// Numbas version: exam_results_page_options
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Includes powers, division, mulitplication, brackets.&nbsp; Includes subscripts.</p>", "licence": "None specified"}, "statement": "", "advice": "<p><strong>a)</strong></p>\n<p>Rewrite the expression with the substituted values, use brackets to help clarify the seperation of the numbers, and highlight negative values.</p>\n<p>$(\\var{a}) + (\\var{b}) - 3 \\times (\\var{c})$</p>\n<p>and now put all this in the calculator, as seen,</p>\n<p>$(\\var{a}) + (\\var{b}) - 3 \\times (\\var{c})&nbsp;= \\var{a+b-3*c}$</p>\n<p></p>\n<p><strong>b)</strong></p>\n<p>Rewrite the expression with the substituted values, use brackets to help clarify the seperation of the numbers, and highlight negative values. Remember that algebraically we don't write a multiplication sign, but this is a multiplication, i.e.&nbsp;</p>\n<p>$(\\var{f})^2 \\times [(\\var{d} - (\\var{c})]$</p>\n<p>and now put all this in the calculator, as seen,</p>\n<p>$(\\var{f})^2 \\times [(\\var{d} - (\\var{c})] = \\var{(f^2)*(d-c)}$</p>\n<p></p>\n<p><strong>c)&nbsp;</strong></p>\n<p>Rewrite the expression with the substituted values, use brackets to help clarify the seperation of the numbers, and highlight negative values.</p>\n<p>$\\frac{[(\\var{g}) + 3 \\times (\\var{h})]^2}{(\\var{g}) \\times (\\var{h})}$</p>\n<p>and now put all this in the calculator, as seen,</p>\n<p>$\\frac{[(\\var{g}) + 3 \\times (\\var{h})]^2}{(\\var{g}) \\times (\\var{h})} = \\var{((g + 3h)^2)/(g*h)} $</p>\n<p>This answer should be rounded&nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-9.9..-0.1 except 0) ", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-9.9..10 except 0) ", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-9.9..-0.1 except 0) ", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9.9..10 except 0) ", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-9.9..10 except 0) ", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(-9.9..10 except 0) ", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(-9.9..10 except 0) ", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the value of</p>\n<p>$a + b - 3c$</p>\n<p>Given:<br/>$a = \\var{a}$<br/>$b = \\var{b}$<br/>$c = \\var{c}$</p>\n<p></p>", "minValue": "a+b-3c", "maxValue": "a+b-3c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the value of</p>\n<p>$M^2(A_x - A_y)$</p>\n<p>Given:<br/>$A_x = \\var{d}$<br/>$A_y = \\var{c}$<br/>$M = \\var{f}$</p>\n<p></p>", "minValue": "(d-c)*f^2", "maxValue": "(d-c)*f^2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the value of</p>\n<p>$\\frac{(x_1 + 3x_2)^2}{x_1x_2}$</p>\n<p>Given:<br/>$x_1 = \\var{g}$<br/>$x_2 = \\var{h}$<br/><br/></p>\n<p></p>", "minValue": "((g+3h)^2)/(g*h)", "maxValue": "((g+3h)^2)/(g*h)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}