// Numbas version: finer_feedback_settings {"name": "INU0111 Maths S1 Exam 2023-4", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 5400, "percentPass": "50", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": false, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "ARR short EXAM", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

£{c} is invested into a project. For the next {y} years, the project receives £{a} pa (per anum = each year). What is the ARR (Accounting Rate of Return)?

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A woman invests £{prin}, at a rate of {rate}% per anum for {years} years. Calculate the compound interest.

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You have calculated the total amount. You should give the interest only

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Here is some information about two projects over 5 years. Calculate the ARR and decide which one is the best investment.

\n

Project A: The capital investment is £{ca}. In the first two years, the income is £{a1}, in the third year it is £{a3} and in the final two years it is £{a4}

\n

Project B: The capital investment is £{cb}. In the first year, there is no income, in years 2,3 and 4 the income is £{b2} and in the final year the income is £{b5}

\n

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What is the average income for Project A?

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What is the average income for Project B?

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What is the ARR for Project A?

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What is the ARR for Project B?

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Differentiate the following 

\n

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\\[ \\simplify{{a}x^3+{b}x^2+{c}x+{d}} \\]

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\\[ \\simplify{{f}x^3+{g}x^2+{h}x+{j}} \\]

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A rectangle of length x cm, where  x varies, has a constant area of {A}cm2.

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Write the width of the rectangle,y, in terms of x.

\n

width = [[0]]

\n

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Express the perimeter of the rectangle in terms of x

\n

Perimeter = [[0]]

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f'(x) = [[0]]= 0

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Solve the equation to find the value of x that gives the turning point for the perimeter

\n

x = [[0]]

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Find the second derivative so that you can decide on the nature of the turning point

\n

f''(x) = [[0]]

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Is this a maximum or a minimum?

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Discount the sum of £{p} that is to be received in {y} years time at a discount rate of {r}%

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A line passes through the points ({a},{b}) and ({c},{d})

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What is the gradient of the line?

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What is the y intercept?

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What is the equation of the line?

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Factorise three quadratic equations of the form $x^2+bx+c$.

\n

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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Factorise the following quadratic equations

\n

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$\\simplify{x^2+{v1+v2}x+{v1*v2}}$

\n

[[0]] 

\n

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {"mark": {"script": "question.is_factorised(this);", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(x+{v1})(x+{v2})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$\\simplify{x^2+{v3+v4}x+{v3*v4}}$

\n

[[0]] 

\n

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$\\simplify{x^2+{v5+v6}x+{v5*v6}}$

\n

[[0]] 

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Find the gradient and y intercept of the following equations

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$\\simplify[!collectNumbers]{y={a}x+{b}}$

\n

Gradient = [[0]]

\n

y intercept = [[1]]

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$\\simplify[!collectNumbers]{y={c}+{d}x}$

\n

Gradient = [[0]]

\n

y intercept = [[1]]

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Peter's Portals manufactures doors and windows for building firms. It takes 0.5 hours to make a door and 1.5 hours to make a window. The profit on a door is £30 and on a window is £50. The company can spend only 42 hours per week manufacturing doors and windows and must make at least 30 doors and at least 12 windows each week. How many doors and windows should the company make to maximize profit? What is the profit?

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Let the number of doors be x and the number of windows be y

\n

Write an inequality for the number of doors

\n

$x \\geq$ [[0]]

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Let the number of doors be x and the number of windows be y

\n

Write an inequality for the number of windows

\n

$y \\geq$ [[0]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "12", "maxValue": "12", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The company can only allow for 42 hours per week making doors and windows. Write an inequality involving x and y

", "answer": "0.5x+1.5y<=42", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The graph of these inequalities looks like this.

\n

\n

Calculate the profit in £ at (30,18)  

", "minValue": "1800", "maxValue": "1800", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the profit in £ at (48,12)

", "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "290", "maxValue": "290", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "1440", "maxValue": "1440", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "2040", "maxValue": "2040", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Which option will give the best profit?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["30 doors and 18 windows", "48 doors 12 windows", "We can not be sure"], "matrix": ["0", "2", "0"], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "NPV with table for answers EXAM", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

The table shows information on initial investment and income per year for two projects. The discounting rate is 8%.

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

Year

\n
\n

Project A (£)

\n
\n

Project B (£)

\n
\n

0

\n
\n

-{ca}

\n
\n

-{cb}

\n
\n

1

\n
\n

{a1}

\n
\n

{b1}

\n
\n

2

\n
\n

{a2}

\n
\n

{b2}

\n
\n

3

\n
\n

{a3}

\n
\n

{b3}

\n
\n

4

\n
\n

{a4}

\n
\n

{b4}

\n
\n

5

\n
\n

{a5}

\n
\n

{b5}

\n
", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ca": {"name": "ca", "group": "Ungrouped variables", "definition": "random(25000..32000)", "description": "", "templateType": "anything", "can_override": false}, "cb": {"name": "cb", "group": "Ungrouped variables", "definition": "random(26000..35000)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(11000..14000)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(10000..12000)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(10000..12000)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "random(10000..12000)", "description": "", "templateType": "anything", "can_override": false}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "random(11000..15000)", "description": "", "templateType": "anything", "can_override": false}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "random(11000..15000)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(11000..14000)", "description": "", "templateType": "anything", "can_override": false}, "b3": {"name": "b3", "group": "Ungrouped variables", "definition": "random(11000..14000)", "description": "", "templateType": "anything", "can_override": false}, "b4": {"name": "b4", "group": "Ungrouped variables", "definition": "random(12000..14000)", "description": "", "templateType": "anything", "can_override": false}, "b5": {"name": "b5", "group": "Ungrouped variables", "definition": "random(11000..15000)", "description": "", "templateType": "anything", "can_override": false}, "pva1": {"name": "pva1", "group": "Ungrouped variables", "definition": "a1/(1.08)^1", "description": "", "templateType": "anything", "can_override": false}, "pva2": {"name": "pva2", "group": "Ungrouped variables", "definition": "a2/1.08^2", "description": "", "templateType": "anything", "can_override": false}, "pva3": {"name": "pva3", "group": "Ungrouped variables", "definition": "a3/1.08^3", "description": "", "templateType": "anything", "can_override": false}, "pva4": {"name": "pva4", "group": "Ungrouped variables", "definition": "a4/1.08^4", "description": "", "templateType": "anything", "can_override": false}, "pva5": {"name": "pva5", "group": "Ungrouped variables", "definition": "a5/1.08^5", "description": "", "templateType": "anything", "can_override": false}, "npva": {"name": "npva", "group": "Ungrouped variables", "definition": "pva1+pva2+pva3+pva4+pva5-ca", "description": "", "templateType": "anything", "can_override": false}, "pvb1": {"name": "pvb1", "group": "Ungrouped variables", "definition": "b1/1.08^1", "description": "", "templateType": "anything", "can_override": false}, "pvb2": {"name": "pvb2", "group": "Ungrouped variables", "definition": "b2/1.08^2", "description": "", "templateType": "anything", "can_override": false}, "pvb3": {"name": "pvb3", "group": "Ungrouped variables", "definition": "b3/1.08^3", "description": "", "templateType": "anything", "can_override": false}, "pvb4": {"name": "pvb4", "group": "Ungrouped variables", "definition": "b4/1.08^4", "description": "", "templateType": "anything", "can_override": false}, "pvb5": {"name": "pvb5", "group": "Ungrouped variables", "definition": "b5/1.08^5", "description": "", "templateType": "anything", "can_override": false}, "npvb": {"name": "npvb", "group": "Ungrouped variables", "definition": "pvb1+pvb2+pvb3+pvb4+pvb5-cb", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ca", "cb", "b1", "a1", "a2", "a3", "a4", "a5", "b2", "b3", "b4", "b5", "pva1", "pva2", "pva3", "pva4", "pva5", "npva", "pvb1", "pvb2", "pvb3", "pvb4", "pvb5", "npvb"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the present value for Project A in year 1

", "minValue": "pva1", "maxValue": "pva1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the present value for Project A in year 2

", "minValue": "pva2", "maxValue": "pva2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Now complete the table for present value (PV) for each year, and for net present value (NPV) for both projects giving all of your answers to 2 decimal places.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
YearProject APVProject BPV
0-{ca}-{cb}
1{a1}[[0]]{b1}[[5]]
2{a2}[[1]]{b2}[[6]]
3{a3}[[2]]{b3}[[7]]
4{a4}[[3]]{b4}[[8]]
5{a5}[[4]]{b5}[[9]]
NPV[[10]][[11]]
\n

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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "pva2", "maxValue": "pva2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "pva2", "maxValue": "pva2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pva3", "maxValue": "pva3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pva4", "maxValue": "pva4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer 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"correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pvb1", "maxValue": "pvb1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pvb2", "maxValue": "pvb2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pvb3", "maxValue": "pvb3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pvb4", "maxValue": "pvb4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pvb5", "maxValue": "pvb5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "npva", "maxValue": "npva", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "npva", "maxValue": "npva", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, 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"contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

In a sale, everything was reduced by {percent}%. If the original price of a pair of boots was £{price}, then what was the sale price in pounds?

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A second-hand sewing machine was sold on eBay for £{SP}. This represented a loss of {percentloss}% from what was paid originally by the seller. Find the original price  in pounds paid by the seller.

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A supermarket sells two sizes of bottles of vinegar. The volumes are {largevol}ml and {smallvol}ml. 

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What is the volume scale factor?

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The small bottle has a height of {smallht}cm . What is the height of the large bottle?

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The bottles all have a rectangular label. The area of the label on the large bottle is {largearea}sqaure cm. What is the area of the label on the small bottle.

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Simple exercise in collecting terms in different powers of \\(x\\)

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Simplify the following expressions by combining \"like\" terms.

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The idea is to collect together and combine any terms that are the same kind of term so:

\n

$\\var{b}$ and $\\var{f}$ are ordinary numbers. We can combine them to get $\\var{b+f}$

\n

We can combine $\\var{a}x$ and $\\var{d}x$ to get $\\var{a+d}x$.

\n

There are also $\\var{c}$ times $x^2$. So our answer is:

\n

$\\simplify{{c}x^2+{a+d}x+{b+f}}$

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$\\simplify[!collectNumbers]{{a}x+{b}+{c}x^2+{d}x+{f}}$

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$\\simplify[!collectNumbers]{{f}x+{b}+{c}x^2+{d}x+{a}}$

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$\\simplify[!collectNumbers]{{f}x+{b}+{c}x^3+{d}x^3+{a}}$

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Rearrange the following equation

\n

\\[{cy -b = ax}\\] 

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We need to rearrange the equation to express it in y.

\n

\\[ cy= ax + b\\]

\n

\\[ y= (ax+b)/c \\]

\n

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y=[[0]]

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