// Numbas version: exam_results_page_options {"name": "An Introduction to Numbas", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", ""], "questions": [{"name": "Numbas - Getting Started", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ahmed Al-Razaz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4865/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

This lab will introduce you to Numbas and teach you how to enter your answers correctly.

Labs and formal tests that you complete in Numbas will be marked as soon as you finish the questions.

Although recommended, you do not have to complete a lab or homework in one go. You can save your progress by pressing the ‘Pause’ button on the left-hand side of the screen.

To submit your answer press the 'submit answer' button.

To see the worked solution press the 'reveal answers' button

Answer the following question and submit your answer:

", "advice": "

1+1=2

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1 + 1 =

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Some of the questions will have different variations.

To attempt a question again with different numbers, press the 'try another like this one' button.

Complete this question and then try another one:

", "advice": "

{A} + {B} = {C}

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{A} + {B} =

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To enter a fraction you must put a forward slash (/) between the numerator and the denominator

e.g., ,$\\frac{3}{5}$= 3/5

For fractions with more than one term, the numerator and the denominator need to be in brackets

e.g., $\\frac{3+2x}{5+y}$ = (3+2x)/(5+5y)

Complete the following calculations and display the correct answer as a fraction in its simplest form:

", "advice": "

To add fractions there are Three Simple Steps:

Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add the top numbers (the numerators), put that answer over the denominator
Step 3: Simplify the fraction (if needed)

Answer (a):

$\\frac{1}{4}$ + $\\frac{1}{4}$

Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

$\\frac{1+1}{4}$ = $\\frac{2}{4}$

Step 3. Simplify the fraction:

Hint: divide the top and bottom by 2.

$\\frac{1}{2}$

In picture form it looks like this:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\frac{1}{4}$	+	$\\frac{1}{4}$	=	$\\frac{2}{4}$	=	$\\frac{1}{2}$
$\"1/4\"$		$\"1/4\"$		$\"2/4\"$		$\"1/2\"$

... and do you see how $\\frac{2}{4}$ is simpler as $\\frac{1}{2}$

Answer (b):

Step 1. The denominators are already the same. Go straight to step 2.

Step 2. Add the top expressions and put the answer over the same denominator:

$\\frac{6x+9y}{7y+2}$

Step 3. Simplify the fraction: the fraction is already as simple as possible!

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$\\frac{1}{4}$ + $\\frac{1}{4}$

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$\\frac{6x}{7y+2}$ + $\\frac{9y}{7y+2}$

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Find the result of this calculation: (This is an example of a randomised question - the next time you use this example you will probably be given a different calculation to do):

$\\var{a}\\times\\var{b}+\\var{c}=\\;$[[0]]

You have to input a whole number - it could be in decimal form. If the answer was $2$ then you could input 2 or 2.0 - try both forms.

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Decimals

Many calculations will result in numbers which need to be entered in decimal notation, and the question will ask for a certain number of decimal places.

Often there is a small tolerance built in so that if you get the result wrong by 1 in the last decimal place then it will be marked as correct. But accuracy is important, so make sure that you get the calculations correct.

For example:

Input $\\displaystyle \\frac{\\var{a1}}{\\var{b1}}$ as a decimal correct to 2 decimal places here: [[0]]

Try entering the correct value and submitting. Then vary the last decimal place by 1 either way and submitting, and then the last place by 2 either way and submitting.

Try putting in the fraction as it is (i.e. $\\var{a1}/\\var{b1}$ ) and see what happens.

The system gives an error message as what you have put in is not a direct representation of a number. But you can always re-enter.

So be careful - always check after submitting your answer that the input field contains the answer that you thought you entered.

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Fractions

You will find that some questions may ask you to input fractions and not decimals.

For example, find the following sum as a fraction:

$\\displaystyle \\frac{1}{\\var{a1}}+\\frac{1}{\\var{b1}}=\\;$[[0]]

(input as a fraction and not a decimal)

Hint: the answer is {a1+b1}/{a1*b1}

Try inputting the decimal version of this to as many places as you like (for example given by the calculator on the PC - you can copy this from the calculator and paste into the input field) and see what happens.

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Simplify into a single fraction. Do not enter as a decimal.

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Input as a fraction.

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As this question is in practice mode, if you click on the Reveal answers button all of the question fields are filled with the correct answers. Also, if available, there will be a full solution given under the heading Advice. Just scroll down to see this. However, there is no advice available for this question as it is not needed.

Finally as you are in practice mode, if you click on the Try another question like this one button at the bottom you will get this question again but with different numbers (usually!), and you can try it again. This is true for all practice mode questions which are randomised.

", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacements": [], "unitTests": []}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "

In this example we show how to enter numbers, either as

Whole numbers (integers).
Decimals (to a number of decimal places)
Fractions

", "tags": ["checked2015", "Decimals", "decimals", "Fractions", "fractions", "input", "introduction", "numbas", "Numbas", "numbers", "tolerance", "whole numbers"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Details on inputting numbers into Numbas.

"}, "advice": "

No advice available.

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To test your input of powers try the following examples:

Input as a single power of $x$:

$\\simplify[all]{e^({a}*x)e^({b}*x)}=\\;$[[0]]

(The answer is $\\simplify[all]{e^({a+b}x)}$ but you have to enter it properly.)

Your input is shown in mathematical notation in a box next to your input so that you can check that you have entered it correctly.

Click on Submit part to check on your answer.

Click on the input field and edit your answer by inputting without brackets around the powers to see what happens.

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Input $x^{\\var{c}}x^{\\var{d}}$ as a single power of $x$.

For example, you would input $x^{-6}x^{-5}$ as x^(-11).

$x^{\\var{c}}x^{\\var{d}}=\\;$[[0]]

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Input in the form $x^a*y^b$ for suitable values of $a$ and $b$.

", "showStrings": false, "partialCredit": 0, "strings": ["xy", "x*y"]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "all", "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "

Input $(x \\cdot y)^{\\var{f}}$ in the form $x^a \\times y^b$ for suitable values of $a$ and $b$.

$(x \\cdot y)^{\\var{f}}=\\;$[[0]]

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In this example we show you how to input powers. It is important that you get this right as many questions ask for such inputs.

The standard way of inputting powers is as follows:

$a^b$ is input as a^b - and this is the only way to input powers.

But you have to be careful with inputting expressions such as $e^{2x}$ and $(xy)^2$. In these cases brackets should be used, as we now show:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Power	Correct Input	Incorrect Input
$e^{2x}$	`e^(2*x)`	`e^2*x` (system thinks this is $e^2 \\times x$)
$(xy)^2$	`(x*y)^2`	`x*y^2` (system thinks this is $x \\times y^2$)

So make sure that you use brackets to properly define your powers. This is a major source of input inaccuracies.

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Information on inputting powers

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Inputting polynomials such as $3x^2+5x-2$ is easy : just input 3*x^2+5*x-2.

Try this:

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

", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "x^2+{a+c}x*y+{a*c}y^2", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": true, "expectedvariablenames": ["x", "y"], "notallowed": {"showStrings": false, "message": "

Do not include brackets in your answer.

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Now consider this problem.

Expand the brackets and input the resulting expression:

$\\simplify[all]{(x+{a}y)(x+{c}y)}=\\;$[[0]]

Make sure that you input an expression in your answer such as $xy$ as x*y.

(Do not include brackets in your answer.)

", "showCorrectAnswer": true, "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "

In this example, we look at how you enter algebraic expressions - those involving symbols.

The box next to your input shows what you've written in mathematical notation and is very important as you can check it against the expression you had in mind.

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Inputting algebraic expressions into Numbas.

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Examples

Suppose we wanted to input the expression $\\displaystyle \\frac{\\var{a}+\\var{b}x}{\\var{c}+\\var{d}y}$ into the system.

Which of the following input expressions are incorrect?

[[0]]

Choose the incorrect input(s): (You lose 3 marks if you choose the wrong one!)

If you click on Submit part, then on Show feedback, you will be given more detail on your choices.

You can click on Reveal at the top of the window to see solutions, but it's best to work these through yourself. Remember you can always redo the question by clicking on Try another question like this one at the bottom.

", "scripts": {}, "gaps": [{"displayType": "checkbox", "choices": ["

({a}+{b}x)/({c}+{d}y)

", "

{a}+{b}x/({c}+{d}y)

", "

{a}+{b}x/{c}+{d}y

", "

({a}+{b}x)/{c}+{d}y

"], "showCorrectAnswer": true, "matrix": [-3, 1, 1, 1], "distractors": ["This is the correct input, so your choice is wrong!", "Good choice as the system thinks this is $\\simplify[std]{ {a}+{b}x/({c}+{d}y)}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$", "Good choice as the system thinks this is $\\simplify[std]{ {a}+{b}x/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$", "Good choice as the system thinks this is $\\simplify[std]{ ({a}+{b}x)/{c}+{d}y}$ and not $\\simplify[std]{ ({a}+{b}x)/({c}+{d}y)}$"], "variableReplacements": [], "type": "m_n_2", "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "minMarks": 0, "minAnswers": 0, "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 1, "marks": 0}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0}, {"prompt": "

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

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

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

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

Input the expression $\\displaystyle \\simplify[std]{({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 * b}) * (y -{3* d}))}$ here: [[0]]

", "scripts": {}, "gaps": [{"answer": "({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 b}) * (y -{3* d}))", "vsetrange": [0, 1], "scripts": {}, "answersimplification": "std", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.0001, "checkvariablenames": false, "type": "jme", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "

Ratios of Algebraic Expressions.

By this we mean expressions of the form $\\displaystyle \\frac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are algebraic expressions.

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

Once again, the box displaying your input in mathematical notation beside the input boxes in parts 2, 3 and 4 is very useful as it shows what the system thinks you have entered.

For complicated expressions this is essential as you can check you have written what you really meant.

", "tags": ["algebraic input", "brackets", "checked2015", "input", "introduction", "mathematical expressions", "numbas", "Numbas", "ratios", "Ratios"], "rulesets": {"std": ["all", "!collectNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Inputting ratios of algebraic expressions.

"}, "advice": "

a) The correct input is ({a}+{b}x)/({c}+{d}y) - the rest are incorrect and you should have ticked those.

b) A correct input is ({b} + {a}y) / ({c} + {d}z). Also correct is ({a}y+{b}) / ({c} + {d}z) etc.

c) A correct input is ({d}z + {b}) / ((x + {a})*(y + {c})).

Note the denominator (the bottom of the ratio) has to have two brackets, i.e. ((x + {a})*(y + {c})) as otherwise the expression ({d}z + {b}) / (x + {a})*(y + {c}) is seen by the system as $\\displaystyle \\left(\\simplify[std]{({d} * z + {b}) / (x + {a})}\\right) (y + \\var{c})$

d) A correct input is ({a} -({b}x + {c})*e ^ ( -{2}x)) / ((x + {2*b})*(y -{3*d}))

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