// Numbas version: finer_feedback_settings
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Some also require fraction division.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "", "advice": "<p>{advicetext}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"qn\\\":\\\"$\\\\\\\\cos(\\\\\\\\alpha) +\\\\\\\\cos(\\\\\\\\alpha)\\\\\\\\tan^2(\\\\\\\\alpha)$\\\",\\n\\\"ans\\\":\\\"$\\\\\\\\sec(\\\\\\\\alpha)$\\\",\\n\\\"dis1\\\":\\\"$\\\\\\\\sin(\\\\\\\\alpha)$\\\",\\n\\\"dis2\\\":\\\"$\\\\\\\\cos(\\\\\\\\alpha)$\\\",\\n\\\"dis3\\\":\\\"$\\\\\\\\csc(\\\\\\\\alpha)$\\\",\\n\\\"adv\\\":1\\n},\\n{\\n\\\"qn\\\":\\\"$\\\\\\\\csc^2(\\\\\\\\beta)-\\\\\\\\cot^2(\\\\\\\\beta)$\\\",\\n\\\"ans\\\":\\\"$1$\\\",\\n\\\"dis1\\\":\\\"$2$\\\",\\n\\\"dis2\\\":\\\"$\\\\\\\\sec^2(\\\\\\\\beta)$\\\",\\n\\\"dis3\\\":\\\"$\\\\\\\\sin^2(\\\\\\\\beta)$\\\",\\n\\\"adv\\\":2\\n},\\n{\\n\\\"qn\\\":\\\"$\\\\\\\\displaystyle{\\\\\\\\frac{\\\\\\\\sec(\\\\\\\\theta)}{\\\\\\\\tan(\\\\\\\\theta)}}$\\\",\\n\\\"ans\\\":\\\"$\\\\\\\\csc(\\\\\\\\theta)$\\\",\\n\\\"dis1\\\":\\\"$\\\\\\\\sin(\\\\\\\\theta)$\\\",\\n\\\"dis2\\\":\\\"$\\\\\\\\cos(\\\\\\\\theta)$\\\",\\n\\\"dis3\\\":\\\"$\\\\\\\\tan(\\\\\\\\theta)$\\\",\\n\\\"adv\\\":3\\n},\\n{\\n\\\"qn\\\":\\\"$\\\\\\\\displaystyle{\\\\\\\\frac{\\\\\\\\sin^4x-\\\\\\\\cos^4x}{\\\\\\\\sin^2x-\\\\\\\\cos^2x}}$\\\",\\n\\\"ans\\\":\\\"$1$\\\",\\n\\\"dis1\\\":\\\"$\\\\\\\\sin^2x-\\\\\\\\cos^2x$\\\",\\n\\\"dis2\\\":\\\"$\\\\\\\\cos^2x-\\\\\\\\sin^2x$\\\",\\n\\\"dis3\\\":\\\"$\\\\\\\\tan^2x$\\\",\\n\\\"adv\\\":4\\n}\\n]\"))", 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code to select the relevant advice (worked solution) for the randomly selected question.</p>", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "scenario[\"dis1\"]", "description": "<p>The first incorrect answer (distractor) for the randomly selected question.</p>", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "scenario[\"dis2\"]", "description": "<p>The second incorrect answer (distractor) for the randomly selected question.</p>", "templateType": "anything", "can_override": false}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "scenario[\"dis3\"]", "description": "<p>The third incorrect answer (distractor) for the randomly selected question.</p>", "templateType": "anything", "can_override": false}, "adv2": {"name": "adv2", "group": "Ungrouped variables", "definition": "latex(\"\\\\begin{align}\\\\displaystyle{\n  \\\\csc^2(\\\\beta)-\\\\cot^2(\\\\beta)}&=\n  \\\\frac{1}{\\\\sin^2(\\\\beta)}-\\\\frac{\\\\cos^2(\\\\beta)}{\\\\sin^2(\\\\beta)} \\\\text{ (using reciprocal ratios)}\\\\\\\\&=\n  \\\\frac{1-\\\\cos^2(\\\\beta)}{\\\\sin^2(\\\\beta)} \\\\text{ (by combining fractions)}\\\\\\\\&= \n  \\\\frac{\\\\sin^2(\\\\beta)}{\\\\sin^2(\\\\beta)}  \\\\text{ (from Pythagorean identity)} \\\\\\\\&=\n  1 <br><br>\\\\\\\\ \\\\textrm{ Or alternatively }\\\\\\\\ \\\\csc^2(\\\\beta)-\\\\cot^2(\\\\beta)&=\n  (1+\\\\cot^2(\\\\beta))-\\\\cot^2(\\\\beta)  \\\\text{ (from Pythagorean identity)}\\\\\\\\&=1.\\\\end{align}\")", "description": "<p>The LaTeX code for the advice for scenario 2.</p>", "templateType": "anything", "can_override": false}, "advicetext": {"name": "advicetext", "group": "Ungrouped variables", "definition": "switch(advice=1,adv1,advice=2,adv2,advice=3,adv3,adv4)", "description": "<p>The variable uses the advice code (adv1, adv2, adv3 or adv4) to select the correct advice text.</p>", "templateType": "anything", "can_override": false}, "adv1": {"name": "adv1", "group": "Ungrouped variables", "definition": "latex(\"\\\\begin{align}\n  \\\\cos(\\\\alpha) +\\\\cos(\\\\alpha)\\\\tan^2(\\\\alpha)&=\n  \\\\cos(\\\\alpha)(1 +\\\\tan^2(\\\\alpha))   \\\\text{ (taking out the common factor)} \\\\\\\\&=\n  \\\\cos(\\\\alpha)\\\\sec^2(\\\\alpha)   \\\\text{ (using Pythagorean trig identity)} \\\\\\\\&=  \n  \\\\cos(\\\\alpha)\\\\frac{1}{\\\\cos^2(\\\\alpha)}   \\\\text{ (using reciprocal ratio)} \\\\\\\\&=\n  \\\\frac{1}{\\\\cos(\\\\alpha)}  \\\\text{ (cancelling fractions)} \\\\\\\\&=\n   \\\\sec(\\\\alpha). \\\\text{ (using reciprocal ratio)} \n    <br><br>\\\\end{align}\") ", "description": "<p>The LaTeX code for the advice for scenario 1.</p>", "templateType": "anything", "can_override": false}, "adv3": {"name": "adv3", "group": "Ungrouped variables", "definition": "latex(\"\\\\begin{align}\\\\displaystyle{\n  \\\\frac{\\\\sec(\\\\theta)}{\\\\tan(\\\\theta)}}&=\n  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