// Numbas version: exam_results_page_options {"name": "HELM Book 1.1.5 exercises", "metadata": {"description": "

HELM Book 1.1.5 exercises

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The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{app}

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Move the point to $\\var{value}$. Move the point to close to the correct location, then use the Zoom In button to very accurately place the point. Click the \"Submit answer\" button when you have finished.

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Identify point on number line (fraction version)", "extensions": ["geogebra"], "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": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{app}

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet(\n \"snzz5xmd\"\n,\n [\n \n ],\n [\n [\"C\", \"p0\"]\n ]\n)", "description": "", "templateType": "anything", "can_override": false}, "target_position": {"name": "target_position", "group": "Ungrouped variables", "definition": "vector(value,0)", "description": "", "templateType": "anything", "can_override": false}, "value": {"name": "value", "group": "Ungrouped variables", "definition": "numerator/denominator", "description": "", "templateType": "anything", "can_override": false}, "numerator": {"name": "numerator", "group": "Ungrouped variables", "definition": "random(-10..10 except [0, denominator])", "description": "", "templateType": "anything", "can_override": false}, "denominator": {"name": "denominator", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["app", "target_position", "value", "numerator", "denominator"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "pos:\n value(app,\"C\")\n\nmark:\nfeedback(\"The point is at \\\$\\\\var{latex(string(rational(precround(x(app,'C'),3))))}\\\$.\");\n if(withintolerance(target_position[0],pos[0],0.005),\n correct(\"Your answer is correct to within a tolerance of \\\$\\\\frac{1}{200}\\\$.\" ),\n incorrect(\"Your answer is at least \\\$\\\\frac{1}{200}\\\$ away from the correct position.\"))\n\ninterpreted_answer:\n pos", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Move the point to $\\frac{\\var{numerator}}{\\var{denominator}}$. Move the point to close to the correct location, then use the Zoom In button to very accurately place the point. Click the \"Submit answer\" button when you have finished.

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Identify point on number line (irrational version)", "extensions": ["geogebra"], "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": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{app}

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet(\n \"snzz5xmd\"\n,\n [\n \n ],\n [\n [\"C\", \"p0\"]\n ]\n)", "description": "", "templateType": "anything", "can_override": false}, "target_position": {"name": "target_position", "group": "Ungrouped variables", "definition": "vector(value,0)", "description": "", "templateType": "anything", "can_override": false}, "value": {"name": "value", "group": "Ungrouped variables", "definition": "[-pi,-sqrt(3),-sqrt(2),sqrt(2),sqrt(3),pi][idx]", "description": "", "templateType": "anything", "can_override": false}, "dispvalue": {"name": "dispvalue", "group": "Ungrouped variables", "definition": "[latex(\"-\\\\pi\"),latex(\"-\\\\sqrt{(3)}\"),latex(\"-\\\\sqrt{(2)}\"),latex(\"\\\\sqrt{(2)}\"),latex(\"\\\\sqrt{(3)}\"),latex(\"\\\\pi\")][idx]", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["app", "target_position", "value", "dispvalue", "idx"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "pos:\n value(app,\"C\")\n\nmark:\nfeedback(\"The point is at {precround(pos[0],3)}.\");\n if(withintolerance(target_position[0],pos[0],0.005),\n correct(\"Your answer is correct to within a tolerance of 0.005. \"),\n incorrect(\"Your answer is at least 0.005 away from the correct position.\"))\n\ninterpreted_answer:\n pos", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Move the point to $\\var{dispvalue}$. Move the point to close to the correct location, then use the Zoom In button to very accurately place the point. Click the \"Submit answer\" button when you have finished.

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Signed multiplication and division", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "signed multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "

Multiply two numbers, at least one of which is negative.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Calculate the following:

", "advice": "

Since one value is negative, the answer will be negative. $\\var{v1}\\times\\var{v2}=\\var{v1*v2}$

Since both values are negative, the answer will be positive. $\\var{v1}\\times\\var{v2}=\\var{v1*v2}$

$\\var{v1}\\times\\var{v2} = $ [[0]]

Divide two numbers, at least one of which is negative. The answer is always an integer.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Calculate the following:

", "advice": "

Since one value is negative, the answer will be negative. $\\dfrac{\\var{v1}}{\\var{v2}}=\\var{v1/v2}$

Since both values are negative, the answer will be positive. $\\dfrac{\\var{v1}}{\\var{v2}}=\\var{v1/v2}$

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$\\dfrac{\\var{v1}}{\\var{v2}} = $ [[0]]

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Evaluate:

", "advice": "

Use BODMAS to compute brackets first, then $\\times$ and $\\div$, then $+$ and $-$. Remember that subtracting a negative number is the same as adding a positive number.

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$\\var{dexpr}$= [[0]]

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Evaluate:

", "advice": "

Use BODMAS to compute brackets first, then $\\times$ and $\\div$, then $+$ and $-$. Remember that subtracting a negative number is the same as adding a positive number.

$\\var{dexpr}$= [[0]]

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Evaluate:

", "advice": "

Use BODMAS to compute brackets first, then $\\times$ and $\\div$, then $+$ and $-$. Remember that subtracting a negative number is the same as adding a positive number.

$\\var{dexpr}$= [[0]]

Compute the modulus of either (a) a signed decimal, or (b) a sum or difference of two decimals.

Used in HELM Book 1.1.5 Exercises

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Compute the following:

", "advice": "

{advice}

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(a) $\\var{dexpr}$ = [[0]]

Compute the modulus of either (a) a signed decimal, or (b) a sum or difference of two decimals.

Used in HELM Book 1.1.5 Exercises

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Compute the following:

", "advice": "

{advice}

(a) $\\var{dexpr}$ = [[0]]

Find reciprocals of (a) a proper fraction, (b) an improper fraction, (c) an integer

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Compute the reciprocals of the following numbers: (To enter $\\dfrac{5}{7}$, type 5/7)

", "advice": "

Find the reciprocal by inverting the number.

If a number is a whole number, first write it as a fraction with a denominator of 1.

If a number is negative, its reciprocal is also negative.

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(a) Reciprocal of $\\dfrac{\\var{n1}}{\\var{d1}}$ is [[0]]

(b) Reciprocal of $\\dfrac{\\var{n2}}{\\var{d2}} $ is [[1]]

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Calculate a factorial, or the difference of two factorials, or a fraction of two factorials.

Used in HELM Book 5.1.1 Exercises

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

You can use your calculator for this task

", "advice": "

$\\var{qus} = \\var{ans}$

$\\var{qus} = \\var{fact(n1)} - \\var{fact(n2)} = \\var{ans}$

Divide the numerator and denominator by $\\var{n2}!$ to get $\\var{qus} = \\var{n1}$

Divide the numerator and denominator by $\\var{n2}!$ to get $\\var{qus} = \\var{n1}\\times \\var{n1-1} = \\var{ans}$

Divide the numerator and denominator by $\\var{n2}!$ to get $\\var{qus} = \\var{n1}\\times \\var{n1-1} \\times \\var{n1-2} = \\var{ans}$

Divide the numerator and denominator by $\\var{n2}!$ to get $\\var{qus} = \\var{n1} \\times \\var{n1-1} \\times \\dots \\times \\var{n2+1} = \\var{ans}$

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Compute $\\var{latex(qus)}$

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The answer is either 'True' or 'False'

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Identify the truth value of an inequality (T/F) between two numbers

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What is the truth value of

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The answer is either 'True' or 'False'

Identify the truth value of an inequality (T/F) between two numbers

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What is the truth value of

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The answer is either 'True' or 'False'

Identify the truth value of an inequality (T/F) between two numbers

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What is the truth value of

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The answer is either 'True' or 'False'

Identify the truth value of an inequality (T/F) between two numbers

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What is the truth value of

\$\\var{disp_values[0]}\\var{disp_op}\\var{disp_values[1]}\$

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Work through these practice questions. You can try each question as many times as you like. The numbers will change each time. Some of the questions are randomly chosen, so if you re-open this set of exercises you may see some different questions.

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The answer is either 'True' or 'False'