This example explains how you enter your answers and submit them.
\nThis example and the others are in practice mode, not exam mode - you will see whether or not you have the answer correct.
\nIt is very important that you submit all your answers. If you do not your results will not be recorded.
\nThe list of questions in the exam on the left of the window gives information on whether or not you have completed a question.
\nFor each question the marks you have gained by submitting are shown there, so if nothing is shown you have not attempted the question.
\nGo 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.
", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Entering numbers and algebraic symbols in Numbas.
"}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "variables": {}, "variable_groups": [], "advice": "", "parts": [{"sortAnswers": false, "marks": 0, "customName": "", "type": "gapfill", "customMarkingAlgorithm": "", "gaps": [{"marks": 1, "customName": "", "type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "4", "unitTests": [], "useCustomName": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerStyle": "plain", "showFractionHint": true, "minValue": "4", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "correctAnswerFraction": false, "allowFractions": false}], "showCorrectAnswer": true, "unitTests": [], "useCustomName": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "Questions are often split into parts.
\nIn each part you will see various input fields for your answers.
\nThis is the first part and contains one question for you to answer .
\nIt will be clear from the question what you need to enter in each field.
\nFor example, a question could be:
\n$2+2=\\;$[[0]] (enter a number)
\nYou are expected to enter the answer and then press the Submit part button.
\nTry it: enter the correct value; note that a box appears showing your input; press Submit part - a tick appears. Brilliant!
\nNow 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!
\nThis is the sort of feedback you get in practice mode.
\nTry 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.
\nSo 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.
\nPressing the Reveal answers button at the bottom 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 Exam mode.
\nAlso note that in Practice mode you have available a button at the bottom labelled Try another question like this one. This is useful for you to try other versions of the question, if it is randomised. This question is not randomised, so you will get the same one back again!
", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true}, {"sortAnswers": false, "marks": 0, "customName": "", "type": "gapfill", "customMarkingAlgorithm": "", "gaps": [{"vsetRange": [0, 1], "type": "jme", "useCustomName": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "checkVariableNames": false, "checkingAccuracy": 0.001, "failureRate": 1, "showFeedbackIcon": true, "showCorrectAnswer": true, "answer": "2*x", "valuegenerators": [{"value": "", "name": "x"}], "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "scripts": {}, "showPreview": true, "unitTests": [], "customName": "", "extendBaseMarkingAlgorithm": true, "notallowed": {"strings": ["+"], "partialCredit": 0, "message": "Simplify the expression please!
", "showStrings": false}}, {"vsetRange": [0, 1], "type": "jme", "useCustomName": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "checkVariableNames": false, "checkingAccuracy": 0.001, "failureRate": 1, "showFeedbackIcon": true, "showCorrectAnswer": true, "answer": "x-y", "valuegenerators": [{"value": "", "name": "x"}, {"value": "", "name": "y"}], "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "scripts": {}, "showPreview": true, "unitTests": [], "customName": "", "extendBaseMarkingAlgorithm": true, "notallowed": {"strings": ["+"], "partialCredit": 0, "message": "Simplify further!
", "showStrings": false}}], "showCorrectAnswer": true, "unitTests": [], "useCustomName": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "This is the second part of this example and it contains 2 questions.
\nEnter your answers for both and then press Submit part for both.
\nNote that your input in mathematical notation is displayed next to your input so you can check it has been interpreted as you intended.
\n$x+x=\\;$[[0]] (Enter a multiple of $x$ )
\nEnter 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 the meaning of your input would be ambiguous otherwise.
Simplify the following expression. Once again you see your answer in the best possible mathematical notation next to your input.
\nThis check becomes more important when you input more complicated expressions - see later questions.
\n$2x-x+y-2y=\\;$[[1]]
\nTry getting one right and one wrong and see the sort of feedback you get. The greyed-out tick indicates that you were awarded some of the available marks but not all.
\nAlso 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 submitted without answering the question. Move the cursor over the mark and you will get a message saying what the problem is.
\nThe Submit all parts button at the bottom allows you to submit all your answers at once without submitting each part separately. In this case, the answers in both parts will be submitted.
", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true}], "rulesets": {}}, {"name": "Clare's copy of Input 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}], "tags": [], "advice": "No advice available.
", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Details on inputting numbers into Numbas.
"}, "variables": {"ans1": {"group": "Ungrouped variables", "templateType": "anything", "name": "ans1", "description": "", "definition": "precround(a1/b1,2)"}, "a1": {"group": "Ungrouped variables", "templateType": "anything", "name": "a1", "description": "", "definition": "random(2,3,4,5,6,8,9,10,12)"}, "tol": {"group": "Ungrouped variables", "templateType": "anything", "name": "tol", "description": "", "definition": "0.01"}, "b1": {"group": "Ungrouped variables", "templateType": "anything", "name": "b1", "description": "", "definition": "random(7,11,13)"}, "c": {"group": "Ungrouped variables", "templateType": "anything", "name": "c", "description": "", "definition": "random(2..9)"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": "", "definition": "random(1..9)"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": "", "definition": "random(3..9)"}}, "parts": [{"customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "customName": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "gaps": [{"minValue": "a*b+c", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "useCustomName": false, "maxValue": "a*b+c", "customName": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacements": [], "allowFractions": false, "type": "numberentry", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "sortAnswers": false, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "prompt": "This is an example of a randomised question - the next time you use this example you will be asked to do a different calculation.
\nFind the result of this calculation:
\n$\\var{c}+\\var{a}\\times\\var{b}=\\;$[[0]]
\nYou must input a whole number; for example, if the answer were $2$ then you could input 2 or 2.0 - try both forms.
Many calculations will result in numbers which must be entered in decimal notation correct to a certain number of decimal places.
\nSometimes 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.
\nHere is an example with built in tolerance:
\nExpress $\\displaystyle \\frac{\\var{a1}}{\\var{b1}}$ as a decimal correct to 3 decimal places here: [[0]]
\nTry putting in the correct value and submitting.
\nThen vary the last decimal place by 1 either way and submit again, and then then last place by 2 either way and submit again.
\nTry putting in the original fraction as the answer(i.e. $\\var{a1}/\\var{b1}$ ) and see what happens.
\n\nMost of the time you will be required to be precise and round off correctly.
\nHere is the last example without built in tolerance:
\nExpress $\\displaystyle \\frac{\\var{a1}}{\\var{b1}}$ as a decimal correct to 3 decimal places here: [[1]]
\nThis time it will accept the correct value only!
"}, {"customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "customName": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "gaps": [{"customMarkingAlgorithm": "", "showFeedbackIcon": true, "showPreview": true, "variableReplacementStrategy": "originalfirst", "notallowed": {"showStrings": false, "strings": ["+", "."], "partialCredit": 0, "message": "Simplify into a single fraction. Do not enter as a decimal.
"}, "unitTests": [], "musthave": {"showStrings": false, "strings": ["/"], "partialCredit": 0, "message": "Input as a fraction.
"}, "variableReplacements": [], "checkingAccuracy": 0.001, "valuegenerators": [], "answer": "{a1+b1}/{a1*b1}", "marks": 1, "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "customName": "", "type": "jme", "answerSimplification": "all, fractionNumbers", "checkingType": "absdiff", "checkVariableNames": false, "failureRate": 1, "vsetRange": [0, 1], "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "sortAnswers": false, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "prompt": "Some questions may ask you to input fractions and not decimals.
\nFind the following sum as a fraction:
\n$\\displaystyle \\frac{1}{\\var{a1}}+\\frac{1}{\\var{b1}}=\\;$[[0]]
\n(input as a fraction and not a decimal)
\nYou input the answer as {a1+b1}/{a1*b1}.
Try inputting the decimal version of this to as many places as you like, and see what happens.
"}, {"customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "customName": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "variableReplacements": [], "type": "information", "extendBaseMarkingAlgorithm": true, "prompt": "As this question is in practice mode, if you click on the Reveal answers button at the bottom of the screen 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.
\nFinally 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.
"}], "preamble": {"js": "", "css": ""}, "functions": {}, "variable_groups": [], "ungrouped_variables": ["c", "a1", "b", "b1", "tol", "a", "ans1"], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "statement": "In this example we show how to enter numbers, either as whole numbers (integers), decimals (rounded to a number of decimal places), or fractions.
"}, {"name": "Input 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "tags": ["Numbas", "brackets", "input", "introduction", "numbas", "powers"], "advice": "", "rulesets": {}, "parts": [{"prompt": "Write $e^{\\simplify{{a}x}}$. [[0]]
\nYour input is shown in mathematical notation in a box next to your input so that you can check that you have entered it correctly.
\nClick on Submit part to check your answer.
\nClick on the input field and remove the brackets, then re-submit and see what happens.
\n\n
", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 1e-05, "vsetrange": [0.0, 0.1], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "e^({a}*x)", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "
Input $x^{\\var{c}}x^{\\var{d}}$ as a single power of $x$.
\nFor example, you would input $x^{-6}x^{-5}$ as x^(-11).
$x^{\\var{c}}x^{\\var{d}}=\\;$[[0]]
", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "x^({c+d})", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "Input $(xy)^{\\var{f}}$ in the form $x^ay^b$ for suitable values of $a$ and $b$.
\n$(xy)^{\\var{f}}=\\;$[[0]]
", "gaps": [{"notallowed": {"message": "Input in the form $x^ay^b$ for suitable values of $a$ and $b$.
", "showstrings": false, "strings": ["xy", "x*y"], "partialcredit": 0.0}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "x^{f}*y^{f}", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}], "statement": "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.
\n$a^b$ is input as a^b.
But you have to be careful with inputting such expressions as
\n\\[e^{2x},\\;x^{-2},\\;(xy)^2\\]
\nIn these cases the exponent must be enclosed in brackets.
\n| Power | Correct Input | Incorrect Input | Why it's wrong |
|---|---|---|---|
| $e^{2x}$ | \ne^(2*x) | \n e^2*x | \n The system thinks this is $(e^2) \\cdot x$ | \n
| $x^{-2}$ | \nx^(-2) | \n x^-2 | \n This produces an error | \n
| $(xy)^2$ | \n(x*y)^2 | \n x*y^2 | \n The system thinks this is $x \\cdot (y^2)$ | \n
So make sure that you use brackets to properly define your powers. This is a major source of input inaccuracies.
\nTo test your input of powers, try the following examples.
", "variable_groups": [], "progress": "in-progress", "type": "question", "variables": {"a": {"definition": "random(6..12)*s", "name": "a"}, "s": {"definition": "random(1,-1)", "name": "s"}, "f": {"definition": "random(-5,-4,-3,-2,-1)", "name": "f"}, "c": {"definition": "random(-12..-6)", "name": "c"}, "d": {"definition": "random(-12..-6)", "name": "d"}}, "metadata": {"notes": "", "description": "Information on inputting powers
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Input 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "tags": ["Numbas", "algebraic expressions", "input", "introduction", "notation", "numbas", "polynomials", "symbols"], "advice": "", "rulesets": {}, "parts": [{"prompt": "Inputting polynomials such as $3x^2+5x-2$ is easy: just input 3*x^2+5*x-2.
Input this polynomial: $\\simplify[all]{{a}*x^{b}+{c}*x+{d}}=\\;$[[0]]
", "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "{a}*x^{b}+{c}x+{d}", "checkvariablenames": false, "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "Now consider this problem.
\nExpand the brackets and input the resulting expression:
\n$\\simplify[all]{(x+{a}y)(x+{c}y)}=\\;$[[0]]
\n(Do not include brackets in your answer.)
\nTwo adjacent letters are treated as a single variable: xy is not interpreted as the product of $x$ and $y$, $x \\times y$. You must use the multiplication symbol to separate the two variables, i.e. enter x*y. If you don't do this you will often be given a warning that your answer might not have been interpreted as you intended.
Do not include brackets in your answer.
", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "expectedvariablenames": ["x", "y"], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "x^2+{a+c}x*y+{a*c}y^2", "checkvariablenames": true, "type": "jme"}], "type": "gapfill", "marks": 0.0}], "statement": "In this example, we look at how you input algebraic expressions - those involving symbols.
\nThe box next to your input shows your answer in mathematical notation and is very important as you can use it to check your answer has been interpreted as you intended.
", "variable_groups": [], "progress": "in-progress", "type": "question", "variables": {"a": {"definition": "random(2..9)", "name": "a"}, "s": {"definition": "random(1,-1)", "name": "s"}, "b": {"definition": "random(2..4)", "name": "b"}, "c": {"definition": "s*random(1..9)", "name": "c"}, "d": {"definition": "random(1..9)", "name": "d"}}, "metadata": {"notes": "", "description": "Inputting algebraic expressions into Numbas.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Clare's copy of Input 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}], "statement": "This question concerns ratios of algebraic expressions.
\nBy this we mean expressions of the form $\\displaystyle \\frac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are algebraic expressions.
\nIf you want to input such an expression into the system you HAVE TO BE CAREFUL AND USE BRACKETS or mistakes will occur.
\nOnce again, the preview answer box displaying your input in mathematical notation beside the input boxes in parts a, b and c is very useful as it shows what the system thinks you have entered.
", "ungrouped_variables": ["c", "a", "d", "b"], "preamble": {"js": "", "css": ""}, "variables": {"c": {"description": "", "name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}, "d": {"description": "", "name": "d", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9 except [round(b*c/a),c])"}, "b": {"description": "", "name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..15#2)"}, "a": {"description": "", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..16#2)"}}, "variable_groups": [], "metadata": {"description": "Instructions on inputting ratios of algebraic expressions.
", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!collectNumbers"]}, "parts": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "Suppose we wanted to input the expression $\\displaystyle \\frac{\\var{a}+\\var{b}x}{\\var{c}+\\var{d}y}$ into the system.
\nWhich of the following input expressions are incorrect?
\n[[0]]
\nChoose the incorrect input(s).
\nAfter you have clicked Submit part, click on Show Feedback and you will be given more detail on your choices.
", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "m_n_2", "showFeedbackIcon": true, "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
({a}+{b}x)/({c}+{d}y){a}+{b}x/({c}+{d}y){a}+{b}x/{c}+{d}y({a}+{b}x)/{c}+{d}yInput the expression $\\displaystyle \\frac{\\var{b}+\\var{a}y}{\\var{d}+\\var{c}z}$. [[0]]
", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "jme", "checkingAccuracy": 0.001, "showFeedbackIcon": true, "checkingType": "absdiff", "failureRate": 1, "unitTests": [], "scripts": {}, "checkVariableNames": false, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "1", "showCorrectAnswer": true, "answerSimplification": "std", "valuegenerators": [{"name": "y", "value": ""}, {"name": "z", "value": ""}], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "answer": "({b}+{a}y)/({d}+{c}z)", "extendBaseMarkingAlgorithm": true, "customName": "", "useCustomName": false, "vsetRange": [0, 1], "showPreview": true}], "sortAnswers": false, "marks": 0}, {"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "Input the expression $\\displaystyle \\frac {\\var{d} z + \\var{b}} {(x + \\var{a}) (y + \\var{c})}$. [[0]]
", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "jme", "checkingAccuracy": 0.001, "showFeedbackIcon": true, "checkingType": "absdiff", "failureRate": 1, "unitTests": [], "scripts": {}, "checkVariableNames": false, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "1.5", "showCorrectAnswer": true, "answerSimplification": "std", "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}, {"name": "z", "value": ""}], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "answer": "({d} * z + {b}) / ((x + {a}) * (y + {c}))", "extendBaseMarkingAlgorithm": true, "customName": "", "useCustomName": false, "vsetRange": [0, 1], "showPreview": true}], "sortAnswers": false, "marks": 0}, {"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "Input the expression $\\displaystyle \\simplify[std]{({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 * b}) * (y -{3* d}))}$. [[0]]
", "scripts": {}, "customName": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "useCustomName": false, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"type": "jme", "checkingAccuracy": 0.0001, "showFeedbackIcon": true, "checkingType": "absdiff", "failureRate": 1, "unitTests": [], "scripts": {}, "checkVariableNames": false, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "2.5", "showCorrectAnswer": true, "answerSimplification": "std", "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "answer": "({a} -(({b} * x + {c}) * e ^ (( -{2}) * x))) / ((x + {2 b}) * (y -{3* d}))", "extendBaseMarkingAlgorithm": true, "customName": "", "useCustomName": false, "vsetRange": [0, 1], "showPreview": true}], "sortAnswers": false, "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "functions": {}, "advice": "The correct input is ({a}+{b}x)/({c}+{d}y) - the rest are incorrect and you should have chosen those.
A correct input is ({b} + {a}y) / ({c} + {d}z). Also correct is ({a}y+{b}) / ({c} + {d}z) etc.
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 $\\displaystyle \\left(\\simplify[std]{({d} * z + {b}) / (x + {a})}\\right) (y + \\var{c})$
A correct input is ({a} -({b}x + {c})*e ^ ( -{2}x)) / ((x + {2*b})*(y -{3*d})).
The Numbas system recognises all standard functions but you must use brackets for the arguments of the functions and you must not use capital letters in the function name,
\ne.g. sin(x) is the correct way to input $\\sin x$ , ln(x) is the correct way to enter $\\ln x$, sqrt(x) is the correct way to enter $\\sqrt x$ etc.
Each of the following is an example of incorrect input: sinx, Sinx, Sin(x), lnx, Ln(x), sqrt 2
Try inputting each of the following:
", "ungrouped_variables": ["a", "c", "b", "d"], "preamble": {"js": "", "css": ""}, "variables": {"c": {"description": "", "name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}, "d": {"description": "", "name": "d", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}, "b": {"description": "", "name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..9)"}, "a": {"description": "", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}}, "variable_groups": [], "metadata": {"description": "", "licence": "All rights reserved"}, "rulesets": {}, "parts": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "Input:
\nInput:
\nInput:
\nHere is the correct inputs for first part of c) :
\n{a}t^({-b})*e^({-c}t)*sin({b}t) + (t + {d}t ^ 3)*e ^ ({c}t)
5 questions which introduce the student to the Numbas system.
\nrebelmaths
"}, "timing": {"timedwarning": {"message": "", "action": "none"}, "allowPause": true, "timeout": {"message": "", "action": "none"}}, "showQuestionGroupNames": false, "navigation": {"browse": true, "startpassword": "", "showresultspage": "oncompletion", "onleave": {"message": "", "action": "none"}, "allowregen": true, "preventleave": true, "showfrontpage": true, "reverse": true}, "duration": 0, "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}], "extensions": [], "custom_part_types": [], "resources": []}