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{"name": "CF Maths In class test three mock paper question 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["td", "t1", "tr", "tsum", "r1", "r2", "r3", "tans", "a", "r", "nthterm"], "name": "CF Maths In class test three mock paper question 4", "tags": [], "advice": "<p>To find common ratio $r$,&nbsp;we know&nbsp;term number $\\var{r2}$ divided by term number $\\var{r1}$ is $r^{\\var{r2}-\\var{r1}}$. It is then easy to find the common ratio.</p>\n<p>To find the $n$<sup>th&nbsp;</sup>term, multiply&nbsp;the first term a by the common ratio r to the power of n-1, ie ${a}{r^{n-1}}$</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>In a geometric series, term number $\\var{r1}$ is $\\simplify{{t1}/{td}^{r1}}$ and term number $\\var{r2}$ is $\\simplify{{t1}/{td}^{r2}}$.&nbsp;</p>\n<p>What is term number $\\var{r3}$?&nbsp;Give your answer to 2 decimal places.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{t1}/{td}^{r3}", "minValue": "{t1}/{td}^{r3}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>In a gemetric series the first term is $\\var{a}$, and the $\\var{tr}$ th term is $\\var{nthterm}$. Assumming the common ration $r$ is positive, find the sum to infinity. Give your answer to 2 decimal places.&nbsp;</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{a}/(1-{r})", "minValue": "{a}/(1-{r})", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "{r2}>{r1}"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": "<p>the first term for part two</p>"}, "tsum": {"definition": "random(11..29 except 21 except 22 except 23)", "templateType": "anything", "group": "Ungrouped variables", "name": "tsum", "description": ""}, "r1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "r1", "description": ""}, "r2": {"definition": "random(2..5 except r1)", "templateType": "anything", "group": "Ungrouped variables", "name": "r2", "description": ""}, "r3": {"definition": "r1+r2", "templateType": "anything", "group": "Ungrouped variables", "name": "r3", "description": ""}, "tr": {"definition": "random(4..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "tr", "description": ""}, "t1": {"definition": "(td)^5*random(10..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "r": {"definition": "random(0.1..0.9)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": "<p>the common ratio for part two</p>"}, "td": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "td", "description": ""}, "nthterm": {"definition": "{a}*{r}^({tr}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "nthterm", "description": ""}, "tans": {"definition": "t1/td^r3", "templateType": "anything", "group": "Ungrouped variables", "name": "tans", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}