// Numbas version: finer_feedback_settings
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Below is the recorded temperature data for a given day in 6 hour intervals:</p>\n<p data-start=\"102\" data-end=\"193\">00:00 - 06:00 &rarr; {temp_1}&deg;C<br data-start=\"122\" data-end=\"125\"/>06:00 - 12:00 &rarr; {temp_2}&deg;C<br data-start=\"145\" data-end=\"148\" data-is-only-node=\"\"/>12:00 - 18:00 &rarr; {temp_3}&deg;C<br data-start=\"168\" data-end=\"171\"/>18:00 - 00:00 &rarr; {temp_4}&deg;C</p>\n<p data-start=\"195\" data-end=\"247\" data-is-last-node=\"\" data-is-only-node=\"\">Calculate the total heating degree days for the day.</p>\n<p data-start=\"195\" data-end=\"247\" data-is-last-node=\"\" data-is-only-node=\"\"></p>\n<p></p>", "advice": "<p><strong>Using the heating degree day (HDD) formula:</strong></p>\n<p>HDD = (Base Temperature&minus;Outside Temperature)&times;Time Fraction</p>\n<p></p>\n<p>HDD = ({base_temp}&deg;C - {temp_1}&deg;C &times; 6/24) + ({base_temp}&deg;C - {temp_2}&deg;C &times; 6/24) + ({base_temp}&deg;C - {temp_3}&deg;C &times; 6/24) + ({base_temp}&deg;C - {temp_4}&deg;C &times; 6/24)</p>\n<p></p>\n<p>HDD = ({base_temp - temp_1}&deg;C &times; 0.25) + ({base_temp - temp_2}&deg;C &times; 0.25) + ({base_temp - temp_3}&deg;C &times; 0.25) + ({base_temp - temp_4}&deg;C &times; 0.25)</p>\n<p></p>\n<p><strong>Remember to not include temperatures that exceed our base temperature.</strong></p>\n<p>HDD = ({dd1/0.25} &times; 0.25) + ({dd2/0.25} &times; 0.25) + ({dd3/0.25} &times; 0.25) + ({dd4/0.25} &times; 0.25)</p>\n<p>HDD = {dd1} + {dd2} + {dd3} + {dd4}</p>\n<p>HDD = {dd1+dd2+dd3+dd4}</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"temp_1": {"name": "temp_1", "group": "Ungrouped variables", "definition": "random(base_temp - 3 .. base_temp + 1#0.5)", "description": "<p>Temperature for the first 6 hour period</p>", "templateType": "randrange", "can_override": false}, "temp_2": {"name": "temp_2", "group": "Ungrouped variables", "definition": "random(base_temp - 3 .. base_temp + 1#0.5)", "description": "", "templateType": "randrange", "can_override": false}, "temp_3": {"name": "temp_3", "group": "Ungrouped variables", "definition": "random(base_temp - 3 .. base_temp + 1#0.5)", "description": "", "templateType": "randrange", "can_override": false}, "temp_4": {"name": "temp_4", "group": "Ungrouped variables", "definition": "random(base_temp - 3 .. base_temp + 1#0.5)", "description": "", "templateType": "randrange", "can_override": false}, "base_temp": {"name": "base_temp", "group": "Ungrouped variables", "definition": "random(17 .. 20#1)", "description": "<p>The building's base temperature</p>", "templateType": "randrange", "can_override": false}, "dd1": {"name": "dd1", "group": "Ungrouped variables", "definition": "max((base_temp-temp_1)*0.25,0)", "description": "<p>Degree day for the 6 hour period.</p>", "templateType": "anything", "can_override": false}, "dd2": {"name": "dd2", "group": "Ungrouped variables", "definition": "max((base_temp-temp_2)*0.25,0)", "description": "", "templateType": "anything", "can_override": false}, "dd3": {"name": "dd3", "group": "Ungrouped variables", "definition": "max((base_temp-temp_3)*0.25,0)", "description": "", "templateType": "anything", "can_override": false}, "dd4": {"name": "dd4", "group": "Ungrouped variables", "definition": "max((base_temp-temp_4)*0.25,0)", "description": "", "templateType": "anything", "can_override": false}, "total_hdd": {"name": "total_hdd", "group": "Ungrouped variables", "definition": "dd1+dd2+dd3+dd4", "description": "<p>Variable to store the total heating degree days for the entire period</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["temp_1", "temp_2", "temp_3", "temp_4", "base_temp", "dd1", "dd2", "dd3", "dd4", "total_hdd"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "total_hdd", "maxValue": "total_hdd", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Calculate Energy Efficiency Improvements Using Heating Degree Days", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Simon Stuttaford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/26443/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p data-start=\"56\" data-end=\"303\">Dan, the facilities manager, is under pressure to prove that his investment in insulation has led to significant energy savings. The heating energy consumption and heating degree days (HDD) for two consecutive years are as follows:</p>\n<ul data-start=\"305\" data-end=\"507\">\n<li data-start=\"305\" data-end=\"405\">\n<p data-start=\"307\" data-end=\"318\"><strong data-start=\"307\" data-end=\"316\">2023:</strong></p>\n<ul data-start=\"321\" data-end=\"405\">\n<li data-start=\"321\" data-end=\"368\">Heating energy consumption: <strong>{heating_energy_pre}kWh</strong></li>\n<li data-start=\"371\" data-end=\"405\">Heating degree days: <strong>{hdd_pre}</strong></li>\n</ul>\n</li>\n<li data-start=\"407\" data-end=\"507\">\n<p data-start=\"409\" data-end=\"420\"><strong data-start=\"409\" data-end=\"418\">2024:</strong></p>\n<ul data-start=\"423\" data-end=\"507\">\n<li data-start=\"423\" data-end=\"470\">Heating energy consumption: <strong>{heating_energy_post}kWh</strong></li>\n<li data-start=\"473\" data-end=\"507\">Heating degree days: <strong>{hdd_post}</strong></li>\n</ul>\n</li>\n</ul>\n<p data-start=\"509\" data-end=\"663\">Dan needs to determine the energy efficiency improvement by calculating the <strong data-start=\"585\" data-end=\"607\">kWh per degree day</strong> for each year and then finding the percentage change.</p>\n<p data-start=\"809\" data-end=\"881\"></p>", "advice": "<p><strong>kWh per degree day in 2023:</strong></p>\n<p>{heating_energy_pre}kWh / {hdd_pre} = {energy_degree_day_pre}</p>\n<p><strong>kWh per degree day in 2024:</strong></p>\n<p>{heating_energy_post}kWh / {hdd_post} = {energy_degree_day_post}</p>\n<p><strong>Percentage improvement:</strong></p>\n<p>({energy_degree_day_pre} - {energy_degree_day_post}) / {energy_degree_day_pre} &times; 100 = {improvement}%</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"heating_energy_pre": {"name": "heating_energy_pre", "group": "Ungrouped variables", "definition": "random(200000 .. 600000#1)", "description": "<p>Building heating energy consumption before insulation, in kWh</p>", "templateType": "randrange", "can_override": false}, "heating_energy_post": {"name": "heating_energy_post", "group": "Ungrouped variables", "definition": "random(200000 .. 600000#1)", "description": "<p>Building heating energy consumption after insulation, in kWh</p>", "templateType": "randrange", "can_override": false}, "hdd_pre": {"name": "hdd_pre", "group": "Ungrouped variables", "definition": "random(2000 .. 5000#1)", "description": "<p>Heating degree days in the year before insulation.&nbsp;</p>", "templateType": "randrange", "can_override": false}, "hdd_post": {"name": "hdd_post", "group": "Ungrouped variables", "definition": "random(2000 .. 5000#1)", "description": "<p>Heating degree days in the year after insulation.&nbsp;</p>", "templateType": "randrange", "can_override": false}, "energy_degree_day_pre": {"name": "energy_degree_day_pre", "group": "Ungrouped variables", "definition": "precround(dec(heating_energy_pre/hdd_pre),3)", 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