// Numbas version: exam_results_page_options
{"name": "1.4.1.Exercises", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.4.1.Exercises", "tags": [], "metadata": {"description": "<p>The exercises for HELM Book 1.4.1</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify the following fractions as much as possible.</p>", "advice": "<p>Fully factorise the numerator and the denominator, then look for common factors that can be cancelled.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q1frac": {"name": "q1frac", "group": "Q1", "definition": "expression((q1n*q1gcd)+\"/\"+(q1d*q1gcd))", "description": "", "templateType": "anything", "can_override": false}, "q1gcd": {"name": "q1gcd", "group": "Q1", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "q1n,q1d": {"name": "q1n,q1d", "group": "Ungrouped variables", "definition": "repeat(random(2..20),2)", "description": "", "templateType": "anything", "can_override": false}, "alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "shuffle([\"a\",\"b\",\"c\",\"d\",\"f\",\"g\",\"h\",\"k\",\"m\",\"n\",\"p\",\"q\",\"r\",\"s\",\"t\",\"u\",\"v\",\"w\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "q2v": {"name": "q2v", "group": "Q2", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q2idx": {"name": "q2idx", "group": "Q2", "definition": "repeat(random(1..10),2)", "description": "<p>index on [numerator variable, denominator variable]</p>", "templateType": "anything", "can_override": false}, "q2a,q2b": {"name": "q2a,q2b", "group": "Ungrouped variables", "definition": "[random(1..20),random(1..20)]", "description": "", "templateType": "anything", "can_override": false}, "q2c": {"name": "q2c", "group": "Q2", "definition": "[q2a/gcd(q2a,q2b),q2b/gcd(q2a,q2b), random(2..10)]", "description": "<p>Two coprime numbers and a common multiplier</p>", "templateType": "anything", "can_override": false}, "q2num": {"name": "q2num", "group": "Q2", "definition": "simplify(expression(q2c[0]*q2c[2]+\"*\"+q2v+\"^\"+q2idx[0]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q2den": {"name": "q2den", "group": "Q2", "definition": "simplify(expression(q2c[1]*q2c[2]+\"*\"+q2v+\"^\"+q2idx[1]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q2simnum": {"name": "q2simnum", "group": "Q2", "definition": "simplify(expression(q2c[0]+\"*\"+q2v+\"^\"+q2simidx[0]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q2simden": {"name": "q2simden", "group": "Q2", "definition": "simplify(expression(q2c[1]+\"*\"+q2v+\"^\"+q2simidx[1]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q2simidx": {"name": "q2simidx", "group": "Q2", "definition": "if(q2idx[0]>q2idx[1],\n  [q2idx[0]-q2idx[1],0], //numerator bigger\n  [0,q2idx[1]-q2idx[0]]  //denominator bigger, or equality\n)", "description": "<p>simplified indices on [numerator, denominator]</p>", "templateType": "anything", "can_override": false}, "q7num": {"name": "q7num", "group": "Q7", "definition": "simplify(expression(\n   q7numc+\"*(\"+q7numx +\")\"\n),[\"all\",\"expandBrackets\"])", "description": "", "templateType": "anything", "can_override": false}, "q7den": {"name": "q7den", "group": "Q7", "definition": "simplify(expression(\n   q7denc + \"*(\" + q7denx +\")\"\n),[\"all\",\"expandBrackets\"])", "description": "", "templateType": "anything", "can_override": false}, "q7numx": {"name": "q7numx", "group": "Q7", "definition": "  [ \"x+\"+q7rnd,\n  \"x+\"+q7rnd,\n  \"1\",\n  \"x+\"+q7rnd][q7idx]", "description": "<p>The numerator x-term</p>", "templateType": "anything", "can_override": false}, "q7numc,q7denc": {"name": "q7numc,q7denc", "group": "Ungrouped variables", "definition": "repeat(weighted_random([ [1,0.5],[random(2..10),0.5] ]),2)", "description": "<p>The numerator and denominator constant multipliers</p>", "templateType": "anything", "can_override": false}, "q7denx": {"name": "q7denx", "group": "Q7", "definition": "  [ \"x+\"+q7rnd,\n  \"x+\"+random(-9..9 except q7rnd),\n  \"x+\"+q7rnd,\n  \"1\"][q7idx]", "description": "<p>the denominator x-term</p>", "templateType": "anything", "can_override": false}, "q7idx": {"name": "q7idx", "group": "Q7", "definition": "weighted_random([ [0,0.5],[random(1..3),0.5]    ])", "description": "<p>0: same x-term on top and bottom. This is the most likely outcome.</p>\n<p>1: different x-terms on top and bottom</p>\n<p>2: no x-term on top</p>\n<p>3: no x-term on bottom</p>", "templateType": "anything", "can_override": false}, "q7v": {"name": "q7v", "group": "Q7", "definition": "random(alphabet)", "description": "<p>The chosen variable</p>", "templateType": "anything", "can_override": false}, "q7rnd": {"name": "q7rnd", "group": "Q7", "definition": "random(-9..9)", "description": "<p>The random number for the numerator x-term</p>", "templateType": "anything", "can_override": false}, "q7simnum": {"name": "q7simnum", "group": "Q7", "definition": "simplify(expression(\n  [string(q7numc/gcd(q7numc,q7denc)),\n    q7numc/gcd(q7numc,q7denc)+\"*(\"+q7numx+\")\",\n    string(q7numc/gcd(q7numc,q7denc)),\n    q7numc/gcd(q7numc,q7denc)+\"*(\"+q7numx+\")\"\n  ][q7idx]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q7simden": {"name": "q7simden", "group": "Q7", "definition": "simplify(expression(\n  [string(q7denc/gcd(q7numc,q7denc)),\n    q7denc/gcd(q7numc,q7denc)+\"*(\"+q7denx+\")\",\n    q7denc/gcd(q7numc,q7denc)+\"*(\"+q7denx+\")\",\n    string(q7denc/gcd(q7numc,q7denc))\n  ][q7idx]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q3num": {"name": "q3num", "group": "Q3-6", "definition": "simplify(expression(q3gcd+\"*\"+q3var+\"+\"+q3gcd*q3nc),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q3den": {"name": "q3den", "group": "Q3-6", "definition": "simplify(expression(q3gcd*q3dc+\"*\"+q3var+\"+\"+q3gcd),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q3simnum": {"name": "q3simnum", "group": "Q3-6", "definition": "simplify(expression(q3var+\"+\"+q3nc),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q3simden": {"name": "q3simden", "group": "Q3-6", "definition": "simplify(expression(q3dc+\"*\"+q3var+\"+\"+1),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q4den": {"name": "q4den", "group": "Q3-6", "definition": "expression(q3gcd*q3dc+\"*\"+q3var)", "description": "", "templateType": "anything", "can_override": false}, "q4num": {"name": "q4num", "group": "Q3-6", "definition": "q3num", "description": "", "templateType": "anything", "can_override": false}, "q4simnum": {"name": "q4simnum", "group": "Q3-6", "definition": "q3simnum", "description": "", "templateType": "anything", "can_override": false}, "q4simden": {"name": "q4simden", "group": "Q3-6", "definition": "expression(q3dc+\"*\"+q3var)", "description": "", "templateType": "anything", "can_override": false}, "q5den": {"name": "q5den", "group": "Q3-6", "definition": "q3gcd*q3dc", "description": "", "templateType": "anything", "can_override": false}, "q5num": {"name": "q5num", "group": "Q3-6", "definition": "q3num", "description": "", "templateType": "anything", "can_override": false}, "q5simnum": {"name": "q5simnum", "group": "Q3-6", "definition": "q3simnum", "description": "", "templateType": "anything", "can_override": false}, "q5simden": {"name": "q5simden", "group": "Q3-6", "definition": "q3dc", "description": "", "templateType": "anything", "can_override": false}, "q6num": {"name": "q6num", "group": "Q3-6", "definition": "q3num", "description": "", "templateType": "anything", "can_override": false}, "q6den": {"name": "q6den", "group": "Q3-6", "definition": "expression(q3gcd*q3dc+\"*\"+q3var+\"+1\")", "description": "", "templateType": "anything", "can_override": false}, "q6simnum": {"name": "q6simnum", "group": "Q3-6", "definition": "q6num", "description": "", "templateType": "anything", "can_override": false}, "q6simden": {"name": "q6simden", "group": "Q3-6", "definition": "q6den", "description": "", "templateType": "anything", "can_override": false}, "q3gcd": {"name": "q3gcd", "group": "Q3-6", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "q3nc": {"name": "q3nc", "group": "Q3-6", "definition": "random(-9..9 except [-1,0,1])", "description": "<p>numerator constant</p>", "templateType": "anything", "can_override": false}, "q3dc": {"name": "q3dc", "group": "Q3-6", "definition": "random(2..9 except q3nc)", "description": "<p>denominator constant (x-coefficient)</p>", "templateType": "anything", "can_override": false}, "q3var": {"name": "q3var", "group": "Q3-6", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q8v": {"name": "q8v", "group": "Q8", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q8xcoef": {"name": "q8xcoef", "group": "Q8", "definition": "[q8xcoefdraft,\n  [q8xcoefdraft[0],q8xcoefdraft[0],q8xcoefdraft[2]],\n  [q8xcoefdraft[0],q8xcoefdraft[1],q8xcoefdraft[0]],\n  [q8xcoefdraft[0],q8xcoefdraft[0],q8xcoefdraft[2]],\n  [q8xcoefdraft[0],q8xcoefdraft[1],q8xcoefdraft[0]],\n][q8idx]", "description": "<p>x-coefficients</p>", "templateType": "anything", "can_override": false}, "q8c": {"name": "q8c", "group": "Q8", "definition": "[q8cdraft,\n  [q8cdraft[0], -1*q8cdraft[0], q8cdraft[2]],\n  [q8cdraft[0], q8cdraft[1], -1*q8cdraft[0]],\n  [q8cdraft[0], q8cdraft[0], q8cdraft[2]],\n  [q8cdraft[0], q8cdraft[1], q8cdraft[0]]\n][q8idx]", "description": "", "templateType": "anything", "can_override": false}, "q8fc,q8f1,q8f2": {"name": "q8fc,q8f1,q8f2", "group": "Ungrouped variables", "definition": "[simplify(expression(q8xcoef[0]+\"*\"+q8v+\"+\"+q8c[0]),\"all\"),\n  simplify(expression(q8xcoef[1]+\"*\"+q8v+\"+\"+q8c[1]),\"all\"),\n  simplify(expression(q8xcoef[2]+\"*\"+q8v+\"+\"+q8c[2]),\"all\")]", "description": "<p>The common factor, the numerator factor, the denominator factor</p>", "templateType": "anything", "can_override": false}, "q8num": {"name": "q8num", "group": "Q8", "definition": "simplify(expression(\n    \"(\"+string(q8fc)+\")*(\"+string(q8f1)+\")\"\n  ),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}, "q8den": {"name": "q8den", "group": "Q8", "definition": "simplify(expression(\n    \"(\"+string(q8fc)+\")*(\"+string(q8f2)+\")\"\n  ),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}, "q8cdraft": {"name": "q8cdraft", "group": "Q8", "definition": "shuffle(-12..12 except 0)[0..3]", "description": "", "templateType": "anything", "can_override": false}, "q8idx": {"name": "q8idx", "group": "Q8", "definition": "weighted_random([ \n  [0,0.6],[1,0.1],[2,0.1],[3,0.1],[4,0.1]\n])", "description": "<p>0: random quadratic on top and bottom</p>\n<p>1: difference of two squares on top</p>\n<p>2: difference of two squares on bottom</p>\n<p>3: perfect square on top</p>\n<p>4: perfect square on bottom</p>", "templateType": "anything", "can_override": false}, "q8xcoefdraft": {"name": "q8xcoefdraft", "group": "Q8", "definition": "shuffle([1,1,random(1,2,3,5,7)])", "description": "", "templateType": "anything", "can_override": false}, "q9n": {"name": "q9n", "group": "Q9", "definition": "q9m[0]/gcd(q9m[0],q9m[1])", "description": "<p>multiplier for the numerator</p>", "templateType": "anything", "can_override": false}, "q9d": {"name": "q9d", "group": "Q9", "definition": "q9m[1]/gcd(q9m[0],q9m[1])", "description": "<p>multiplier for the denominator. Constrained to be coprime to q9n.</p>", "templateType": "anything", "can_override": false}, "q9m": {"name": "q9m", "group": "Q9", "definition": "repeat(random(2..9),2)", "description": "<p>multipliers for the numerator and denominator. These will be divided by their gcd to make them coprime.</p>", "templateType": "anything", "can_override": false}, "q9c": {"name": "q9c", "group": "Q9", "definition": "repeat(random(-9..9 except [-1,0,1]),2)", "description": "<p>numerator constant, denominator constant</p>", "templateType": "anything", "can_override": false}, "q9v": {"name": "q9v", "group": "Q9", "definition": "random(alphabet)", "description": "<p>the letter to use</p>", "templateType": "anything", "can_override": false}, "q9num": {"name": "q9num", "group": "Q9", "definition": "simplify(expression(\n    q9n+\"*(\"+q9v+\"+\"+q9c[0]+\")*(\"+q9v+\"+\"+q9c[1]+\")\"\n),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}, "q9den": {"name": "q9den", "group": "Q9", "definition": "simplify(expression(\n    q9d+\"*(\"+q9v+\"+\"+q9c[1]+\")\"\n),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}, "q9numsim": {"name": "q9numsim", "group": "Q9", "definition": "simplify(expression(\n    q9n+\"*(\"+q9v+\"+\"+q9c[0]+\")\"\n),\"all\")", "description": "<p>simplilfied numerator</p>", "templateType": "anything", "can_override": false}, "q9densim": {"name": "q9densim", "group": "Q9", "definition": "expression(string(q9d))", "description": "", "templateType": "anything", "can_override": false}, "q10gcd": {"name": "q10gcd", "group": "Q10", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "q10vars": {"name": "q10vars", "group": "Q10", "definition": "[\n  abs(q10vartemp[0])/gcd(gcd(q10vartemp[0],q10vartemp[1]),gcd(q10vartemp[1],q10vartemp[2])),\n  abs(q10vartemp[1])/gcd(gcd(q10vartemp[0],q10vartemp[1]),gcd(q10vartemp[1],q10vartemp[2])),\n  q10vartemp[2]/gcd(gcd(q10vartemp[0],q10vartemp[1]),gcd(q10vartemp[1],q10vartemp[2]))\n]", "description": "<p>make sure that the 3 constants are coprime.</p>", "templateType": "anything", "can_override": false}, "q10v": {"name": "q10v", "group": "Q10", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q10num": {"name": "q10num", "group": "Q10", "definition": "expression(string(q10gcd*q10vars[0]))", "description": "", "templateType": "anything", "can_override": false}, "q10den": {"name": "q10den", "group": "Q10", "definition": "simplify(expression(\n    q10vars[1]+\"*\"+q10gcd+\"*\"+q10v+\"+\"+q10vars[2]+\"*\"+q10gcd\n),\"all\")    ", "description": "", "templateType": "anything", "can_override": false}, "q10numsim": {"name": "q10numsim", "group": "Q10", "definition": "expression(string(q10vars[0]))", "description": "", "templateType": "anything", "can_override": false}, "q10densim": {"name": "q10densim", "group": "Q10", "definition": "simplify(expression(\n    q10vars[1]+\"*\"+q10v+\"+\"+q10vars[2]\n),\"all\")   ", "description": "", "templateType": "anything", "can_override": false}, "q10vartemp": {"name": "q10vartemp", "group": "Q10", "definition": "shuffle(-10..10 except 0)[0..3]", "description": "", "templateType": "anything", "can_override": false}, "q11gcd": {"name": "q11gcd", "group": "Q11", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "q11vartmp": {"name": "q11vartmp", "group": "Q11", "definition": "shuffle(-10..10 except 0)[0..3]", "description": "", "templateType": "anything", "can_override": false}, "q11vars": {"name": "q11vars", "group": "Q11", "definition": "[\n  abs(q11vartmp[0])/gcd(gcd(q11vartmp[0],q11vartmp[1]),gcd(q11vartmp[1],q11vartmp[2])),\n  abs(q11vartmp[1])/gcd(gcd(q11vartmp[0],q11vartmp[1]),gcd(q11vartmp[1],q11vartmp[2])),\n  q11vartmp[2]/gcd(gcd(q11vartmp[0],q11vartmp[1]),gcd(q11vartmp[1],q11vartmp[2]))\n]", "description": "", "templateType": "anything", "can_override": false}, "q11v": {"name": "q11v", "group": "Q11", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q11num": {"name": "q11num", "group": "Q11", "definition": "expression(q11gcd*q11vars[0]+\"*\"+q11v)", "description": "", "templateType": "anything", "can_override": false}, "q11den": {"name": "q11den", "group": "Q11", "definition": "simplify(expression(\n    q11vars[1]+\"*\"+q11gcd+\"*\"+q11v+\"^2+\"+q11vars[2]+\"*\"+q11gcd+\"*\"+q11v\n),\"all\")    ", "description": "", "templateType": "anything", "can_override": false}, "q11numsim": {"name": "q11numsim", "group": "Q11", "definition": "expression(string(q11vars[0]))", "description": "", "templateType": "anything", "can_override": false}, "q11densim": {"name": "q11densim", "group": "Q11", "definition": "simplify(expression(\n    q11vars[1]+\"*\"+q11v+\"+\"+q11vars[2]\n),\"all\")    ", "description": "", "templateType": "anything", "can_override": false}, "q12gcd": {"name": "q12gcd", "group": "Q12", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "q12vartmp": {"name": "q12vartmp", "group": "Q12", "definition": "shuffle(-10..10 except 0)[0..3]", "description": "", "templateType": "anything", "can_override": false}, "q12vars": {"name": "q12vars", "group": "Q12", "definition": "[\n  abs(q12vartmp[0])/gcd(gcd(q12vartmp[0],q12vartmp[1]),gcd(q12vartmp[1],q12vartmp[2])),\n  abs(q12vartmp[1])/gcd(gcd(q12vartmp[0],q12vartmp[1]),gcd(q12vartmp[1],q12vartmp[2])),\n  q12vartmp[2]/gcd(gcd(q12vartmp[0],q12vartmp[1]),gcd(q12vartmp[1],q12vartmp[2]))\n]", "description": "", "templateType": "anything", "can_override": false}, "q12v": {"name": "q12v", "group": "Q12", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q12num": {"name": "q12num", "group": "Q12", "definition": "expression(q12gcd*q12vars[0]+\"*\"+q12v+\"^2\")", "description": "", "templateType": "anything", "can_override": false}, "q12den": {"name": "q12den", "group": "Q12", "definition": "simplify(expression(\n    q12vars[1]+\"*\"+q12gcd+\"*\"+q12v+\"^3+\"+q12vars[2]+\"*\"+q12gcd+\"*\"+q12v+\"^2\"\n),\"all\")    ", "description": "", "templateType": "anything", "can_override": false}, "q12densim": {"name": "q12densim", "group": "Q12", "definition": "simplify(expression(\n    q12vars[1]+\"*\"+q12v+\"+\"+q12vars[2]\n),\"all\")    ", "description": "", "templateType": "anything", "can_override": false}, "q12numsim": {"name": "q12numsim", "group": "Q12", "definition": "expression(string(q12vars[0]))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "not((q7numc=q7denc) and (q7denc=q7numx) and (q7numx=q7denx))", "maxRuns": "33"}, "ungrouped_variables": ["q1n,q1d", "q2a,q2b", "q7numc,q7denc", "q8fc,q8f1,q8f2", "alphabet"], "variable_groups": [{"name": "Q1", "variables": ["q1gcd", "q1frac"]}, {"name": "Q2", "variables": ["q2v", "q2idx", "q2c", "q2num", "q2den", "q2simidx", "q2simnum", "q2simden"]}, {"name": "Q7", "variables": ["q7v", "q7idx", "q7rnd", "q7numx", "q7denx", "q7num", "q7den", "q7simnum", "q7simden"]}, {"name": "Q3-6", "variables": ["q3var", "q3gcd", "q3nc", "q3dc", "q3num", "q3den", "q3simnum", "q3simden", "q4num", "q4den", "q4simnum", "q4simden", "q5num", "q5den", "q5simnum", "q5simden", "q6num", "q6den", "q6simnum", "q6simden"]}, {"name": "Q8", "variables": ["q8idx", "q8v", "q8xcoefdraft", "q8xcoef", "q8cdraft", "q8c", "q8num", "q8den"]}, {"name": "Q9", "variables": ["q9m", "q9n", "q9d", "q9c", "q9v", "q9num", "q9den", "q9numsim", "q9densim"]}, {"name": "Q10", "variables": ["q10gcd", "q10vartemp", "q10vars", "q10v", "q10num", "q10den", "q10numsim", "q10densim"]}, {"name": "Q11", "variables": ["q11gcd", "q11vartmp", "q11vars", "q11v", "q11num", "q11den", "q11numsim", "q11densim"]}, {"name": "Q12", "variables": ["q12gcd", "q12vartmp", "q12vars", "q12v", "q12num", "q12den", "q12densim", "q12numsim"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Question 1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible, $\\displaystyle{\\var{q1frac}}.\\qquad$ (To enter $\\displaystyle{\\frac{7}{9}}$, type 7/9.)</p>", "minValue": "{q1frac}", "maxValue": "{q1frac}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": true, "customName": "Question 2", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify the following fraction as much as possible.$\\qquad$ (To enter $x^5$, type x^5 )</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q2num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q2den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q2simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q2simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 3", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible.$\\qquad$ (If the answer is a whole number, enter 1 for the denominator.)</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q3num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q3den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q3simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q3simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 4", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q4num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q4den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q4simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q4simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 5", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q5num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q5den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q5simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q5simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 6", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q6num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q6den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q6simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q6simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 7", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q7num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q7den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q7simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q7simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 8", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q8num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q8den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q8f1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q8f2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 9", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q9num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q9den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q9numsim}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q9densim}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Question 10", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q10num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q10den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": 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