// Numbas version: finer_feedback_settings
{"question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-ordered", "questions": [{"name": "Transformation - Enlargement", "extensions": [], "custom_part_types": [], "resources": [["question-resources/graph_enlargement_rectangle_pos2_00.svg", "/srv/numbas/media/question-resources/graph_enlargement_rectangle_pos2_00.svg"], ["question-resources/graph_enlargement_rightangle_pos2_00.svg", "/srv/numbas/media/question-resources/graph_enlargement_rightangle_pos2_00.svg"], ["question-resources/graph_enlargement_triangle_pos2_00.svg", "/srv/numbas/media/question-resources/graph_enlargement_triangle_pos2_00.svg"], ["question-resources/graph_enlargement_rectangle_pos2_00_correct_image.svg", "/srv/numbas/media/question-resources/graph_enlargement_rectangle_pos2_00_correct_image.svg"], ["question-resources/graph_enlargement_rightangle_pos2_00_correct_image.svg", "/srv/numbas/media/question-resources/graph_enlargement_rightangle_pos2_00_correct_image.svg"], ["question-resources/graph_enlargement_triangle_pos2_00_correct_image.svg", "/srv/numbas/media/question-resources/graph_enlargement_triangle_pos2_00_correct_image.svg"], ["question-resources/graph_enlargement_triangle_neg2_00_EoiLScE.svg", "/srv/numbas/media/question-resources/graph_enlargement_triangle_neg2_00_EoiLScE.svg"], ["question-resources/graph_enlargement_triangle_neg2_00_correct_image_2mu3W4r.svg", "/srv/numbas/media/question-resources/graph_enlargement_triangle_neg2_00_correct_image_2mu3W4r.svg"]], "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": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}], "variable_groups": [{"variables": ["enlargement_images", "images", "chosen_image", "answer_scale", "correct_image", "answer_x", "answer_y"], "name": "Translation"}], "functions": {}, "rulesets": {}, "ungrouped_variables": [], "metadata": {"description": "<p>Identify the centre of enlargement and the scale factor in a transformation of an image A to an image B</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<p>You can find how image <strong>A</strong> has been enlarged to transform onto image <strong>B</strong> by drawing lines between the vertices of the image and extending them till they intersect.</p>\n<p>{image('resources/question-resources/'+chosen_image[\"correct_image\"])}</p>\n<p>The centre of enlargement is the point where all the lines intersect. In this case, the centre of enlargement is $(\\var{answer_x},\\var{answer_y})$.</p>\n<p>To find the scale factor,&nbsp;identify a point&nbsp;on <strong>A</strong> and the corresponding point on&nbsp;<strong>B</strong>, and look at the coordinates of each relative to the centre of enlargement.</p>\n<p>The relative coordinates of the point on&nbsp;<strong>B</strong> are obtained by multiplying the relative coordinates of the point on&nbsp;<strong>A</strong>.</p>\n<p>From the graph we can see the scale factor is $\\var{answer_scale}$.</p>", "statement": "<p>Describe the transformation of image <strong>A</strong> to image <strong>B</strong>.</p>\n<p>{image('resources/question-resources/'+chosen_image[\"image\"])}</p>", "preamble": {"js": "", "css": ""}, "variables": {"answer_y": {"name": "answer_y", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"answer_y\"]"}, "correct_image": {"name": "correct_image", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"correct_image\"]"}, "answer_scale": {"name": "answer_scale", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"answer_scale\"]"}, "answer_x": {"name": "answer_x", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"answer_x\"]"}, "enlargement_images": {"name": "enlargement_images", "description": "<p>Is a list of the images in the images in the questions.</p>", "templateType": "anything", "group": "Translation", "definition": "['graph_enlargement_triangle_pos2_00.svg','graph_enlargement_triangle_neg2_00bJC2lDk.svg','graph_enlargement_rightangle_pos2_00.svg','graph_enlargement_rectangle_pos2_00.svg']"}, "chosen_image": {"name": "chosen_image", "description": "", "templateType": "anything", "group": "Translation", "definition": "random(images)"}, "images": {"name": "images", "description": "<p>Uses JSON data to select the answer based on the image that is selected.</p>", "templateType": "json", "group": "Translation", "definition": "json_decode(safe(\"[\\n    {\\n        \\\"image\\\": \\\"graph_enlargement_triangle_pos2_00.svg\\\",\\n        \\\"answer_x\\\": 0,\\n        \\\"answer_y\\\": 0,\\n        \\\"answer_scale\\\": 2,\\n        \\\"correct_image\\\": \\\"graph_enlargement_triangle_pos2_00_correct_image.svg\\\"\\n    },\\n    {\\n        \\\"image\\\": \\\"graph_enlargement_triangle_neg2_00_EoiLScE.svg\\\",\\n        \\\"answer_x\\\": 0,\\n        \\\"answer_y\\\": 0,\\n        \\\"answer_scale\\\": -2,\\n        \\\"correct_image\\\": \\\"graph_enlargement_triangle_neg2_00_correct_image_2mu3W4r.svg\\\"\\n    },\\n    {\\n        \\\"image\\\": \\\"graph_enlargement_rightangle_pos2_00.svg\\\",\\n        \\\"answer_x\\\": 0,\\n        \\\"answer_y\\\": 0,\\n        \\\"answer_scale\\\": 2,\\n        \\\"correct_image\\\": \\\"graph_enlargement_rightangle_pos2_00_correct_image.svg\\\"\\n    },\\n    {\\n        \\\"image\\\": \\\"graph_enlargement_rectangle_pos2_00.svg\\\",\\n        \\\"answer_x\\\": 0,\\n        \\\"answer_y\\\": 0,\\n        \\\"answer_scale\\\": 2,\\n        \\\"correct_image\\\": \\\"graph_enlargement_rectangle_pos2_00_correct_image.svg\\\"\\n    }\\n]\"))"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>Centre of enlargement: ([[0]],&nbsp;[[1]])</p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{answer_x}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{answer_x}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{answer_y}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{answer_y}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>Scale factor:&nbsp;[[0]]</p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{answer_scale}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{answer_scale}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}], "tags": ["centre of enlargement", "Centre of enlargement", "Enlargement", "enlargement", "Scale factor", "scale factor", "taxonomy", "transformation", "Transformation"], "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Transformation - Reflection", "extensions": [], "custom_part_types": [], "resources": [["question-resources/graph_reflection_circ_x_zsnE02O.svg", "/srv/numbas/media/question-resources/graph_reflection_circ_x_zsnE02O.svg"], ["question-resources/graph_reflection_circ_x_correct_oKe609k.svg", "/srv/numbas/media/question-resources/graph_reflection_circ_x_correct_oKe609k.svg"], ["question-resources/graph_reflection_circ_y_gx01gno.svg", "/srv/numbas/media/question-resources/graph_reflection_circ_y_gx01gno.svg"], ["question-resources/graph_reflection_circ_y_correct_O200k08.svg", "/srv/numbas/media/question-resources/graph_reflection_circ_y_correct_O200k08.svg"], ["question-resources/graph_reflection_circle_yx_6UIuin2.svg", "/srv/numbas/media/question-resources/graph_reflection_circle_yx_6UIuin2.svg"], ["question-resources/graph_reflection_circle_yx_correct_qTO6FYY.svg", "/srv/numbas/media/question-resources/graph_reflection_circle_yx_correct_qTO6FYY.svg"], ["question-resources/graph_reflection_rect_x_TIdTdJL.svg", "/srv/numbas/media/question-resources/graph_reflection_rect_x_TIdTdJL.svg"], ["question-resources/graph_reflection_rect_x_correct_Rs0CpMG.svg", "/srv/numbas/media/question-resources/graph_reflection_rect_x_correct_Rs0CpMG.svg"], ["question-resources/graph_reflection_rect_y_MmV3ZAK.svg", "/srv/numbas/media/question-resources/graph_reflection_rect_y_MmV3ZAK.svg"], ["question-resources/graph_reflection_rect_y_correct_Robg15m.svg", "/srv/numbas/media/question-resources/graph_reflection_rect_y_correct_Robg15m.svg"], ["question-resources/graph_reflection_rect_yx_76qXVib.svg", "/srv/numbas/media/question-resources/graph_reflection_rect_yx_76qXVib.svg"], ["question-resources/graph_reflection_rect_yx_correct_ojRIhWk.svg", "/srv/numbas/media/question-resources/graph_reflection_rect_yx_correct_ojRIhWk.svg"], ["question-resources/graph_reflection_triangle_x_wjCxAeu.svg", "/srv/numbas/media/question-resources/graph_reflection_triangle_x_wjCxAeu.svg"], ["question-resources/graph_reflection_triangle_x_correct_bf48jod.svg", "/srv/numbas/media/question-resources/graph_reflection_triangle_x_correct_bf48jod.svg"], ["question-resources/graph_reflection_triangle_y_PN3pJ31.svg", "/srv/numbas/media/question-resources/graph_reflection_triangle_y_PN3pJ31.svg"], ["question-resources/graph_reflection_triangle_y_correct_vRjIlRy.svg", "/srv/numbas/media/question-resources/graph_reflection_triangle_y_correct_vRjIlRy.svg"], ["question-resources/graph_reflection_triangle_y-x_9JedlAc.svg", "/srv/numbas/media/question-resources/graph_reflection_triangle_y-x_9JedlAc.svg"], ["question-resources/graph_reflection_triangle_y-x_correct_hte3xZa.svg", "/srv/numbas/media/question-resources/graph_reflection_triangle_y-x_correct_hte3xZa.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}], "rulesets": {}, "functions": {}, "ungrouped_variables": [], "metadata": {"description": "<p>Determine the way in which an image A has been reflected onto an image B.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "variable_groups": [{"variables": ["images", "chosen_image", "distractors", "answer", "correct_image"], "name": "Reflection"}], "advice": "<p>The line of reflection is {chosen_image['answer']}. This is represented as a green dashed line on the graph below.</p>\n<p>{image('resources/question-resources/'+chosen_image[\"correct_image\"])}</p>", "statement": "<p>Determine how the image A has been reflected onto image B.</p>", "preamble": {"js": "", "css": ""}, "variables": {"answer": {"templateType": "anything", "description": "<p>Takes the correct answer from chosen_image.</p>", "name": "answer", "group": "Reflection", "definition": "chosen_image[\"answer\"]"}, "chosen_image": {"templateType": "anything", "description": "<p>Takes from images the chosen image and it's variables</p>", "name": "chosen_image", "group": "Reflection", "definition": "random(images)"}, "distractors": {"templateType": "anything", "description": "<p>Takes the distractors from chosen_image.</p>", "name": "distractors", "group": "Reflection", "definition": "chosen_image[\"distractors\"]"}, "correct_image": {"templateType": "anything", "description": "<p>Takes the correct image (the advice) from chosen_image</p>", "name": "correct_image", "group": "Reflection", "definition": "chosen_image[\"correct_image\"]"}, "images": {"templateType": "json", "description": "<p>Uses JSON data to assign answers with images and distractors (other options when answering)</p>\n<p></p>", "name": "images", "group": "Reflection", "definition": "json_decode(safe(\"[\\n    {\\n        \\\"image\\\": \\\"graph_reflection_circ_x_zsnE02O.svg\\\",\\n        \\\"answer\\\": \\\"y = 0\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_circ_x_correct_oKe609k.svg\\\",\\n        \\\"distractors\\\": [\\\"x = 0\\\", \\\"y = x\\\", \\\"y = -x\\\"]\\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_triangle_y_PN3pJ31.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_triangle_y_correct_vRjIlRy.svg\\\",\\n        \\\"answer\\\": \\\"x = 0\\\",\\n        \\\"distractors\\\": [\\\"y = -x\\\", \\\"y = 0\\\", \\\"y = x\\\"]    \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_triangle_x_wjCxAeu.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_triangle_x_correct_bf48jod.svg\\\",\\n        \\\"answer\\\": \\\"y = 0\\\",\\n        \\\"distractors\\\": [\\\"x = 0\\\", \\\"y = x\\\", \\\"y = -x\\\"]     \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_triangle_y-x_9JedlAc.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_triangle_y-x_correct_hte3xZa.svg\\\",\\n        \\\"answer\\\": \\\"y = -x\\\",\\n        \\\"distractors\\\": [\\\"x = 0\\\", \\\"y = 0\\\", \\\"y = x\\\"]    \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_rect_x_TIdTdJL.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_rect_x_correct_Rs0CpMG.svg\\\",\\n        \\\"answer\\\": \\\"y = 0\\\",\\n        \\\"distractors\\\": [\\\"x = 0\\\", \\\"y = x\\\", \\\"y = -x\\\"]       \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_rect_yx_76qXVib.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_rect_yx_correct_ojRIhWk.svg\\\",\\n        \\\"answer\\\": \\\"y = x\\\",\\n        \\\"distractors\\\": [\\\"x = 0\\\", \\\"y = 0\\\", \\\"y = -x\\\"]         \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_rect_y_MmV3ZAK.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_rect_y_correct_Robg15m.svg\\\",\\n        \\\"answer\\\": \\\"x = 0\\\",\\n        \\\"distractors\\\": [\\\"y = x\\\", \\\"y = 0\\\", \\\"y = -x\\\"]      \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_circle_yx_6UIuin2.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_circle_yx_correct_qTO6FYY.svg\\\",\\n        \\\"answer\\\": \\\"y = x\\\",\\n        \\\"distractors\\\": [\\\"x = 0\\\", \\\"y = 0\\\", \\\"y = -x\\\"]      \\n    },\\n    {\\n        \\\"image\\\": \\\"graph_reflection_circ_y_gx01gno.svg\\\",\\n        \\\"correct_image\\\": \\\"graph_reflection_circ_y_correct_O200k08.svg\\\",\\n        \\\"answer\\\": \\\"x = 0\\\",\\n        \\\"distractors\\\": [\\\"y = x\\\", \\\"y = 0\\\", \\\"y = -x\\\"]     \\n    }\\n]\"))"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "choices": ["<p>$\\var{latex(answer)}$</p>", "<p>$\\var{latex(distractors[0])}$</p>", "<p>$\\var{latex(distractors[1])}$</p>", "<p>$\\var{latex(distractors[2])}$</p>"], "matrix": ["1", 0, 0, 0], "displayColumns": 0, "maxMarks": 0, "type": "1_n_2", "minMarks": 0, "marks": 0, "prompt": "<p>{image('resources/question-resources/'+chosen_image[\"image\"])}</p>\n<p>Reflection in the line:</p>", "variableReplacements": [], "showFeedbackIcon": true, "displayType": "radiogroup", "shuffleChoices": true, "scripts": {}, "distractors": ["", "", "", ""], "showCorrectAnswer": true}], "tags": ["reflection", "Reflection", "taxonomy", "transformation", "Transformation"], "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Transformation - Translation", "extensions": [], "custom_part_types": [], "resources": 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{"description": "<p>Describe a given linear transformation as a vector in Cartesian coordinates.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "variable_groups": [{"variables": ["translation_images", "images", "chosen_image", "answer_x", "answer_y", "correct_image", "word_x", "word_y"], "name": "Reflection"}], "advice": "<p>To find the translation, we need to find the amount of translation (movement) in the x direction and the y direction to form a column vector.</p>\n<p>This can be done by selecting a fixed point on image <strong>A</strong> and finding the x distance and y distance between it and the same point on image <strong>B</strong>.</p>\n<p>Moving from left to right / bottom to top on the graph is a positive translation.<br/>Moving from right to left / top to bottom on the graph is a negative translation.</p>\n<p>The graph below show the translation from image <strong>A</strong> to image <strong>B</strong>.<br/>This shows a<strong> {word_x}</strong> x translation by <strong>{answer_x}</strong> and&nbsp;<strong>{word_y}</strong> y translation by <strong>{answer_y}</strong>.</p>\n<p>{image('resources/question-resources/'+chosen_image[\"correct_image\"])}</p>", "statement": "<p>Describe the transformation which moves image A onto image B.</p>\n<p>Your answer will be in the form \\begin{pmatrix}x \\\\ y\\end{pmatrix}</p>", "preamble": {"js": "", "css": ""}, "variables": {"answer_y": {"templateType": "anything", "description": "<p>Takes the y coordinate correct answer from chosen_image.</p>", "name": "answer_y", "group": "Reflection", "definition": "chosen_image[\"answer_y\"]"}, "word_y": {"templateType": "anything", "description": "<p>Allows the student to know whether their y value moves in the positive or negative direction.</p>", "name": "word_y", "group": "Reflection", "definition": "if(answer_y > 0, \"a positive\",\n  //else\n  if(answer_y < 0, \"a negative\",\n    //else\n    \"no\"\n    )\n)"}, "chosen_image": {"templateType": "anything", "description": "<p>Takes from images the chosen image and it's variables</p>", "name": "chosen_image", "group": "Reflection", "definition": "random(images)"}, "answer_x": {"templateType": "anything", "description": "<p>Takes the x coordinate correct answer from chosen_image.</p>", "name": "answer_x", "group": "Reflection", "definition": "chosen_image[\"answer_x\"]"}, "word_x": {"templateType": "anything", "description": "<p>Allows the student to know whether their x value moves in the positive or negative direction.</p>", "name": "word_x", "group": "Reflection", "definition": "if(answer_x > 0, \"positive\",\n  //else\n  if(answer_x < 0, \"negative\",\n    //else\n    0\n    )\n)"}, "translation_images": {"templateType": "anything", "description": "<p>List of reflection&nbsp;questions (images)</p>", "name": "translation_images", "group": "Reflection", "definition": 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