// Numbas version: finer_feedback_settings {"shuffleQuestions": false, "questions": [{"metadata": {"notes": "", "description": "

Entering numbers and algebraic symbols in Numbas.

", "licence": "None specified"}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variables": {}, "ungrouped_variables": [], "name": "How to enter numbers and algebraic symbols - Getting Started", "advice": "", "functions": {}, "statement": "

This example explains how you enter your answers and submit them.

This example and the others are in practice mode - you will be given information on whether or not you have the answer correct or not.

Assessed mode does not give you this information.

It is very important that you submit all your answers. If you do not your results will not be recorded. Note that the list of questions in the exam on the left of the window gives information on whether or not you have completed a question. For each question the marks you have gained by submitting are shown there, so if nothing is shown you have not attempted the question.

Go to the next question. You can then come back. Note that until you quit the exam for good you can go back to any question and change your answers if you want to.

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Questions are often split into parts.

In each part you will see various input fields for your answers.

This is the first part and contains one question for you to answer .

It will be clear from the question what you need to enter in each field.

For example, a question could be:

$2+2=\\;$[[0]] (enter a number)

You are expected to enter the answer and then press the Submit part button.

Try it. Enter the correct value, note that a box appears showing your input, press Submit part - a tick appears. Brilliant!!

Now enter an incorrect value. Press Submit part and a cross appears. Note the Show feedback button: clicking on that gives a more detailed feedback - in this case there is not much to say!

This is the sort of feedback you get in practice mode.

Try putting in 2+2 as your answer and see what happens as well.

You will be given an error message; click on OK and continue.

So you must be careful and always check that the answer in the input field is what you expect it to be before you move on.

Pressing the Reveal button at the top of the screen gives you the answers for all parts and usually also gives you a full solution for each part. This is only available in practice mode and certainly not available in assessed mode.

Also note that in practice mode you have available a button at the bottom, Try another question like this one. This is useful for you to try other versions of the question. This question is not randomised, so you will get the same one back again!

Simplify the expression please!

"}, "expectedvariablenames": [], "showpreview": true, "vsetrange": [0, 1], "scripts": {}, "answer": "2*x"}, {"checkingaccuracy": 0.001, "vsetrangepoints": 5, "marks": 1, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "notallowed": {"partialCredit": 0, "showStrings": false, "strings": ["+"], "message": "

Simplify further!

"}, "expectedvariablenames": [], "showpreview": true, "vsetrange": [0, 1], "scripts": {}, "answer": "x-y"}], "type": "gapfill", "prompt": "

This is the second part of this example and it contains 2 questions.

You enter your answers for both and then press Submit part.

Note that your input in mathematical notation is displayed next to your input so you can check it has been interpreted correctly.

$x+x=\\;$[[0]] (Enter a multiple of $x$ )

Enter your answer as 2*x. You could just enter 2x without the *, but we advise you to use * for all multiplications as there are some cases where it is necessary in order to avoid ambiguity.

Simplify the following expression. Once again you see your input rendered in the best possible mathematical notation next to where you type.

This check becomes more important when you input more complicated expressions.

$2x-x+y-2y=\\;$[[1]]

Try getting one right and one wrong and see the sort of feedback you get. (The grey tick indicates that you some, but not all, of the available marks)

Also try inputting x+x for the answer to the first question in this part and see what happens after you submit.

Note the red exclamation marks next to the input field when you enter something the system does not like or you have pressed Submit part without answering the question. Move the cursor over the mark and you will get a message saying what the problem is.

The Submit all parts button at the bottom allows you to answer everything in the question at once without submitting each part separately. In this case, the answers in both parts will be submitted.

", "showCorrectAnswer": true, "scripts": {}}]}, {"metadata": {"notes": "", "description": "

Details on inputting numbers into Numbas.

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No advice available.

", "functions": {}, "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", "Fractions", "input", "introduction", "Numbas", "numbas", "numbers", "tolerance", "whole numbers"], "parts": [{"marks": 0, "gaps": [{"marks": 1, "maxValue": "a*b+c", "correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "minValue": "a*b+c", "showPrecisionHint": false}], "type": "gapfill", "prompt": "

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.

Do not enter your answer as a decimal. Enter as a whole number without the decimal point.

"}, "expectedvariablenames": [], "showpreview": true, "vsetrange": [0, 1], "scripts": {}, "answer": "{a*b+c}"}], "type": "gapfill", "prompt": "

Sometimes I could force you to enter a whole number not in decimal form. But this should be no problem as you will be warned, as below.

Enter the result of this calculation, but enter as a whole number and not as a decimal.

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

Enter the correct answer as a decimal i.e. in the form 2.0 and see what happens:

", "showCorrectAnswer": true, "scripts": {}}, {"marks": 0, "gaps": [{"marks": 1, "maxValue": "{ans1+tol}", "correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "minValue": "{ans1-tol}", "showPrecisionHint": false}], "type": "gapfill", "prompt": "

Decimals

Many calculations will result in numbers which need to be entered in decimal notation.

I will always ask for the decimal to be input to 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.

", "showCorrectAnswer": true, "scripts": {}}, {"marks": 0, "gaps": [{"checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkvariablenames": false, "marks": 1, "type": "jme", "showCorrectAnswer": true, "expectedvariablenames": [], "checkingtype": "absdiff", "notallowed": {"partialCredit": 0, "showStrings": false, "strings": ["+", "."], "message": "

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

"}, "showpreview": true, "vsetrange": [0, 1], "musthave": {"partialCredit": 0, "showStrings": false, "strings": ["/"], "message": "

Input as a fraction.

"}, "scripts": {}, "answersimplification": "all, fractionNumbers", "answer": "{a1+b1}/{a1*b1}"}], "type": "gapfill", "prompt": "

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)

You input the answer as {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.

", "showCorrectAnswer": true, "scripts": {}}, {"showCorrectAnswer": true, "marks": 0, "scripts": {}, "type": "information", "prompt": "

As this question is in practice mode, if you click on the Reveal button at the top of the window all 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.

"}]}, {"metadata": {"notes": "", "description": "

Information on inputting powers

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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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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.

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]]

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

"}, "showpreview": true, "vsetrange": [0, 1], "scripts": {}, "answersimplification": "all", "answer": "x^{f}*y^{f}"}], "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]]

", "showCorrectAnswer": true, "scripts": {}}]}, {"metadata": {"notes": "", "description": "

Inputting algebraic expressions into Numbas.

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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.

", "tags": ["algebraic expressions", "checked2015", "input", "introduction", "notation", "Numbas", "numbas", "polynomials", "symbols"], "parts": [{"marks": 0, "gaps": [{"checkingaccuracy": 0.001, "vsetrangepoints": 5, "marks": 1, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "expectedvariablenames": [], "showpreview": true, "vsetrange": [0, 1], "answersimplification": "all", "scripts": {}, "answer": "{a}*x^{b}+{c}x+{d}"}], "type": "gapfill", "prompt": "

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, "scripts": {}}, {"marks": 0, "gaps": [{"checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkvariablenames": true, "marks": 1, "type": "jme", "showCorrectAnswer": true, "expectedvariablenames": ["x", "y"], "checkingtype": "absdiff", "notallowed": {"partialCredit": 0, "showStrings": false, "strings": ["("], "message": "

Do not include brackets in your answer.

"}, "showpreview": true, "vsetrange": [0, 1], "scripts": {}, "answersimplification": "all", "answer": "x^2+{a+c}x*y+{a*c}y^2"}], "type": "gapfill", "prompt": "

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, "scripts": {}}]}, {"metadata": {"notes": "", "description": "

Inputting ratios of algebraic expressions.

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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}))

", "functions": {}, "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.

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

", "

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

", "

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

", "

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

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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.

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

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

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

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

", "showCorrectAnswer": true, "scripts": {}}]}, {"metadata": {"notes": "", "description": "

Dealing with functions in Numbas.

Correct inputs for these questions are as follows, although there may be other correct ways of inputting these:

a)

sin(cos({a}x)+{b})
cos(sin({a}x + {b}))

b)

abs((x + {c}) / (x + {d}))
ln(abs((x + {a}) / (x + {d})))

c)

{a}t^({-b})*e^({-c}t)*sin({b}t) + (t + {d}t ^ 3)*e ^ ({c}t)
arctan(({c}y ^ 2 + {d}) / ((y + {a})*(y + {b})))

", "functions": {}, "statement": "

FUNCTIONS

The Numbas system recognises all standard functions but you must use brackets for the arguments of the functions, e.g. sin(x) not sinx, ln(a) not lna.
The absolute value function is written abs(a).
$\\arcsin(x)$, $\\arccos(x)$ and $\\arctan(x)$ are all recognized as the standard inverse trig functions, and you input them as they are written.

Here are some examples for you to try:

(If you want help, press Reveal at the top of the screen to see correct inputs in the Advice section.)

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Input:

$\\sin(\\cos(\\var{a}x)+\\var{b})$: [[0]]
$\\cos(\\sin(\\var{b}x)+\\var{a})$: [[1]]

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

Input:

$\\displaystyle \\simplify[all]{Abs((x + {c}) / (x + {d}))}$: [[0]]
$\\displaystyle \\simplify[all]{ln(Abs((x + {a}) / (x + {d})))}$: [[1]]

", "showCorrectAnswer": true, "scripts": {}}, {"marks": 0, "gaps": [{"checkingaccuracy": 0.001, "vsetrangepoints": 5, "marks": 1, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "expectedvariablenames": [], "showpreview": true, "vsetrange": [0, 1], "answersimplification": "all", "scripts": {}, "answer": "{a} * t ^ { -b} * e ^ (( -{c}) * t) * sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)"}, {"checkingaccuracy": 0.001, "vsetrangepoints": 5, "marks": 1, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "expectedvariablenames": [], "showpreview": true, "vsetrange": [0, 1], "answersimplification": "all", "scripts": {}, "answer": "arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))"}], "type": "gapfill", "prompt": "

Input:

$\\simplify[all]{{a} * t ^ { -b} * e ^ (( -{c}) * t) * Sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)}$: [[0]]
$\\displaystyle \\simplify[all]{arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))}$: [[1]]

", "showCorrectAnswer": true, "scripts": {}}]}], "type": "exam", "name": "Getting Started", "feedback": {"showtotalmark": true, "showanswerstate": true, "advicethreshold": 0, "allowrevealanswer": true, "showactualmark": true, "enterreviewmodeimmediately": false, "showexpectedanswerswhen": "never", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "resources": [], "metadata": {"notes": "

AJY changed name of exam from Input to Getting Started 05/09/2013.

", "description": "

6 questions which introduce the user to the Numbas system.

", "licence": "Creative Commons Attribution 4.0 International"}, "percentPass": 0, "allQuestions": true, "pickQuestions": 0, "showQuestionGroupNames": false, "duration": 0, "extensions": [], "question_groups": [{"name": "", "pickQuestions": 0, "questions": [{"name": "How to enter algebraic expressions - Getting Started", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..4)", "name": "b", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "a", "description": ""}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..9)", "name": "d", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s*random(1..9)", "name": "c", "description": ""}, "s": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s", "description": ""}}, "ungrouped_variables": ["a", "s", "b", "c", "d"], "rulesets": {}, "showQuestionGroupNames": false, "functions": {}, "parts": [{"scripts": {}, "gaps": [{"answer": "{a}*x^{b}+{c}x+{d}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "

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.

", "strings": ["("], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "all", "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "

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.

", "tags": ["algebraic expressions", "checked2015", "input", "introduction", "notation", "Numbas", "numbas", "polynomials", "symbols"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "

Inputting algebraic expressions into Numbas.

"}, "advice": ""}, {"name": "How to enter algebraic fractions - Getting Started", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..15#2)", "name": "b", "description": ""}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9 except [round(b*c/a),c])", "name": "d", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..16#2)", "name": "a", "description": ""}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "c", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "d"], "functions": {}, "parts": [{"prompt": "

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.

", "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})).

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

"}, {"name": "How to enter functions - Getting Started", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "d", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..9)", "name": "b", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "a", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "c", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "d"], "functions": {}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

Input:

$\\sin(\\cos(\\var{a}x)+\\var{b})$: [[0]]
$\\cos(\\sin(\\var{b}x)+\\var{a})$: [[1]]

", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "sin(cos({a}x)+{b})", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": true, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": ["x"], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "cos(sin({b}x)+{a})", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

Input:

$\\displaystyle \\simplify[all]{Abs((x + {c}) / (x + {d}))}$: [[0]]
$\\displaystyle \\simplify[all]{ln(Abs((x + {a}) / (x + {d})))}$: [[1]]

", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "abs((x + {c}) / (x + {d}))", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "ln(abs((x + {a}) / (x + {d})))", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

Input:

$\\simplify[all]{{a} * t ^ { -b} * e ^ (( -{c}) * t) * Sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)}$: [[0]]
$\\displaystyle \\simplify[all]{arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))}$: [[1]]

", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "{a} * t ^ { -b} * e ^ (( -{c}) * t) * sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}, {"answer": "arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "showPreview": true, "checkVariableNames": false, "checkingType": "absdiff", "vsetRange": [0, 1], "type": "jme", "failureRate": 1, "scripts": {}, "answerSimplification": "all", "expectedVariableNames": [], "unitTests": [], "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "

FUNCTIONS

The Numbas system recognises all standard functions but you must use brackets for the arguments of the functions, e.g. sin(x) not sinx, ln(a) not lna.
The absolute value function is written abs(a).
$\\arcsin(x)$, $\\arccos(x)$ and $\\arctan(x)$ are all recognized as the standard inverse trig functions, and you input them as they are written.

Here are some examples for you to try:

(If you want help, press Reveal Answers to see correct inputs in the Advice section.)

", "tags": ["arctan", "brackets", "checked2015", "functions", "input", "introduction", "Numbas", "numbas", "standard functions"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Dealing with functions in Numbas.

"}, "advice": "

Correct inputs for these questions are as follows, although there may be other correct ways of inputting these:

a)

sin(cos({a}x)+{b})
cos(sin({a}x + {b}))

b)

abs((x + {c}) / (x + {d}))
ln(abs((x + {a}) / (x + {d})))

c)

{a}t^({-b})*e^({-c}t)*sin({b}t) + (t + {d}t ^ 3)*e ^ ({c}t)
arctan(({c}y ^ 2 + {d}) / ((y + {a})*(y + {b})))

"}, {"name": "How to enter numbers - Getting Started", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.01", "description": "", "name": "tol"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2,3,4,5,6,8,9,10,12)", "description": "", "name": "a1"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "name": "c"}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(7,11,13)", "description": "", "name": "b1"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "name": "a"}, "ans1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(a1/b1,2)", "description": "", "name": "ans1"}}, "ungrouped_variables": ["a", "c", "b", "ans1", "a1", "b1", "tol"], "functions": {}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

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.

", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "a*b+c", "maxValue": "a*b+c", "unitTests": [], "correctAnswerStyle": "plain", "showFeedbackIcon": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

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.

", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "{ans1-tol}", "maxValue": "{ans1+tol}", "unitTests": [], "correctAnswerStyle": "plain", "showFeedbackIcon": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

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}

", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "{a1+b1}/{a1*b1}", "vsetRangePoints": 5, "notallowed": {"message": "

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

", "showStrings": false, "partialCredit": 0, "strings": ["+", "."]}, "checkingType": "absdiff", "vsetRange": [0, 1], "showFeedbackIcon": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "checkingAccuracy": 0.001, "expectedVariableNames": [], "variableReplacements": [], "failureRate": 1, "musthave": {"message": "

Input as a fraction.

", "showStrings": false, "partialCredit": 0, "strings": ["/"]}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showPreview": true, "checkVariableNames": false, "unitTests": [], "scripts": {}, "answerSimplification": "all, fractionNumbers", "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "customMarkingAlgorithm": "", "type": "information", "prompt": "

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.

", "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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Questions are often split into parts. In each part you will see various input fields for your answers.

This is the first part and contains one question for you to answer. It will be clear from the question what you need to enter in each field.

For example, a question could be:

$2+2=\\;$[[0]] (enter a number)

You are expected to enter the answer and then press the Submit part button. Try it. Enter the correct value and press Submit part - a tick appears. Brilliant!!

Now enter an incorrect value. Press Submit part and a cross appears. Note the feedback underneath the button - in this case there is not much to say!

This is the sort of feedback you get in practice mode.

Try putting in 2+2 as your answer and see what happens as well. You will be given an error message; click on OK and continue. So you must be careful and always check that the answer in the input field is what you expect it to be before you move on.

Pressing the Reveal answers button gives you the answers for all parts and usually also gives you a full solution for each part. This is only available in practice mode and certainly not available in a real assessment.

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This is the second part of this example and it contains 2 questions. You enter your answers for both and then press Submit part.

Note that your input in mathematical notation is displayed next to your input so you can check it has been interpreted correctly.

$x+x=\\;$[[0]] (Enter a multiple of $x$ )

Enter your answer as 2*x. You could just enter 2x without the *, but we advise you to use * for all multiplications as there are some cases where it is necessary in order to avoid ambiguity.

Simplify the following expression. Once again you see your input rendered in the best possible mathematical notation next to where you type. This check becomes more important when you input more complicated expressions.

$2x-x+y-2y=\\;$[[1]]

Try getting one right and one wrong and see the sort of feedback you get (the grey tick indicates that you have some, but not all, of the available marks). Also try inputting x+x for the answer to the first question in this part and see what happens after you submit.

The Submit all parts button at the bottom allows you to answer everything in the question at once without submitting each part separately. In this case, the answers in both parts will be submitted.

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Simplify the expression please!

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Simplify further!

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This example explains how you enter your answers and submit them.

This example and the others are in practice mode - you will be given information on whether or not you have the answer correct or not.

If you use Numbas for a real assessment, it does not give you this information.

Go to the next question. You can then come back. Note that until you quit the exam for good you can go back to any question and change your answers if you want to.

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Entering numbers and algebraic symbols in Numbas.

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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 $b$.

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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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