// Numbas version: finer_feedback_settings {"question_groups": [{"questions": [{"name": "Basic Algebraic input for numbas", "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": ["a", "c", "b", "d"], "tags": ["algebraic input", "brackets", "input", "introduction", "mathematical expressions", "Numbas", "numbas", "ratios", "Ratios", "rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {"std": ["all", "!collectNumbers"]}, "parts": [{"prompt": "

To input powers use the ^ symbol.

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For example to input $x^3$ type x^3.

\n

To input $2^{x+1}$ type 2^(x+1). Note you need to use brackets here.

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Input $x^{\\var{a}}$=[[0]]

\n

Input $3^{2x+5}$=[[1]]

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To input $3x^2+5x-2$ type 3x^2+5x-2

\n

Input this polynomial: $\\simplify[all]{{a}*x^{b}+{c}*x+{d}}=\\;$[[0]]

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To input two variables multiplied together you need to use * for multiplied. 

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For example to input $ab$ you need to type a*b.

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Input the following:

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$xy$=[[0]]

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$xyz$=:[[1]]

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If you want to input such an expression into the system you HAVE TO BE CAREFUL AND USE BRACKETS or mistakes will occur.

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To input $\\displaystyle \\frac{2-3x}{5+4x}$ type (2-3x)/(5+4x)

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Input the expression: $\\displaystyle \\frac{\\var{b}+\\var{a}y}{\\var{d}+\\var{c}z}$= [[0]]

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To input square roots you need to write \"sqrt(..)\"

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For example to input $\\sqrt{x}$, type sqrt(x)

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Input the following

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$\\sqrt{y}=$[[0]]

\n

$\\sqrt{2x+3}=$[[1]]

\n

$\\sqrt{\\frac{L}{g}}=$[[2]]

\n

$\\sqrt{\\frac{2x+7}{x^2+1}}=$[[3]]

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This first question just goes through how to input different algebraic equations into the computer. 

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You can refer back to this question when doing the other questions if needed.

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Note that what the computer understands by what you have inputed appears to the right of the box you are typing in.

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Instructions on inputting ratios of algebraic expressions.

\n

rebelmaths

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Here is a video on Transposition  https://www.youtube.com/watch?v=0oq4arfe-SM 

", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "

Given $ax=b$, we can rearrange the equation to that find $x=$ [[0]].

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $ax=b$, we divide both sides by $a$ to get $x$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$ax$$=$$b$
 
$\\displaystyle{\\frac{ax}{a}}$$=$$\\displaystyle{\\frac{b}{a}}$
 
$x$$=$$\\displaystyle{\\frac{b}{a}}$
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Given $cy=d$,  $y=$ [[0]].

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $cy=d$, we divide both sides by $c$ to get $y$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$cy$$=$$d$
 
$\\displaystyle{\\frac{cy}{c}}$$=$$\\displaystyle{\\frac{d}{c}}$
 
$y$$=$$\\displaystyle{\\frac{d}{c}}$
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Rearrange $\\displaystyle{\\frac{z}{f}=g}$ to determine the value of $z$.

\n

$z=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{\\frac{z}{f}}=g$, we multiply both sides by $f$ to get $z$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{z}{f}}$$=$$g$
 
$\\displaystyle{\\frac{z}{f}}\\times f$$=$$g\\times f$
 
$z$$=$$fg$
\n

\n

We input our answer as f*g or g*f.

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Solve $\\displaystyle{h=-\\frac{a}{j}}$ for $a$.

\n

$a=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{h=-\\frac{a}{j}}$, we multiply both sides by $-j$ to get $a$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$h$$=$$\\displaystyle{-\\frac{a}{j}}$
 
$h\\times(-\\var{j})$$=$$\\displaystyle{-\\frac{a}{j}\\times(-j)}$
 
$-hj$$=$$a$
 
$a$$=$$-hj$
\n

\n

We input our answer as -h*j or -j*h.

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Rearrange $\\displaystyle{a=\\frac{b}{c}}$ to determine the value of $c$.

\n

$c=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{a=\\frac{b}{c}}$, we need to do two things to get $c$ by itself:

\n
    \n
  1. multiply both sides by $c$ to get $c$ off the bottom of the fraction, then
    2. \n
  2. divide both sides by $a$ to get $c$ by itself.
    3. \n
\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$a$$=$$\\displaystyle{\\frac{b}{c}}$
 
$a\\times c$$=$$\\displaystyle{\\frac{b}{c}}\\times c$ (see step 1 above)
 
$ac$$=$$b$
 
$\\displaystyle{\\frac{ac}{a}}$$=$ $\\displaystyle{\\frac{b}{a}}$(see step 2 above)
$c$$=$$\\displaystyle{\\frac{b}{a}}$
\n

\n

Notice, it looks like we have just swapped $a$ and $c$ diagonally over the equals sign.

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Rearrange $\\displaystyle{s=\\frac{d}{t}}$ to determine the value of $t$.

\n

$t=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{s=\\frac{d}{t}}$, we need to do two things to get $t$ by itself:

\n
    \n
  1. multiply both sides by $t$ to get $t$ off the bottom of the fraction, then
    2. \n
  2. divide both sides by $s$ to get $t$ by itself.
    3. \n
\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$s$$=$$\\displaystyle{\\frac{d}{t}}$
 
$s\\times t$$=$$\\displaystyle{\\frac{d}{t}}\\times t$ (see step 1 above)
 
$st$$=$$d$
 
$\\displaystyle{\\frac{st}{s}}$$=$ $\\displaystyle{\\frac{d}{s}}$(see step 2 above)
$t$$=$$\\displaystyle{\\frac{d}{s}}$
\n

\n

Notice, it looks like we have just swapped $s$ and $t$ diagonally over the equals sign.

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Rearranging equations by multiplying or dividing: One step

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Transposition With Steps (y=ax+b)", "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": ["a", "c", "b"], "tags": ["rearrange", "rebel", "REBEL", "rebelmaths", "transposition"], "advice": "

https://www.youtube.com/watch?v=yT_Z4OzPRaY

", "rulesets": {}, "parts": [{"prompt": "

What is the first operation?

", "matrix": ["0", "0", 0, "1"], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["

divide by {a}

", "

subtract {a}

", "

divide by {b}

", "

subract {b}

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 1, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "

Step 1: [[0]] = [[1]]

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What is the next operation?

", "matrix": ["1", "0", 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["

divide by {a}

", "

multiply by {a}

", "

subtract {a}

", "

add {2}

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 1, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "

Step 2: [[0]] = [[1]]

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Step 3: $x$ = [[0]]

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Rearrange the following equation to make $x$ the subject:

\n

\\[y=\\simplify{{a}x+{b}}\\]

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..9 except [a,b])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "

Transposition

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Transposition With Steps (y=a(x+b))", "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": ["a", "c", "b", "d"], "tags": ["REBEL", "rebel", "Rebel", "rebelmaths", "tranposition", "transpose"], "advice": "

https://www.youtube.com/watch?v=J1NAcToXYjE

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What is the first operation?

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multiply out bracket

", "

subtract {a}

", "

divide by {b}

", "

subract {b}

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Step 1: [[0]] = [[1]]

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What is the next operation?

", "matrix": ["0", "0", 0, "1"], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["

add {d}

", "

multiply by {a}

", "

subtract {a}

", "

subract {d}

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 1, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "

Step 2: [[0]] = [[1]]

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Step 3: $x$ = [[0]]

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Rearrange the following equation to make $x$ the subject:

\n

\\[y=\\simplify{{a}(x+{b})}\\]

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..9 except [a,b])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "

Transposing formulae

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Transposition Q1", "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": ["a", "c", "b", "atimesc"], "tags": ["rebel", "REBEL", "rebelmaths", "transposition"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

Transpose the formula $y=x+\\var{a}$ to make $x$ the subject

\n

$x= $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "y-{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Write $x$ in terms of $y$ if 

\n

$y =\\dfrac{x}{\\var{b}}$.

\n

$x= $[[0]]

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Make $c$ the subject of the formula $y=\\var{c}x+c$.

\n

$c= $[[0]] 

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "y-{c}x", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Make $x$ the subject of the formula $y=\\var{a}x+\\var{b}$.

\n

$x= $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(y-{b})/{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Find $x$ in terms of $y$ if

\n

$\\var{c}y  =  \\var{c}x+\\var{a}$

\n

$x= $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c}y-{a})/{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Find $y$ in terms of $x$ if     

\n

$\\var{a}y=\\var{c}x+\\var{a}$

\n

$y= $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c}x+{a})/{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

Note: to input the answer \"$x=y+2$\" the \"$x=$\" is already given and you just need to input \"$y+2$\".

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..9 except[a,b])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "atimesc": {"definition": "{a}*{c}", "templateType": "anything", "group": "Ungrouped variables", "name": "atimesc", "description": ""}}, "metadata": {"description": "

Transposition

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Transposition of Formulae", "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": ["m", "c", "a"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths", "transpose"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

Make x the subject of

\n

$y = \\var{m} x + \\var{c}$

\n

$x = $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "(y-{c})/{m}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Make x the subject of

\n

$\\var{a}y = \\var{m} x + \\var{c}$

\n

$x = $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({a}y-{c})/{m}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Make R the subject of

\n

$I=\\frac{V}{R}$

\n

$R = $[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "V/verb:I", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Make P the subject of

\n

$A = P(1+r)^n$

\n

$P=$[[0]]

\n

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "A/(1+r)^n ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "m": {"definition": "random(1..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}}, "metadata": {"description": "

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "transposing formula 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": ["a", "c", "b", "d"], "tags": ["REBEL", "rebel", "Rebel", "rebelmaths", "transpose"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepsPenalty": 1, "prompt": "

$\\simplify[std]{{a}y + {b}x = {c} + {d}xy}\\;$

\n

$y =$ [[0]].

\n

You can click on \"Show steps\" for more information, but you will lose one mark if you do so.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

To re-arrange $ay + bx = c + dxy$ we should first collect all of the terms involving $y$ to the one side

\n

$ay - dxy = c - bx$

\n

we should then factorize out $y$ to find

\n

$y(a-dx) = c - bx$

\n

and then divide by $a-dx$ to get $y$ on its own

\n

$y = \\frac{c - bx}{a - dx}$

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({c} - {b}x)/({a} - {d}x)", "marks": "5", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

Rearrange the following equation to make $y$ the subject. 

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "

Another transposition question.

\n

rebalmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Rearrange equations", "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": ["a", "b"], "tags": ["algebra", "biology", "rearranging equations", "Rebel", "REBEL", "rebel", "rebelmaths", "transpose"], "preamble": {"css": "", "js": ""}, "advice": "

start by multiplying both sides by the denominator

\n

for example if you have $V=\\frac{5S}{S+12}$ then multiply both sides by $(S+12)$

\n

this gives:  $V(S+12)=\\frac{5S}{S+12} (S+12) $

\n

the (S+12) term on the right hand side cancels out to give: $V(S+12)=5S$

\n

now expand out the brackets:  $VS+12V=5S$

\n

then collect the like terms, you want to get all the terms with S in them onto one side, so subtract VS from both sides:

\n

$VS-VS+12V=5S-VS$

\n

this becomes $12V=5S-VS$

\n

now you can factorise the right hand side: $12V=S(5-V)$

\n

then divide both sides by (5-V) to leave S on its own: $\\frac{12V}{5-V}=S$

\n

", "rulesets": {}, "parts": [{"prompt": "

Rearrange the following equation to make S the subject.

\n

\n

$ V=\\frac{\\var{a}S}{S+\\var{b}}$

\n

\n

to write a fraction you type (numerator)/(denominator)

\n

S=[[0]]

\n

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({b}*V)/({a}-V)", "marks": "5", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(5..16)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "

rearranging the Michelas-Menten equation to make the substrate the subject.

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "L2 Transposition With Steps", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Peter Chleboun", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/37/"}], "tags": [], "progress": "in-progress", "metadata": {"notes": "", "description": ""}, "statement": "

Rearrange the following equation to make $x$ the subject:

\n

\\[y=\\simplify{{a}(x/{{b}}+{c})^2}\\]

", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "definition": "random(2..9)"}, "b": {"name": "b", "definition": "random(2..9 except a)"}, "c": {"name": "c", "definition": "random(1..9 except [a,b])"}}, "functions": {}, "parts": [{"type": "1_n_2", "marks": 1.0, "prompt": "

What is the first operation?

", "minmarks": 0.0, "maxmarks": 1.0, "shufflechoices": true, "displaytype": "radiogroup", "displaycolumns": 0.0, "minanswers": 0.0, "maxanswers": 0.0, "choices": ["

square root

", "

divide by {a}

", "

multiply by {b}

", "

subtract {c}

"], "matrix": [0.0, 1.0, 0.0, 0.0], "distractors": ["", "", "", ""]}, {"type": "gapfill", "marks": 0.0, "prompt": "

Step 1: [[0]] = [[1]]

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What is the next operation?

", "minmarks": 0.0, "maxmarks": 1.0, "shufflechoices": true, "displaytype": "radiogroup", "displaycolumns": 0.0, "minanswers": 0.0, "maxanswers": 0.0, "choices": ["

divide by {a}

", "

square root

", "

multiply by {b}

", "

subtract {c}

"], "matrix": [0.0, 1.0, 0.0, 0.0], "distractors": ["", "", "", ""]}, {"type": "gapfill", "marks": 0.0, "prompt": "

Step 2: [[0]] = [[1]]

", "gaps": [{"type": "jme", "marks": 1.0, "answer": "sqrt(y/{a})", "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkvariablenames": false, "expectedvariablenames": []}, {"type": "jme", "marks": 1.0, "answer": "x/{{b}}+{c}", "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkvariablenames": false, "expectedvariablenames": []}]}, {"type": "1_n_2", "marks": 1.0, "prompt": "

What is the next operation?

", "minmarks": 0.0, "maxmarks": 1.0, "shufflechoices": true, "displaytype": "radiogroup", "displaycolumns": 0.0, "minanswers": 0.0, "maxanswers": 0.0, "choices": ["

divide by {a}

", "

square root

", "

multiply by {b}

", "

subtract {c}

"], "matrix": [0.0, 0.0, 0.0, 1.0], "distractors": ["", "", "", ""]}, {"type": "gapfill", "marks": 0.0, "prompt": "

Step 3: [[0]] = [[1]]

", "gaps": [{"type": "jme", "marks": 1.0, "answer": "sqrt(y/{a})-{c}", "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkvariablenames": false, "expectedvariablenames": []}, {"type": "jme", "marks": 1.0, "answer": "x/{{b}}", "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkvariablenames": false, "expectedvariablenames": []}]}, {"type": "1_n_2", "marks": 1.0, "prompt": "

What is the final operation?

", "minmarks": 0.0, "maxmarks": 1.0, "shufflechoices": true, "displaytype": "radiogroup", "displaycolumns": 0.0, "minanswers": 0.0, "maxanswers": 0.0, "choices": ["

divide by {a}

", "

square root

", "

multiply by {b}

", "

subtract {c}

"], "matrix": [0.0, 0.0, 1.0, 0.0], "distractors": ["", "", "", ""]}, {"type": "gapfill", "marks": 0.0, "prompt": "

Step 4: $x$ = [[0]]

", "gaps": [{"type": "jme", "marks": 1.0, "answer": "{b}*(sqrt(y/{a})-{c})", "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkvariablenames": false, "expectedvariablenames": []}]}], "type": "question", "variable_groups": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "More transposition", "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/"}], "variables": {"n3": {"description": "", "name": "n3", "group": "Ungrouped variables", "definition": "random(-7..7 except 0 n2)", "templateType": "anything"}, "n2": {"description": "", "name": "n2", "group": "Ungrouped variables", "definition": "random(-7..7 except 0)", "templateType": "anything"}, "n1": {"description": "", "name": "n1", "group": "Ungrouped variables", "definition": "random(2..6)", "templateType": "anything"}, "n4": {"description": "", "name": "n4", "group": "Ungrouped variables", "definition": "random(1..10)", "templateType": "anything"}}, "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "transpose", "transposition"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Another transposition question, which requires (basic) factorisation.

\n

rebelmaths

"}, "variable_groups": [], "statement": "", "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "prompt": "

Consider the equation:

\n

\\[\\simplify{x^{{n1}}*y + {n2}*y*x} = \\simplify{{n3}*y} + \\var{n4}\\]

\n

Re-arrange this equation to make $y$ the subject:

\n

$y = $[[0]]

", "showFeedbackIcon": true, "steps": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "information", "scripts": {}, "marks": 0, "prompt": "

It may be helpful to factor out y. For example: 

\n

\\[\\simplify{x^{{n1}}*y+{n2}*y*x - {n3}*y}=y(\\simplify{x^{{n1}} + {n2}*x - {n3}})\\]

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Here, we first have to collect all terms involving $y$ on the same side. Hence, we get:

\n

\\[\\simplify{x^{{n1}}*y+{n2}*y*x - {n3}*y} = \\var{n4}\\]

\n

We then spot that $y$ appears exactly once in each term on the left, so factorise:

\n

\\[y(\\simplify{x^{{n1}} + {n2}*x - {n3}}) = \\var{n4}\\]

\n

and simple division gives the answer.

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Make $x$ the subject of the following formula

\n

$p=\\sqrt{{\\var{b}x}}$

\n

$x=$ [[0]]

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Square both sides to get

\n

$p^2=\\var{b}x$

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Make $x$ the subject of the following formula

\n

$p=\\sqrt{{\\var{a}+\\var{b}x}}$

\n

$x=$ [[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Square both sides

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Make $x$ the subject of the following formula

\n

$p=\\sqrt{\\frac{\\var{a}+\\var{b}x}{\\var{c}}}$

\n

$x=$ [[0]]

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Questions with increasing difficulty.

\n

rebelmaths

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Make $x$ the subject of the following formula

\n

$p=\\sqrt{\\frac{\\var{a}+\\var{b}x}{\\var{c}}}$

\n

$x=$ [[0]]

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rebelmaths

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The formula $P=\\frac{F}{A}$ is used in mechanics where $P=$Pressure, $F=$Force and $A=$Area.

\n

Rearrange the forumla to make $F$ the subject. 

\n

Note if inputting $xy$ for an  answer you need to input $x*y$.

\n

$F=$[[0]]

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The formula $v=u+at$ is used in mechanics where $v=$final velocity, $u=$initial velocity and $t=$time.

\n

Rearrange the forumla to make $u$ the subject. 

\n

$u=$[[0]]

\n

Rearrange the forumla to make $a$ the subject. 

\n

$a=$[[1]]

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rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}], "pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0}], "showQuestionGroupNames": false, "duration": 0, "type": "exam", "shuffleQuestions": false, "questions": [], "percentPass": 0, "feedback": {"showactualmark": true, "allowrevealanswer": true, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showtotalmark": true, "advicethreshold": 0, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "pickQuestions": 0, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Transposition of formulae. Changing the subject of an equation. 

\n

rebel rebelmaths

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