// 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}, "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.

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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]]

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

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To input $3x^2+5x-2$ type 3x^2+5x-2

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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]]

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

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

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

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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.

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\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
 $cy$ $=$ $d$ $\\displaystyle{\\frac{cy}{c}}$ $=$ $\\displaystyle{\\frac{d}{c}}$ $y$ $=$ $\\displaystyle{\\frac{d}{c}}$
", "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 $z$.

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$z=$ [[0]]

\n

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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

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

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

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$a=$ [[0]]

\n

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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.

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\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 $c$.

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$c=$ [[0]]

\n

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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
3. divide both sides by $a$ to get $c$ by itself.
4. \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 $t$.

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$t=$ [[0]]

\n

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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
3. divide both sides by $s$ to get $t$ by itself.
4. \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}, "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]]

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Write $x$ in terms of $y$ if

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

\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]]

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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 \"$y+2$\".

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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}, "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]]

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Make x the subject of

\n

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

\n

$x =$[[0]]

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Make R the subject of

\n

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

\n

$R =$[[0]]

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Make P the subject of

\n

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

\n

$P=$[[0]]

\n

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rebelmaths

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

\n

$y =$ [[0]].

\n

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

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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

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

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

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Another transposition question.

\n

rebalmaths

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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

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Practice of basic transpositions. Doesn't include roots

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