// Numbas version: exam_results_page_options {"question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "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.

\n

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.

\n

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

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "x^{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "3^(2x+5)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

To input $3x^2+5x-2$ type 3x^2+5x-2

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{a}*x^{b}+{c}x+{d}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

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

\n

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

\n

Input the following:

\n

$xy$=[[0]]

\n

$xyz$=:[[1]]

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

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

\n

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

\n

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

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

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

\n

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

\n

Input the following

\n

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

\n

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

\n

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

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "sqrt(y)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "sqrt(2x+3)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "sqrt(L/g)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "sqrt((2x+7)/(x^2+1))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

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

\n

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

\n

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

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..16#2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(3..15#2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9 except [round(b*c/a),c])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "

Instructions on inputting ratios of algebraic expressions.

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Rearranging equations by multiplying or dividing: One step", "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": [], "tags": ["algebra", "balancing equations", "ephlth", "linear equations", "Linear equations", "one step equations", "rearranging equations", "REBEL", "rebel", "rebelmaths", "Solving equations", "solving equations"], "preamble": {"css": "", "js": ""}, "advice": "

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}}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["b", "a"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "b/a", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "

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}}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["d", "c"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "d/c", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "

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.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["f", "g"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "f*g", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "

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.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["j", "h"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "-j*h", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "

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.

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

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.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["d", "s"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "d/s", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": "100", "condition": ""}, "variables": {}, "metadata": {"description": "

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 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]]

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

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": "Transposition Practical examples", "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": [], "tags": ["rebel", "REBEL", "rebelmaths", "transposition"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "

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]]

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

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]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "v-a*t", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "(v-u)/t", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"description": "

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "percentPass": 0, "name": "MATH6051 Transposition Homework 1", "duration": 0, "timing": {"timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}, "allowPause": true}, "showstudentname": true, "navigation": {"browse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "onleave": {"action": "none", "message": ""}, "reverse": true, "showfrontpage": true}, "showQuestionGroupNames": false, "feedback": {"intro": "", "showtotalmark": true, "advicethreshold": 0, "feedbackmessages": [], "allowrevealanswer": true, "showanswerstate": true, "showactualmark": true}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Practice of basic transpositions. Doesn't include roots

"}, "type": "exam", "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": []}