times \\pi \\times (\\var{mccall[1]})^3 \\\\<br/>&amp;= \\var{dpformat((4/3)*pi*mccall[1]^3, 5)}\\,&nbsp; \\mathrm{cm}^3 \\\\<br/>&amp;= \\var{precround(((4/3)* pi) *(mccall[1])^3, 1)}\\, \\mathrm{cm}^3 \\quad&nbsp;\\text{to 1 d.p.} \\\\<br/>\\end{align}</p>\n<p></p>\n<h4>e)</h4>\n<p>We can see from the diagram that the trapezium has two parallel sides with length $\\var{trap_length_a}$ $\\mathrm{cm}$, $\\var{trap_length_b}$ $\\mathrm{cm}$ and height $\\var{trap_h}$ $\\mathrm{cm}$.<br/>Replacing the letters $a$, $b$ and $h$ in the formula for the area of a trapezium with&nbsp;$\\var{trap_length_a}$, $\\var{trap_length_b}$ and&nbsp;$\\var{trap_h}$ respectively gives,&nbsp;</p>\n<p></p>\n<p><span data-jme-visible=\"trap_areadp1 = trap_areadp2\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\frac{1}{2} (a + b) h \\\\ <br/>&amp;= \\frac{1}{2} \\times (\\var{trap_length_a} + \\var{trap_length_b}) \\times \\var{trap_h} \\\\ <br/>&amp;= \\var{precround((0.5) (trap_length_a + trap_length_b) trap_h, 1)}\\, \\mathrm{cm}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<p><span data-jme-visible=\"trap_areadp1 &lt;&gt; trap_areadp2\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\frac{1}{2} (a + b) h \\\\ <br/>&amp;= \\frac{1}{2} \\times (\\var{trap_length_a} + \\var{trap_length_b}) \\times \\var{trap_h} \\\\ <br/>&amp;= \\var{precround((0.5)(trap_length_a +trap_length_b) trap_h, 2)}\\, \\mathrm{cm}^2 \\\\ <br/>&amp;= \\var{precround((0.5) (trap_length_a + trap_length_b) trap_h, 1)}\\, \\mathrm{cm}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"length_cdp2": {"name": "length_cdp2", "group": "Triangle variables", "definition": "precround(sqrt((b[0]-c[0])^2+(b[1]-c[1])^2),2)", "description": "<p>Rounded value for the length of c.</p>", "templateType": "anything", "can_override": false}, "trap_e": {"name": "trap_e", "group": "Trapezium variables", "definition": "vector(trap_b[0],-4)", "description": "<p>Defines the point for the height of the trapezium.</p>", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Cone variables", "definition": "random(3..6#0.1)", "description": "<p>A random variable which will be inputted by the student.</p>", "templateType": "anything", "can_override": false}, "const": {"name": "const", "group": "Quadratic variables", "definition": "random(1..100#1)", "description": "<p>The constant coefficient</p>", "templateType": "anything", "can_override": false}, "name": {"name": "name", "group": "Name variables", "definition": "[\"Andrew\",\"Susan\",\"Tom\",\"Geraldine\",\"Joshua\",\"Chantel\"]", "description": "<p>List of names to randomise. Can change to any name inserted</p>", "templateType": "anything", "can_override": false}, "length_bdp2": {"name": "length_bdp2", "group": "Triangle variables", "definition": "precround(sqrt((a[0]-c[0])^2+(a[1]-c[1])^2),2)", "description": "<p>Rounded value for the length of b.</p>", "templateType": "anything", "can_override": false}, "length_c": {"name": "length_c", "group": "Triangle variables", "definition": "sqrt((b[0]-c[0])^2+(b[1]-c[1])^2)", "description": "<p>For triangle - The length of the vector BC</p>", "templateType": "anything", "can_override": false}, "trap_length_b": {"name": "trap_length_b", "group": "Trapezium variables", "definition": "sqrt((trap_d[0]-trap_a[0])^2+(trap_d[1]-trap_a[1])^2)", "description": "", "templateType": "anything", "can_override": false}, "c_thetadp2": {"name": "c_thetadp2", "group": "Triangle variables", "definition": "precround((180/pi)*arccos(((length_b)^2+(length_c)^2-(length_a)^2)/(2(length_b)(length_c))),2)", "description": "<p>Rounded theta value.&nbsp;</p>", "templateType": "anything", "can_override": false}, "trap_length_a": {"name": "trap_length_a", "group": "Trapezium variables", "definition": "sqrt((trap_c[0]-trap_b[0])^2+(trap_c[1]-trap_b[1])^2)", "description": "", "templateType": "anything", "can_override": false}, "length_b": {"name": "length_b", "group": "Triangle variables", "definition": "sqrt((a[0]-c[0])^2+(a[1]-c[1])^2)", "description": "<p>For triangle - The length of the vector AC&nbsp;</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Triangle variables", "definition": "vector(2,0)", "description": "<p>Position of point B in Geogebra. This point is randomised to make the triangles different.</p>", "templateType": "anything", "can_override": false}, "pronoun": {"name": "pronoun", "group": "Name variables", "definition": "if(mod(n,2)=0,\"he\",\"she\")", "description": "<p>Defines the pronoun in the question.</p>", "templateType": "anything", "can_override": false}, "trap_defs": {"name": "trap_defs", "group": "Trapezium variables", "definition": "[\n  ['A', trap_a],\n  ['B', trap_b],\n  ['C', trap_c],\n  ['D', trap_d],\n  ['E', trap_e]\n ]", "description": "<p>Definition of the points to put into Geogebra</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Cone variables", "definition": "random(11..17#0.1)", "description": "<p>The height&nbsp;for volume of a cone.</p>", "templateType": "anything", "can_override": false}, "trap_h": {"name": "trap_h", "group": "Trapezium variables", "definition": "trap_b[1] + 4", "description": "<p>Height of the trapezium</p>", "templateType": "anything", "can_override": false}, "Triangle_area": {"name": "Triangle_area", "group": "Triangle variables", "definition": "1/2*(length_cdp2)(length_bdp2)(sin(c_thetadp2 * pi/180))", "description": "<p>This calculates the area of the triangle for part&nbsp;<strong>b)</strong></p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Triangle variables", "definition": "vector(-3,0)", "description": "<p>Position of the point A in Geogebra. This point is fixed so the triangle doesn't hang in one corner or the whole page.</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Name variables", "definition": "random(0..4#1)", "description": "<p>n is a random number between 0 and 4 that picks a name from {name} and then picks the next in the list for the other name such that there is always a male and a female in the question.&nbsp;</p>", "templateType": "anything", "can_override": false}, "name2": {"name": "name2", "group": "Name variables", "definition": "[\"Andrew\",\"Susan\",\"Tom\",\"Geraldine\",\"Joshua\",\"Chantel\"]", "description": "<p>List of names to randomise. Can change to any name inserted</p>", "templateType": "anything", "can_override": false}, "trap_rand": {"name": "trap_rand", "group": "Trapezium variables", "definition": "random(1..3#1)", "description": "<p>A random number to define the height of the trapezium.</p>", "templateType": "anything", "can_override": false}, "c_theta": {"name": "c_theta", "group": "Triangle variables", "definition": "(180/pi)*arccos(((length_b)^2+(length_c)^2-(length_a)^2)/(2(length_b)(length_c))) ", "description": "<p>Theta is randomised by the lengths&nbsp;</p>", "templateType": "anything", "can_override": false}, "trap_areadp1": {"name": "trap_areadp1", "group": "Trapezium variables", "definition": "precround(0.5*(trap_length_a + trap_length_b)*trap_h,1)", "description": "<p>Calculates the area of the trapezium</p>", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Triangle variables", "definition": "[\n  ['A',a],\n  ['B',b],\n  ['C',c]\n  ]", "description": "<p>Creates the points in Geogebra is not used directly in the question but to create the image in Geogebra.</p>", "templateType": "anything", "can_override": false}, "length_a": {"name": "length_a", "group": "Triangle variables", "definition": "sqrt((a[0]-b[0])^2+(a[1]-b[1])^2)", "description": "<p>For triangle - The length of the vector AB</p>", "templateType": "anything", "can_override": false}, "trap_d": {"name": "trap_d", "group": "Trapezium variables", "definition": "vector(random(5..7#0.1), -4)", "description": "<p>Creates the point D on the trapezium</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Triangle variables", "definition": "vector(\n  random(2..5#0.1),\n  random(2..5#0.1)\n  )", "description": "<p>Triangle - A variable point which ultimately decides how the triangle looks.</p>", "templateType": "anything", "can_override": false}, "trap_a": {"name": "trap_a", "group": "Trapezium variables", "definition": "vector(1,-4)", "description": "<p>Creates the point A on the trapezium</p>", "templateType": "anything", "can_override": false}, "trap_c": {"name": "trap_c", "group": "Trapezium variables", "definition": "vector(random(4..5.5#0.1), trap_rand)", "description": "<p>Creates the point C on the trapezium</p>", "templateType": "anything", "can_override": false}, "mccall": {"name": "mccall", "group": "RNG", "definition": "[0,random(3.1..3.7#0.1),random(5..20#0.1)]\n", "description": "<p>Matrix of random variables used to create length in the questions.</p>", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Quadratic variables", "definition": "random(1..10#1)", "description": "<p>The x^2 coefficient</p>", "templateType": "anything", "can_override": false}, "trap_areadp2": {"name": "trap_areadp2", "group": "Trapezium variables", "definition": "precround(0.5*(trap_length_a + trap_length_b)*trap_h, 2)", "description": "", "templateType": "anything", "can_override": false}, "trap_b": {"name": "trap_b", "group": "Trapezium variables", "definition": "vector(random(1.5..2.5#0.1), trap_rand)", "description": "<p>Creates the point B on the trapezium</p>", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Quadratic variables", "definition": "random(1..50)", "description": "<p>The x coefficient</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Trapezium variables", "variables": ["trap_a", "trap_b", "trap_c", "trap_d", "trap_h", "trap_rand", "trap_defs", "trap_length_a", "trap_length_b", "trap_e", "trap_areadp1", "trap_areadp2"]}, {"name": "Triangle variables", "variables": ["Triangle_area", "c", "b", "a", "c_theta", "length_a", "length_b", "length_c", "defs", "length_bdp2", "length_cdp2", "c_thetadp2"]}, {"name": "Name variables", "variables": ["name", "name2", "pronoun", "n"]}, {"name": "Quadratic variables", "variables": ["x2", "x1", "const"]}, {"name": "Cone variables", "variables": ["r", "h"]}, {"name": "RNG", "variables": ["mccall"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the area of a frisbee, assuming that the frisbee can be modelled as a circle, given the formula for the area of a circle is</p>\n<p style=\"text-align: center;\">\\[\\mathrm{Area} = \\pi r^2.\\]</p>\n<p style=\"text-align: center;\"><object width=\"320\" height=\"320\" type=\"image/svg+xml\" data=\"resources/question-resources/frisbee_variable_TESZa4J.svg\"></object></p>\n<p>$\\mathrm{Area}$ = [[0]] $\\mathrm{cm}^2$ &nbsp; &nbsp;<em><small>Round your answer to 2 decimal places.</small></em></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pi*{mccall[2]}^2 - 0.05", "maxValue": "pi*{mccall[2]}^2 + 0.05", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the area of the triangle given that the area of any triangle can be calculated using the formula&nbsp;</p>\n<p style=\"text-align: center;\">\\[\\mathrm{Area} = \\frac{1}{2}ab\\sin{C}.\\]</p>\n<p style=\"text-align: center;\">{geogebra_applet('https://www.geogebra.org/m/jcUJu6F4',defs)}</p>\n<p style=\"text-align: left;\">All lengths are in centimetres.</p>\n<p>$\\mathrm{Area} =$&nbsp;[[0]] $\\mathrm{cm}^2$ &nbsp; <em><small>Round your answer to 2 decimal places.</small></em></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Triangle_area-0.05", "maxValue": "Triangle_area+0.05", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the volume of a cone given the formula for the volume of a cone is</p>\n<p style=\"text-align: center;\">\\[\\mathrm{Volume} = \\frac{h}{3} \\pi r^2.\\]</p>\n<p style=\"text-align: center;\"><object width=\"300\" height=\"250\" type=\"image/svg+xml\" data=\"resources/question-resources/icecrea_QqVaCIf.svg\"></object></p>\n<p style=\"text-align: left;\">$\\mathrm{Volume}$ =&nbsp;[[0]] $\\mathrm{cm}^3$ &nbsp; <em><small>Round your answer to 1 decimal place.</small></em></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{(h/3)}*{r}^2*pi -0.5", "maxValue": "{(h/3)}*{r}^2*pi +0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{name[n]} has a tennis ball and {pronoun} wants to find the volume of the ball. Using the diagram and the formula for the volume of a sphere, calculate the volume of the ball.&nbsp;</p>\n<p style=\"text-align: center;\">\\[\\mathrm{Volume}= \\frac{4}{3} \\pi r^3.\\]</p>\n<p style=\"text-align: center;\"><object width=\"220\" height=\"200\" type=\"image/svg+xml\" data=\"resources/question-resources/tennis-ball_with_variable_MBOLQeM.svg\"></object></p>\n<p>$\\mathrm{Volume}$ = [[0]] $\\mathrm{cm}^3$ &nbsp; <em><small>Round your answer to 1 decimal place.</small></em></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "4/3 * pi * {mccall[1]}^3 - 0.5", "maxValue": "4/3 * pi * {mccall[1]}^3 + 0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the area of the trapezium given the formula for the area of a trapezium is</p>\n<p style=\"text-align: center;\">\\[\\mathrm{Area} = \\frac{1}{2}(a+b) h .\\]</p>\n<p style=\"text-align: center;\">{geogebra_applet('https://www.geogebra.org/m/Gtjzajb6',trap_defs)}</p>\n<p><align></align></p>\n<p style=\"text-align: left;\">All&nbsp;lengths are given in metres.</p>\n<p>$\\mathrm{Area}$ = [[0]] $\\mathrm{m}^2$ &nbsp; <em><small>Round your answer to 1 decimal place.</small></em></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.5({trap_length_a}+{trap_length_b})*{trap_h} - 0.1", "maxValue": "0.5({trap_length_a}+{trap_length_b})*{trap_h} + 0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Rounding and estimating calculations - painting a room", "extensions": ["random_person"], "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/"}], "type": "question", "statement": "<p>{person['name']} just bought a new house. {capitalise(pronouns['their'])}&nbsp;new bedroom's wall and ceiling are currently painted white, but {pronouns['they']} would like to paint these {colour}.</p>\n<p>The dimensions of the&nbsp;floor&nbsp;are $\\var{length}\\,\\mathrm{m} \\times \\var{width}\\,\\mathrm{m}$&nbsp;and&nbsp;the room&nbsp;is&nbsp;$\\var{height}\\,\\mathrm{m}$&nbsp;high.&nbsp;</p>\n<p>{person['name']} want{verbs} to know how much paint to buy so {pronouns['they']} can paint all four walls and the ceiling {colour}.</p>", "variablesTest": {"condition": "mod(rall,15)<>0", "maxRuns": 100}, "variables": {"buckets": {"description": "", "name": "buckets", "group": "Calculations", "templateType": "anything", "definition": "ceil(rall/bucket_area)"}, "bucket_area": {"description": "<p>The area that can be painted with one bucket of paint.</p>", "name": "bucket_area", "group": "Calculations", "templateType": "anything", "definition": "15"}, "colour": {"description": "", "name": "colour", "group": "Random bits", "templateType": "anything", "definition": "random(\"green\", \"red\", \"orange\", \"yellow\", \"blue\", \"purple\", \"pink\")"}, "width": {"description": "", "name": "width", "group": "Random bits", "templateType": "anything", "definition": "random(2.50..5.00 #0.1) + random(0.01..0.09 #0.01)"}, "w": {"description": "", "name": "w", "group": "Calculations", "templateType": "anything", "definition": "ceil(width)"}, "verbs": {"description": "", "name": "verbs", "group": "Person", "templateType": "anything", "definition": "if(person['gender']='neutral','','s')"}, "height": {"description": "", "name": "height", "group": "Random bits", "templateType": "anything", "definition": "random(2.10..2.70 #0.1) + random(0.01..0.09 #0.01)"}, "h": {"description": "", "name": "h", "group": "Calculations", "templateType": "anything", "definition": "ceil(height)"}, "rall": {"description": "", "name": "rall", "group": "Calculations", "templateType": "anything", "definition": "rceiling + rwall1*2 + rwall2*2"}, "pronouns": {"description": "", "name": "pronouns", "group": "Person", "templateType": "anything", "definition": "person['pronouns']"}, "length": {"description": "", "name": "length", "group": "Random bits", "templateType": "anything", "definition": "random(3.50..8.00 #0.1) + random(0.01..0.09 #0.01)"}, "person": {"description": "", "name": "person", "group": "Person", "templateType": "anything", "definition": "random_person()"}, "rwall1": {"description": "", "name": "rwall1", "group": "Calculations", "templateType": "anything", "definition": "l*h"}, "rwall2": {"description": "", "name": "rwall2", "group": "Calculations", "templateType": "anything", "definition": "w*h"}, "rceiling": {"description": "", "name": "rceiling", "group": "Calculations", "templateType": "anything", "definition": "w*l"}, "l": {"description": "", "name": "l", "group": "Calculations", "templateType": "anything", "definition": "ceil(length)"}}, "functions": {}, "tags": ["random names", "taxonomy"], "variable_groups": [{"name": "Random bits", "variables": ["colour", "height", "width", "length"]}, {"name": "Person", "variables": ["person", "pronouns", "verbs"]}, {"name": "Calculations", "variables": ["h", "w", "l", "rwall1", "rwall2", "rceiling", "rall", "bucket_area", "buckets"]}], "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"scripts": {}, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["<p>Overestimate and therefore we round each measurement up.</p>", "<p>Underestimate and therefore we round each measurement down.</p>"], "showFeedbackIcon": true, "shuffleChoices": false, "displayColumns": "1", "variableReplacements": [], "marks": 0, "matrix": ["1", 0], "showCorrectAnswer": true, "maxMarks": 0, "type": "1_n_2"}], "showFeedbackIcon": true, "prompt": "<p>Is it better to overestimate or underestimate in this situation?</p>\n<p>[[0]]<em></em></p>", "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "rall", "showFeedbackIcon": true, "minValue": "rall", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "stepsPenalty": 0, "prompt": "<p>Rounding each measurement to&nbsp;<strong>the nearest metre</strong>, estimate&nbsp;the whole area to be painted {colour}.</p>\n<p>[[0]]&nbsp;m<sup>2</sup></p>\n<p><em></em></p>", "steps": [{"scripts": {}, "variableReplacements": [], "type": "information", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>The room is {length}m long, {width}m wide, and {height}m high.</p>\n<p>Round each measurement in the direction you decided on above.&nbsp;</p>", "marks": 0}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(length)", "showFeedbackIcon": true, "prompt": "<p>Round the length&nbsp;to the nearest metre.</p>", "minValue": "ceil(length)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(width)", "showFeedbackIcon": true, "prompt": "<p>Round the width&nbsp;to the nearest metre.</p>", "minValue": "ceil(width)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(height)", "showFeedbackIcon": true, "prompt": "<p>Round the height&nbsp;to the nearest metre.</p>", "minValue": "ceil(height)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}], "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "buckets", "showFeedbackIcon": true, "minValue": "buckets", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p>One&nbsp;bucket of {colour} paint is enough to paint an area of 15m<sup>2</sup>. How many buckets should {person['name']}&nbsp;buy to ensure {pronouns['they']}&nbsp;{if(person['gender']='neutral','have','has')}&nbsp;enough paint?</p>\n<p>[[0]]</p>", "marks": 0}], "ungrouped_variables": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Estimate the number of buckets of paint to buy,&nbsp;by rounding measurements of a room up to the nearest metre and estimating the total area.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<h4>a)</h4>\n<p>It is much better to have spare&nbsp;paint than not to have enough of it. So it is&nbsp;better to overestimate the area.</p>\n<p>Therefore, we round each measurement&nbsp;<strong>up.</strong></p>\n<h4>b)</h4>\n<p>We round each of our measurements up to the nearest whole metre:</p>\n<p>Length: $\\var{length}\\,\\mathrm{m} \\approx&nbsp;\\var{l}\\,\\mathrm{m}$.</p>\n<p>Width: $\\var{width}\\,\\mathrm{m} \\approx \\var{w}\\,\\mathrm{m}$.</p>\n<p>Height: $\\var{height}\\,\\mathrm{m} \\approx \\var{h}\\,\\mathrm{m}$.</p>\n<p style=\"text-align: left;\">The total area consists of five areas: two walls of $\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (length by height); two walls of $\\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (width by height); and a ceiling of $\\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m}$ (length by width).</p>\n<p>\\[ \\begin{align}<br/>\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m} &amp;= \\var{l*h}\\,\\text{m}^2<br/>\\\\ \\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m} &amp;= \\var{w*h}\\,\\text{m}^2<br/>\\\\ \\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m} &amp;= \\var{l*w}\\,\\text{m}^2<br/>\\end{align}\\]</p>\n<p>Therefore, the total area {person['name']} needs to paint is</p>\n<p>\\[&nbsp;\\var{2*l*h} + \\var{2*w*h} + \\var{l*w} \\,\\mathrm{m}^2 = \\var{rall}\\,\\mathrm{m}^2 \\text{.} \\]</p>\n<h4>c)</h4>\n<p>The exact number of buckets needed is</p>\n<p>\\[\\var{rall}\\,\\text{m}^2 \\div 15\\,\\text{m}^2&nbsp;= \\var{rall/15} \\text{.}\\]</p>\n<p>{person['name']} can only buy a whole number of buckets, so {pronouns['they']}&nbsp;need{verbs} to decide between&nbsp;{buckets-1}&nbsp;and {buckets} paint buckets. As it is better to buy more paint than not buy enough, {pronouns['they']} should buy {buckets} buckets of {colour} paint.</p>"}, {"name": "Calculate the areas of polygons", "extensions": [], "custom_part_types": [], "resources": [["question-resources/trapezium.svg", "/srv/numbas/media/question-resources/trapezium.svg"], ["question-resources/trangle.svg", "/srv/numbas/media/question-resources/trangle.svg"], ["question-resources/parallelogram.svg", "/srv/numbas/media/question-resources/parallelogram.svg"], ["question-resources/Parallelogram_area_animated.gif", "/srv/numbas/media/question-resources/Parallelogram_area_animated.gif"], ["question-resources/rectangle_zISmvoz.svg", "/srv/numbas/media/question-resources/rectangle_zISmvoz.svg"], ["question-resources/hardertrapezium_8GqMwOo.svg", "/srv/numbas/media/question-resources/hardertrapezium_8GqMwOo.svg"], ["question-resources/Trap_advice.svg", "/srv/numbas/media/question-resources/Trap_advice.svg"], ["question-resources/Triangle_advice_lD6eKvD.svg", "/srv/numbas/media/question-resources/Triangle_advice_lD6eKvD.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}], "rulesets": {}, "functions": {}, "ungrouped_variables": [], "metadata": {"description": "<p>This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.</p>\n<p>The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.</p>\n<p>Author of gif: Picknick<br />https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif<br />This file is licensed under the <a href=\"https://en.wikipedia.org/wiki/en:Creative_Commons\" class=\"extiw\" title=\"w:en:Creative Commons\">Creative Commons</a> <a rel=\"nofollow\" class=\"external text\" href=\"https://creativecommons.org/licenses/by-sa/4.0/deed.en\">Attribution-Share Alike 4.0 International</a> license.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "variable_groups": [{"variables": ["h1", "w1", "wh11", "wh11dp"], "name": "Parallelogram"}, {"variables": ["h2", "w2", "wh22", "wh22dp"], "name": "Triangle"}, {"variables": ["h5", "w5a", "w5b", "wabh5dp", "wabh5"], "name": "'Harder' trapezium"}, {"variables": ["w0", "h0", "wh00", "wh00dp"], "name": "Rectangle"}], "advice": "<p><strong>a)</strong></p>\n<p>The area of a rectangle is calculated using the formula</p>\n<p>\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}\\text{.}\\]</p>\n<p>We have a base of $\\var{w0}$m and a height $\\var{h0}$m, therefore</p>\n<p><span data-jme-visible=\"wh00 &lt;&gt; wh00dp\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\mathrm{base} \\times \\mathrm{height} \\\\ <br/>&amp;= \\var{w0} \\times \\var{h0} \\\\ &amp;= \\var{w0*h0} \\\\ <br/>&amp;= \\var{dpformat(w0*h0,1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<p><span data-jme-visible=\"wh00 = wh00dp\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\mathrm{base} \\times \\mathrm{height} \\\\ <br/>&amp;= \\var{w0} \\times \\var{h0} \\\\ <br/>&amp;= \\var{dpformat(w0*h0,1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<p><strong>b)</strong></p>\n<p>The parallelogram is just a slanted rectangle:</p>\n<p style=\"text-align: center;\"></p>\n<p><a href=\"https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif\"><img style=\"width: 304px; height: 228px; display: block; margin-left: auto; margin-right: auto;\" alt=\"Parallelogram\" src=\"resources/question-resources/Parallelogram_area_animated.gif\"/></a></p>\n<h6 id=\"reference\" style=\"text-align: center;\"><em>Animation&nbsp;by <a href=\"https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif\" target=\"_blank\" rel=\"noopener noreferrer\">Picknick</a>.</em></h6>\n<p></p>\n<p>Therefore, the area of a parallelogram is calculated using the formula</p>\n<p>\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]</p>\n<p>We have a base $\\var{w1}$m and perpendicular height $\\var{h1}$m.</p>\n<p><span data-jme-visible=\"wh11 &lt;&gt; wh11dp\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\mathrm{base} \\times \\mathrm{height} \\\\ <br/>&amp;= \\var{w1} \\times \\var{h1} \\\\ &amp;= \\var{{w1}{h1}}\\, \\mathrm{m}^2 \\\\ &nbsp;<br/>&amp;= \\var{dpformat({w1}{h1},1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<p><span data-jme-visible=\"wh11 = wh11dp\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\mathrm{base} \\times \\mathrm{height} \\\\ <br/>&amp;= \\var{w1} \\times \\var{h1} \\\\ <br/>&amp;= \\var{dpformat({w1}{h1},1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<h4 id=\"reference\"><em></em><strong>c)</strong></h4>\n<p>The area of a triangle is calculated using the&nbsp;formula</p>\n<p>\\[\\mathrm{Area} = \\frac{\\mathrm{base} \\times \\mathrm{height}}{2}.\\]</p>\n<p>Note that the&nbsp;triangle is half of a rectangle:</p>\n<p style=\"text-align: center;\"><object width=\"350\" height=\"438\" type=\"image/svg+xml\" data=\"resources/question-resources/Triangle_advice_lD6eKvD.svg\"></object></p>\n<p>Our triangle has a base&nbsp;$\\var{w2}$m and a height $\\var{h2}$m, therefore</p>\n<p><span data-jme-visible=\"wh22 &lt;&gt; wh22dp\">\\begin{align} \\mathrm{Area} &amp;= \\frac{1}{2} \\times \\mathrm{base} \\times \\mathrm{height} \\\\&nbsp;<br/>&amp;= \\frac{1}{2} \\times \\var{w2} \\times \\var{h2} \\\\ <br/>&amp;= \\var{0.5*w2*h2}\\, \\mathrm{m}^2 \\\\ <br/>&amp;= \\var{dpformat(0.5*w2*h2, 1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<p><span data-jme-visible=\"wh22 = wh22dp\">\\begin{align} \\mathrm{Area} &amp;= \\frac{1}{2} \\times \\mathrm{base} \\times \\mathrm{height} \\\\<br/> &amp;= \\frac{1}{2} \\times \\var{w2} \\times \\var{h2} \\\\ <br/>&amp;= \\var{dpformat(0.5*w2*h2, 1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} \\\\ <br/>\\end{align}</span></p>\n<p><strong>d)</strong></p>\n<p></p>\n<p>A trapezium can be interpreted as half of a parallelogram, this is shown below:</p>\n<p style=\"text-align: center;\"><object width=\"350\" height=\"428\" type=\"image/svg+xml\" data=\"resources/question-resources/Trap_advice.svg\"></object></p>\n<p>As we only want the area of one half of this shape, the area is half of</p>\n<p>\\[\\mathrm{area} = (a+b) \\times \\mathrm{height}\\text{,}\\]</p>\n<p style=\"text-align: left;\">with&nbsp;${a} = \\var{w5a}$m, ${b} = \\var{w5b}$m, and height $\\var{h5}$m.</p>\n<p><span data-jme-visible=\"wabh5 &lt;&gt; wabh5dp\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\frac{(a+b)}{2} \\times \\mathrm{height} \\\\ <br/>&amp;= \\frac{(\\var{w5a}+\\var{w5b})}{2} \\times \\var{h5} \\\\ <br/>&amp;= \\var{(w5a+w5b)*0.5} \\times \\var{h5} \\\\ <br/>&amp;= \\var{(w5a+w5b)*(h5)/2}\\, \\mathrm{m}^2 \\\\ <br/>&amp;= \\var{dpformat((w5a+w5b)*(h5)/2, 1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} &nbsp;<br/>\\end{align}</span></p>\n<p><span data-jme-visible=\"wabh5 = wabh5dp\">\\begin{align} <br/>\\mathrm{Area} &amp;= \\frac{(a+b)}{2} \\times \\mathrm{height} \\\\ <br/>&amp;= \\frac{(\\var{w5a}+\\var{w5b})}{2} \\times \\var{h5} \\\\ <br/>&amp;= \\var{(w5a+w5b)*0.5} \\times \\var{h5} \\\\ <br/>&amp;= \\var{dpformat((w5a+w5b)*(h5)/2, 1)}\\, \\mathrm{m}^2 \\quad&nbsp;\\text{to 1 d.p.} &nbsp;<br/>\\end{align}</span></p>", "statement": "<p>Calculate the area of the following shapes.</p>", "preamble": {"css": "", "js": ""}, "tags": ["area", "Area", "area of a parallelogram", "area of a rectangle", "area of a right-angled triangle", "area of a trapezium", "parallelogram", "Rectangle", "rectangle", "right - angled triangle", "shapes", "taxonomy", "trapezium"], "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"text-align: center;\"><object width=\"600\" height=\"350\" type=\"image/svg+xml\" data=\"resources/question-resources/rectangle_zISmvoz.svg\"></object></p>\n<p style=\"text-align: left;\">The area of the rectangle is&nbsp;[[0]] $\\mathrm{m^2}$. &nbsp; &nbsp; &nbsp;<em><small>Round your answer to 1 decimal place.</small></em></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "variableReplacements": [], "precision": "1", "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "{h0}{w0}", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "minValue": "{h0}{w0}", "mustBeReduced": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "precisionPartialCredit": 0, "marks": "2", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>The formula&nbsp;for the area of a rectangle is:</p>\n<p>\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"text-align: center;\"><object width=\"600\" height=\"350\" type=\"image/svg+xml\" data=\"resources/question-resources/parallelogram.svg\"></object></p>\n<p style=\"text-align: left;\">The area of the parallelogram is&nbsp;[[0]] $\\mathrm{m^2}$. &nbsp; &nbsp; &nbsp;&nbsp;<em><small>Round your answer to 1 decimal place.</small></em></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "variableReplacements": [], "precision": "1", "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "{h1}*{w1} + 0.01", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "minValue": "{h1}*{w1} - 0.01", "mustBeReduced": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "precisionPartialCredit": 0, "marks": "2", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>The formula&nbsp;for the area of a parallelogram is:</p>\n<p>\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"text-align: center;\"><object width=\"600\" height=\"350\" type=\"image/svg+xml\" data=\"resources/question-resources/trangle.svg\"></object></p>\n<p style=\"text-align: left;\">The area of the triangle is&nbsp;[[0]] $\\mathrm{m^2}$ &nbsp; &nbsp; &nbsp;<em><small>Round your answer to 1 decimal place.</small></em></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "variableReplacements": [], "precision": "1", "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "{w2}{h2}*0.5 + 0.01", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "minValue": "{w2}{h2}*0.5 - 0.01", "mustBeReduced": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "precisionPartialCredit": 0, "marks": "2", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>The formula&nbsp;for the area of a triangle is:</p>\n<p>\\[\\mathrm{Area} = \\frac{\\mathrm{base} \\times \\mathrm{height}}{2}.\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"text-align: center;\"><object width=\"600\" height=\"350\" type=\"image/svg+xml\" data=\"resources/question-resources/hardertrapezium_8GqMwOo.svg\"></object></p>\n<p style=\"text-align: left;\">The area of the trapezium is&nbsp;[[0]]&nbsp;$\\mathrm{m^2}$. &nbsp; &nbsp;<em><small>Round your answer to 1 decimal place.</small></em></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "variableReplacements": [], "precision": "1", "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "0.5{w5a+w5b}{h5} + 0.01", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "minValue": "0.5{w5a+w5b}{h5} - 0.01", "mustBeReduced": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "precisionPartialCredit": 0, "marks": "2", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>The formula&nbsp;for the area of a trapezium is:</p>\n<p>\\[\\mathrm{Area} = \\frac{(a+b)}{2}\\times \\mathrm{height}.\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}], "variables": {"h2": {"name": "h2", "description": "<p>Height of the triangle.</p>", "templateType": "anything", "group": "Triangle", "definition": "random(1..4.5#0.1)"}, "wh22dp": {"name": "wh22dp", "description": "<p>The Area of a triangle using the two terms, w2 and h2 to one decimal place, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "Triangle", "definition": "precround(0.5*w2*h2, 1)"}, "wabh5": {"name": "wabh5", "description": "<p>The Area of a trapezium using the three terms, w5a, w5b and h5, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "'Harder' trapezium", "definition": "precround((w5a+w5b)*(h5)/2, 5)"}, "w5b": {"name": "w5b", "description": "<p>The bottom parallel side in the trapezium.</p>", "templateType": "anything", "group": "'Harder' trapezium", "definition": "random(7.5..10#0.1)"}, "wh11": {"name": "wh11", "description": "<p>The product of the two terms, w1 and h1, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "Parallelogram", "definition": "precround(w1*h1,3)"}, "w1": {"name": "w1", "description": "<p>The width of the parallelogram.</p>", "templateType": "anything", "group": "Parallelogram", "definition": "random(5..10#0.1)"}, "wabh5dp": {"name": "wabh5dp", "description": "<p>The Area of a trapezium using the three terms, w5a, w5b and h5 to one decimal place, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "'Harder' trapezium", "definition": "precround((w5a+w5b)*(h5)/2, 1)"}, "h1": {"name": "h1", "description": "<p>The height of the parallelogram</p>", "templateType": "anything", "group": "Parallelogram", "definition": "random(1..4.5#0.1)"}, "w0": {"name": "w0", "description": "<p>Width of the rectangle.</p>", "templateType": "anything", "group": "Rectangle", "definition": "random(5..10#0.1)"}, "wh22": {"name": "wh22", "description": "<p>The Area of a triangle using the two terms, w2 and h2, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "Triangle", "definition": "precround(0.5*w2*h2,4)"}, "w2": {"name": "w2", "description": "<p>Base of the triangle.</p>", "templateType": "anything", "group": "Triangle", "definition": "random(5..10#0.1)"}, "h5": {"name": "h5", "description": "<p>Height of the trapezium.</p>", "templateType": "anything", "group": "'Harder' trapezium", "definition": "random(2..5#0.1)"}, "wh00dp": {"name": "wh00dp", "description": "<p>The product of the two terms, w0 and h0, to one decimal place, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "Rectangle", "definition": "precround(w0*h0,1)"}, "wh00": {"name": "wh00", "description": "<p>The product of the two terms, w0 and h0, such that a condition can be satisfied.</p>", "templateType": "anything", "group": "Rectangle", "definition": "precround(w0*h0,3)"}, "h0": {"name": "h0", "description": "<p>Height of the rectangle.</p>", "templateType": "anything", "group": "Rectangle", "definition": "random(1..5#0.1)"}, "w5a": {"name": "w5a", "description": "<p>The top parallel side in the trapezium.</p>", "templateType": "anything", "group": "'Harder' trapezium", "definition": "random(5..6.5#0.1)"}, "wh11dp": {"name": "wh11dp", "description": "<p>The product of the two terms, w1 and h1, to one decimal place such that a condition can be satisfied.</p>", "templateType": "anything", "group": "Parallelogram", "definition": "precround(w1*h1, 1)"}}, "variablesTest": {"maxRuns": 100, "condition": ""}}]}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Apply formulas to calculate the areas of various shapes.</p>"}, "duration": 0, "showstudentname": true, "name": "Jane's copy of Area of geometric shapes", "showQuestionGroupNames": false, "timing": {"allowPause": true, "timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}}, "navigation": {"reverse": true, "onleave": {"action": "none", "message": ""}, "showresultspage": "oncompletion", "browse": true, "showfrontpage": true, "allowregen": true, "preventleave": true}, "feedback": {"showtotalmark": true, "intro": "", "showactualmark": true, "showanswerstate": true, "allowrevealanswer": true, "feedbackmessages": [], "advicethreshold": 0, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "type": "exam", "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "extensions": ["geogebra", "random_person"], "custom_part_types": [], "resources": [["question-resources/icecrea_QqVaCIf.svg", "/srv/numbas/media/question-resources/icecrea_QqVaCIf.svg"], ["question-resources/frisbee_variable_TESZa4J.svg", "/srv/numbas/media/question-resources/frisbee_variable_TESZa4J.svg"], ["question-resources/tennis-ball_with_variable_MBOLQeM.svg", "/srv/numbas/media/question-resources/tennis-ball_with_variable_MBOLQeM.svg"], ["question-resources/trapezium.svg", "/srv/numbas/media/question-resources/trapezium.svg"], ["question-resources/trangle.svg", "/srv/numbas/media/question-resources/trangle.svg"], ["question-resources/parallelogram.svg", "/srv/numbas/media/question-resources/parallelogram.svg"], ["question-resources/Parallelogram_area_animated.gif", "/srv/numbas/media/question-resources/Parallelogram_area_animated.gif"], ["question-resources/rectangle_zISmvoz.svg", "/srv/numbas/media/question-resources/rectangle_zISmvoz.svg"], ["question-resources/hardertrapezium_8GqMwOo.svg", "/srv/numbas/media/question-resources/hardertrapezium_8GqMwOo.svg"], ["question-resources/Trap_advice.svg", "/srv/numbas/media/question-resources/Trap_advice.svg"], ["question-resources/Triangle_advice_lD6eKvD.svg", "/srv/numbas/media/question-resources/Triangle_advice_lD6eKvD.svg"]]}