// Numbas version: finer_feedback_settings {"name": "39. Substitution", "metadata": {"description": "

Selection of questions on substituting values into simple expressions

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], []], "questions": [{"name": "39.a Substitution into addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Substituting a value of $x$ into $x+a$.

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

If $\\var{Letter}=\\var{Var1Sub}$, find the value of

\\[\\simplify[basic]{{Letter}+{Num1}}.\\]

", "advice": "

To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Letter}=\\var{Var1Sub}$ we get

\\[\\simplify[basic]{{Letter}+{Num1}}=\\simplify[basic]{{Var1Sub}+{Num1}}=\\var{Var1Sub+Num1}.\\]

Use this link to find resources to help you revise substitution into a formula

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Var1Sub": {"name": "Var1Sub", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Letter", "Var1Sub", "Num1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Var1Sub+Num1}", "maxValue": "{Var1Sub+Num1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "39.b Substitution into multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Substituting a value of $x$ into $ax$

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

If $\\var{Letter}=\\var{Var1Sub}$, find the value of

\\[\\simplify[!basic]{{Num1}{Letter}}.\\]

", "advice": "

To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Letter}=\\var{Var1Sub}$ we get

\\[\\simplify[!basic]{{Num1}{Letter}}=\\simplify[!basic]{{Num1}{Var1Sub}}=\\var{Var1Sub*Num1}.\\]

Use this link to find resources to help you revise substitution into a formula

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Var1Sub": {"name": "Var1Sub", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Letter", "Var1Sub", "Num1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Var1Sub*Num1}", "maxValue": "{Var1Sub*Num1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "39.c Substitution into division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Substituting a value of $x$ into $x/a$.

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

If $\\var{Letter}=\\var{Var1Sub}$, find the value of

\\[\\simplify[!basic]{{Letter}/{Num1}}.\\]

", "advice": "

To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Letter}=\\var{Var1Sub}$ we get

\\[\\simplify[!basic]{{Letter}/{Num1}}=\\simplify[!basic]{{Var1Sub}/{Num1}}=\\var{Var1Sub/Num1}.\\]

Use this link to find resources to help you revise substitution into a formula

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Var1Sub": {"name": "Var1Sub", "group": "Ungrouped variables", "definition": "random(-6..6)*Num1", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Letter", "Var1Sub", "Num1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Var1Sub/Num1}", "maxValue": "{Var1Sub/Num1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "39.d Substitution into a power", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Substituting a value of $x$ into $x^2$ or $x^3$.

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

If $\\var{Letter}=\\var{Var1Sub}$, find the value of

\\[\\simplify[!basic]{{Letter}^{Num1}}.\\]

", "advice": "

To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Letter}=\\var{Var1Sub}$ we get

\\[\\simplify[!basic]{{Letter}^{Num1}}=\\simplify[!basic]{{Var1Sub}^{Num1}}=\\var{{Var1Sub}^{Num1}}.\\]

Use this link to find resources to help you revise substitution into a formula

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Var1Sub": {"name": "Var1Sub", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(2,3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Letter", "Var1Sub", "Num1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Var1Sub^Num1}", "maxValue": "{Var1Sub^Num1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "39.e Substitution into multiplication and addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Substituting a value of $x$ into $ax+b$

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

If $\\var{Letter}=\\var{Var1Sub}$, find the value of

\\[\\simplify[basic]{{Num1}{Letter}+{Num2}}.\\]

", "advice": "

To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Letter}=\\var{Var1Sub}$ we get

\\[\\simplify[basic]{{Num1}{Letter}+{Num2}}=\\simplify[basic]{{Num1}{Var1Sub}+{Num2}}=\\var{Var1Sub*Num1+Num2}.\\]

Use this link to find resources to help you revise substitution into a formula

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Var1Sub": {"name": "Var1Sub", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Letter", "Var1Sub", "Num1", "Num2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Var1Sub*Num1+Num2}", "maxValue": "{Var1Sub*Num1+Num2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "39.f Two substitutions into multiplication and addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Substituting a values of $x$ and $z$ into $ax+bz$

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

If $\\var{Var1}=\\var{Var1Sub}$ and $\\var{Var2}=\\var{Var2Sub}$, find the value of

\\[\\simplify[basic]{{Num1}{Var1}+{Num2}{Var2}}.\\]

", "advice": "

To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Var1}=\\var{Var1Sub}$ and $\\var{Var2}=\\var{Var2Sub}$ we get

\\[\\simplify[basic]{{Num1}{Var1}+{Num2}{Var2}}=\\simplify[basic]{{Num1}{Var1Sub}+{Num2}{Var2Sub}}=\\var{Num1*Var1Sub+Num2*Var2Sub}.\\]

Use this link to find resources to help you revise substitution into a formula

Substituting a values of $x$ and $z$ into $a(x+z)$

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

If $\\var{Var1}=\\var{Var1Sub}$ and $\\var{Var2}=\\var{Var2Sub}$, find the value of

\\[\\simplify[basic]{{Num1}({Var1}+{Var2})}.\\]

", "advice": "

\\[\\simplify[basic]{{Num1}({Var1}+{Var2})}=\\simplify[basic]{{Num1}({Var1Sub}+{Var2Sub})}=\\simplify[basic]{{Num1}{Var1Sub+Var2Sub}}=\\var{Num1*Var1Sub+Num1*Var2Sub}.\\]

Use this link to find resources to help you revise substitution into a formula

Substituting a values of $x$ and $z$ into $\\frac{ax+bz}{c}$

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

If $\\var{Var1}=\\var{Var1Sub}$ and $\\var{Var2}=\\var{Var2Sub}$, find the value of

\\[\\simplify[basic]{({Num1}{Var1}+{Num2}{Var2})/{Num3}}.\\]

", "advice": "

\\[\\simplify[basic]{({Num1}{Var1}+{Num2}{Var2})/{Num3}}=\\simplify[basic]{({Num1}{Var1Sub}+{Num2}{Var2Sub})/{Num3}}=\\simplify[basic]{({Num1*Var1Sub}+{Num2*Var2Sub})/{Num3}}=\\simplify[basic]{({Num1*Var1Sub+Num2*Var2Sub})/{Num3}}=\\var{(Num1*Var1Sub+Num2*Var2Sub)/Num3}.\\]

Use this link to find resources to help you revise substitution into a formula

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