// Numbas version: exam_results_page_options {"name": "Substitute values into formulas", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"preventleave": false, "showfrontpage": false, "allowregen": true}, "question_groups": [{"questions": [{"preamble": {"js": "", "css": ""}, "parts": [{"showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "gaps": [{"showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "maxValue": "{x2}{n+2}^2+{x1}{n+2}+{const}", "allowFractions": false, "minValue": "{x2}{n+2}^2+{x1}{n+2}+{const}", "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"]}], "prompt": "

A curve is defined by a function $y=\\simplify{{x2}x^2 + {x1}x + {const}}$.

\n

What is the $y$ coordinate value of the point on the curve at $x=\\var{n+2}$?

\n

$y =$ [[0]]

", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "gaps": [{"showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "maxValue": "{n+1}{n}^2-{x2}{n}", "allowFractions": false, "minValue": "{n+1}{n}^2-{x2}{n}", "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"]}], "prompt": "

{name[n]} sells luxury yachts.

\n

The predicted sales of the luxury yachts are defined by

\n

\$S=\\simplify{{n+1}y^2-{x2}y},\$

\n

where
$S$ is the number of sales predicted this year;
$y$ is the number of luxury yachts sold in the previous year.

\n

{pronoun} sold {n} yachts in the previous year.

\n

Calculate $S$, the number of sales predicted this year.

\n

$S =$ [[0]]

", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "gaps": [{"showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "maxValue": "T_F", "allowFractions": false, "minValue": "T_F", "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"]}], "prompt": "

You can convert temperatures from degrees celsius to degrees fahrenheit by using the formula

\n

\$T_F=1.8\\, T_C+32,\$

\n

where
$T_F$ = Temperature in $°F$
$T_C$ = Temperature in $°C$.

\n

Convert $\\var{T_C}°C$ into degrees fahrenheit.

\n

$T_F =$ [[0]] $°F$

", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}], "name": "Substitute values into formulas", "statement": "

Substitute the given values in the equations below.

", "ungrouped_variables": ["r", "x1", "n", "x2", "const", "sales"], "tags": ["predicted value", "substitution", "Substitution", "taxonomy"], "contributors": [{"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/", "name": "Christian Lawson-Perfect"}, {"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/", "name": "Aiden McCall"}], "advice": "

When inserting numbers into your calculator make sure you place brackets correctly.

\n

#### a)

\n

As $x = \\var{n+2}$,

\n

substitute $\\var{n+2}$ 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}

\n

b)

\n

As $y = \\var{n}$,

\n

substitute $\\var{n}$ 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}

\n

c)

\n

As we are given a temperature in degrees Celcius, $T_C = \\var{T_C}°C.$

\n

Substituting $T_C$ 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}

\n

\n

\n", "extensions": ["geogebra"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Substitute given values into formulas.

"}, "variable_groups": [{"variables": ["name", "name2", "pronoun"], "name": "Name variables"}, {"variables": ["T_F", "T_C"], "name": "Temperature conversion"}], "rulesets": {}, "variables": {"r": {"name": "r", "templateType": "anything", "definition": "random(1..50#0.1)", "group": "Ungrouped variables", "description": "

A random variable which will be inputted by the student.

"}, "x2": {"name": "x2", "templateType": "anything", "definition": "random(1..(n+1)*n)", "group": "Ungrouped variables", "description": "

The x^2 coefficient

"}, "T_C": {"name": "T_C", "templateType": "anything", "definition": "random(5..30#1)", "group": "Temperature conversion", "description": "

Creates a random integer value for the temperature in degrees celcius.

"}, "const": {"name": "const", "templateType": "anything", "definition": "random(1..100#1)", "group": "Ungrouped variables", "description": "

The constant coefficient

"}, "name": {"name": "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

"}, "name2": {"name": "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

"}, "pronoun": {"name": "pronoun", "templateType": "anything", "definition": "if(mod(n,2)=0,\"He\",\"She\")", "group": "Name variables", "description": "

Defines the pronoun in the question.

"}, "x1": {"name": "x1", "templateType": "anything", "definition": "random(1..50)", "group": "Ungrouped variables", "description": "

The x coefficient

"}, "T_F": {"name": "T_F", "templateType": "anything", "definition": "T_C*1.8+32", "group": "Temperature conversion", "description": "

Creates a value for Temperature in fahrenheit.

"}, "sales": {"name": "sales", "templateType": "anything", "definition": "(n+1)n^2-x2*n", "group": "Ungrouped variables", "description": ""}, "n": {"name": "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.

"}}}], "pickingStrategy": "all-ordered"}], "contributors": [{"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/", "name": "Christian Lawson-Perfect"}, {"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/", "name": "Aiden McCall"}]}