// Numbas version: exam_results_page_options {"name": "Marte's copy of Substitute values into formulas", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [{"name": "Name variables", "variables": ["name", "name2", "pronoun"]}, {"name": "Temperature conversion", "variables": ["T_F", "T_C"]}], "name": "Marte's copy of Substitute values into formulas", "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "
Substitute given values into formulas.
", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "When inserting numbers into your calculator make sure you place brackets correctly.
\nAs $x = \\var{n+2}$,
\nsubstitute $\\var{n+2}$ into $\\var{x2}x^2 + \\var{x1}x + \\var{const}$.
\n\\begin{align}
\\var{x2}x^2 + \\var{x1}x + \\var{const} &= \\var{x2} (\\var{n+2})^2 + \\var{x1}(\\var{n+2}) + \\var{const} \\\\
&= \\simplify{{x2} ({n+2})^2 + {x1}({n+2}) + {const}}\\,.
\\end{align}
b)
\nAs $y = \\var{n}$,
\nsubstitute $\\var{n}$ into $\\var{n+1}y^2-\\var{x2}y$.
\n\\begin{align}
\\var{n+1}y^2-\\var{x2}y &= \\var{n+1}(\\var{n})^2-\\var{x2}(\\var{n}) \\\\
&= \\simplify{{n+1}({n})^2-{x2}({n})}\\,.
\\end{align}
c)
As we are given a temperature in degrees Celcius, $T_C = \\var{T_C}°C.$
\nSubstituting $T_C$ into $T_C = 1.8\\,T_C + 32$.
\n\\begin{align}
T_F &=1.8\\, T_C+32 \\\\
&=1.8 (\\var{T_C}) + 32 \\\\
&= \\var{dpformat(1.8 {T_C} +32, 1)}\\,°F\\,.
\\end{align}
A curve is defined by a function $y=\\simplify{{x2}x^2 + {x1}x + {const}}$.
\nWhat is the $y$ coordinate value of the point on the curve at $x=\\var{n+2}$?
\n$y =$ [[0]]
", "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{x2}{n+2}^2+{x1}{n+2}+{const}", "mustBeReducedPC": 0, "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "minValue": "{x2}{n+2}^2+{x1}{n+2}+{const}", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "mustBeReduced": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "scripts": {}}, {"type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "prompt": "{name[n]} sells luxury yachts.
\nThe predicted sales of the luxury yachts are defined by
\n\\[S=\\simplify{{n+1}y^2-{x2}y},\\]
\nwhere
$S$ is the number of sales predicted this year;
$y$ is the number of luxury yachts sold in the previous year.
{pronoun} sold {n} yachts in the previous year.
\nCalculate $S$, the number of sales predicted this year.
\n$S =$ [[0]]
", "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{n+1}{n}^2-{x2}{n}", "mustBeReducedPC": 0, "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "minValue": "{n+1}{n}^2-{x2}{n}", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "mustBeReduced": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "scripts": {}}, {"type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "prompt": "You can convert temperatures from degrees celsius to degrees fahrenheit by using the formula
\n\\[T_F=1.8\\, T_C+32,\\]
\nwhere
$T_F$ = Temperature in $°F$
$T_C$ = Temperature in $°C$.
Convert $\\var{T_C}°C$ into degrees fahrenheit.
\n$T_F =$ [[0]] $°F$
", "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "maxValue": "T_F", "mustBeReducedPC": 0, "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "minValue": "T_F", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "mustBeReduced": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "scripts": {}}], "tags": ["predicted value", "substitution", "Substitution", "taxonomy"], "statement": "Substitute the given values in the equations below.
", "variables": {"sales": {"templateType": "anything", "definition": "(n+1)n^2-x2*n", "group": "Ungrouped variables", "description": "", "name": "sales"}, "n": {"templateType": "anything", "definition": "random(0..4#1)", "group": "Ungrouped variables", "description": "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.
", "name": "n"}, "T_C": {"templateType": "anything", "definition": "random(5..30#1)", "group": "Temperature conversion", "description": "Creates a random integer value for the temperature in degrees celcius.
", "name": "T_C"}, "T_F": {"templateType": "anything", "definition": "T_C*1.8+32", "group": "Temperature conversion", "description": "Creates a value for Temperature in fahrenheit.
", "name": "T_F"}, "x1": {"templateType": "anything", "definition": "random(1..50)", "group": "Ungrouped variables", "description": "The x coefficient
", "name": "x1"}, "const": {"templateType": "anything", "definition": "random(1..100#1)", "group": "Ungrouped variables", "description": "The constant coefficient
", "name": "const"}, "r": {"templateType": "anything", "definition": "random(1..50#0.1)", "group": "Ungrouped variables", "description": "A random variable which will be inputted by the student.
", "name": "r"}, "name": {"templateType": "anything", "definition": "[\"Andrew\",\"Susan\",\"Tom\",\"Geraldine\",\"Joshua\",\"Chantel\"]", "group": "Name variables", "description": "List of names to randomise. Can change to any name inserted
", "name": "name"}, "x2": {"templateType": "anything", "definition": "random(1..(n+1)*n)", "group": "Ungrouped variables", "description": "The x^2 coefficient
", "name": "x2"}, "name2": {"templateType": "anything", "definition": "[\"Andrew\",\"Susan\",\"Tom\",\"Geraldine\",\"Joshua\",\"Chantel\"]", "group": "Name variables", "description": "List of names to randomise. Can change to any name inserted
", "name": "name2"}, "pronoun": {"templateType": "anything", "definition": "if(mod(n,2)=0,\"He\",\"She\")", "group": "Name variables", "description": "Defines the pronoun in the question.
", "name": "pronoun"}}, "rulesets": {}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["r", "x1", "n", "x2", "const", "sales"], "extensions": ["geogebra"], "type": "question", "contributors": [{"name": "Marte Br\u00e5talien", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2349/"}]}]}], "contributors": [{"name": "Marte Br\u00e5talien", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2349/"}]}