// Numbas version: exam_results_page_options
{"name": "Q1 Factorise", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["num11", "num12", "num22", "num32"], "name": "Q1 Factorise", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>Example 1;</p>\n<p>$3xy^4 +9xy^2 -6x^2y$</p>\n<p>First check if the equation can be divided across by a constant,</p>\n<p>$3(xy^4 +3xy^2 -2x^2y)$</p>\n<p>Next, check if the equation can be divided across by any term(s)</p>\n<p>$3xy(y^3 +3y -2x)$&nbsp;</p>\n<p>Example 2;</p>\n<p>$9x^2 -&nbsp;49$</p>\n<p>This is the differnce of 2 squares!!</p>\n<p>Always in the form (x - )(x + )</p>\n<p>Get the square root of both numbers in the equation $\\sqrt9 = 3$ and&nbsp;$\\sqrt49 = 7$</p>\n<p>(3x - 7)(3x + 7)</p>\n<p>Example 3;</p>\n<p>$2ab - 6ac - bd + 3cd$</p>\n<p>Gather the terms that has common factors and take them out, similar as part 1</p>\n<p>$2a(b - 3c) - d(b - 3c)$</p>\n<p>Next, since there is a common factor bracket, the equation&nbsp;can be reduced further</p>\n<p>$(b - 3c)(2a&nbsp;- d)$</p>", "rulesets": {}, "parts": [{"prompt": "<p>(i)&nbsp;&nbsp;$\\simplify{{num12[0]} *{ num11[0]}}xy - \\simplify{{num12[0]}*{num11[1]}}xw + \\simplify{{num12[0]}*{num11[2]}}xz$</p>\n<p>[[0]]</p>\n<p>(ii)&nbsp; $\\simplify{{num12[1]} *{ num11[3]}}xy^4&nbsp;+ \\simplify{{num12[1]}*{num11[4]}}xy^2&nbsp;- \\simplify{{num12[1]}*{num11[5]}}x^2y$</p>\n<p>[[1]]</p>\n<p>(iii)&nbsp; $\\simplify{{num12[2]} *{ num11[6]}}x^2 - \\simplify{{num12[2]}*{num11[7]}}xy + \\simplify{{num12[2]}*{num11[8]}}x^3$</p>\n<p>[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num12[0]}x)*({num11[0]}y - {num11[1]}w + {num11[2]}z)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num12[1]}xy)*({num11[3]}y^3 + {num11[4]}y - {num11[5]}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num12[2]}x)*({num11[6]}x - {num11[7]} + {num11[8]}x^2)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>(i)&nbsp;&nbsp;$\\simplify{{num22[0]} *{ num22[0]}}x^2 - \\simplify{{num22[3]}*{num22[3]}}$</p>\n<p>[[0]]</p>\n<p>(ii) &nbsp;$\\simplify{{num22[1]} *{ num22[1]}}x^2 - \\simplify{{num22[4]}*{num22[4]}}$</p>\n<p>[[1]]</p>\n<p>(iii) &nbsp;$\\simplify{{num22[2]} *{ num22[2]}}x^2 - \\simplify{{num22[5]}*{num22[5]}}$</p>\n<p>[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num22[0]}x - {num22[3]})*({num22[0]}x + {num22[3]})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num22[1]}x - {num22[4]})*({num22[1]}x + {num22[4]})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num22[2]}x - {num22[5]})*({num22[2]}x + {num22[5]})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>(i)&nbsp;&nbsp;$\\simplify{{num32[0]} *{ num32[1]}}ab - \\simplify{{num32[0]}*{num32[3]}}ac - \\simplify{{num32[2]}*{num32[1]}}bd + \\simplify{{num32[2]}*{num32[3]}}cd$</p>\n<p>[[0]]</p>\n<p>(ii) &nbsp;$\\simplify{{num32[4]} *{ num32[5]}}a^2 + \\simplify{{num32[4]}*{num32[7]}}a + \\simplify{{num32[6]}*{num32[5]}}a + \\simplify{{num32[6]}*{num32[7]}}$</p>\n<p>[[1]]</p>\n<p>(iii) &nbsp;$\\simplify{{num32[8]} *{ num32[9]}}xy - \\simplify{{num32[8]}*{num32[5]}}x^2y - \\simplify{{num32[3]}*{num32[5]}}x + \\simplify{{num32[3]}*{num32[9]}}$</p>\n<p>[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num32[0]}a - {num32[2]}d)*({num32[1]}b - {num32[3]}c)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num32[4]}a + {num32[6]})*({num32[5]}a + {num32[7]})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({num32[8]}xy + {num32[3]})*({num32[9]} - {num32[5]}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Factorise each of the following:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num22": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num12": {"definition": "shuffle(2..4)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num32": {"definition": "shuffle(1..10)[0..10]", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}, "num11": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}}, "metadata": {"description": "<p>Factorising algebraic expressions</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}