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Includes probability laws, chi-square table entries, Hardy–Weinberg equilibrium expressions, and measures such as mean, median, mode, range, standard deviation, and standard error of the mean. Also provides biological and quantitative relationships for water potential, solute potential, growth and rate parameters, carrying capacity, and Simpson’s diversity index. Includes metric prefixes and notation guidance for variables and degrees of freedom.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ap-biology-equations-and-formulas-exam-reference-information/314373/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ap-biology-equations-and-formulas-exam-reference-information/314373.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What statistical measures and variables are listed in the reference sheet?","Question",{"text":113,"@type":114},"The sheet lists sample mean (x), sample size (n), sample standard deviation (s), observed and expected results (o and e), and degrees of freedom. It also includes the mean, median, mode, and range definitions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which probability and genetics equations are provided?",{"text":118,"@type":114},"It provides probability laws for mutually exclusive events and independent events, plus a chi-square table template. It also includes Hardy–Weinberg equilibrium equations: p^2 + 2pq + q^2 = 1 and p + q = 1 with allele frequency definitions.",{"name":120,"@type":111,"acceptedAnswer":121},"What biological quantitative concepts are covered beyond statistics?",{"text":122,"@type":114},"It includes water potential relationships (pressure potential and solute potential) and the solute potential equation with ionization constant, concentration, gas constant, and temperature in Kelvin. It also provides growth-rate terms and Simpson’s diversity index.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},314373,1789967587,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39,"preview_page_count":4},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","AP® Biology  \n2026 EXAM REFERENCE INFORMATION  \nName:    \nNOTE: You may use any blank space in this booklet for scratch work during the exam. Proctors should collect this reference information at the conclusion of the exam.  \nAP® BIOLOGY EQUATIONS AND FORMULAS  \n\n| | Statistical Analysis and Probability\u003Cbr>Standard Deviation\u003Cbr>|  | x = sample mean n = sample size\u003Cbr>s = sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population)\u003Cbr>o = observed results e = expected results\u003Cbr>∑ = sum ofall\u003Cbr>Degrees of freedom are equal to the number of distinct possible outcomes minus one. |\n| --- | --- | --- | --- |\n| Standard Error of the Mean\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>|  | Chi-Square\u003Cbr>|  |\n| Chi-Square Table\u003Cbr>p\u003Cbr>value Degrees of Freedom 1 2 3 4 5 6 7 8 0.05 3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51 0.01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09\u003Cbr>Laws of Probability\u003Cbr>IfA and B are mutually exclusive, then:\u003Cbr>P(A or B) = P(A)+ P(B) IfA and B are independent, then:\u003Cbr>P(A and B) = P(A)× P(B)\u003Cbr>Hardy–Weinberg Equations\u003Cbr>p2 +2pq + q2 = 1 p = frequency of allele 1 in a population\u003Cbr>p + q = 1 q = frequency of allele 2 in a population |  |  |  |\n|  |  |  | Metric Prefixes\u003Cbr>Factor  Prefix  Symbol\u003Cbr>109 giga G\u003Cbr>106 mega M\u003Cbr>103 kilo k 10−1 deci d 10−2 centi c 10−3 milli m 10−6 micro µ 10−9 nano n 10−12 pico p |\n| Mode = value that occurs most frequently in a data set\u003Cbr>Median = middle value that separates the greater and lesser halves of a data set\u003Cbr>Mean = sum ofall data points divided by number of data points\u003Cbr>Range = value obtained by subtracting the smallest observation (sample minimum) from the greatest (sample maximum) |  |  |  |\n\nAP Biology 1  \n© 2025 College Board  \n\n| Rate and Growth |  | Water Potential ( )\u003Cbr>\u003Cbr> pressure potential\u003Cbr> solute potential\u003Cbr>The water potential will be equal to the solute potential of a solution in an open container because the pressure potential of the solution in an open container is zero.\u003Cbr>The Solute Potential of a Solution\u003Cbr>  −iCRT\u003Cbr>i = ionization constant (1.0 for sucrose because sucrose does not ionize in water)\u003Cbr>C = molar concentration\u003Cbr>R = pressure constant\u003Cbr>(R = 0.0831 liter bars/mole K) T = temperature in Kelvin (°C+273) |\n| --- | --- | --- |\n| | dY = amount of changedt = change in time\u003Cbr>dN = change in population size B = birth rate\u003Cbr>D = death rate N = population size K = carrying capacity\u003Cbr>rmax = maximum per capita growth rate of population |  |\n| Simpson’s Diversity Index\u003Cbr>\u003Cbr>Diversity Index =  ~~ ~~ \u003Cbr>n = total number of organisms of a particular species\u003Cbr>N = total number of organisms of all species\u003Cbr>|  |  |\n\nSurface Area and Volume  \nAP Biology 2  \n© 2025 College Board","cbCaibL1yZm7QGNM","https://ap.wps.com/l/cbCaibL1yZm7QGNM","pdf",2441682,"English","# AP® Biology Equations and Formulas\n## Statistical analysis and probability\n## Standard error of the mean and chi-square\n## Laws of probability and Hardy–Weinberg equations\n## Metric prefixes\n## Descriptive statistics: mode, median, mean, range\n## Water and solute potential\n## Growth and rate parameters\n## Simpson’s diversity index\n## Surface area and volume","[{\"question\":\"What statistical measures and variables are listed in the reference sheet?\",\"answer\":\"The sheet lists sample mean (x), sample size (n), sample standard deviation (s), observed and expected results (o and e), and degrees of freedom. It also includes the mean, median, mode, and range definitions.\"},{\"question\":\"Which probability and genetics equations are provided?\",\"answer\":\"It provides probability laws for mutually exclusive events and independent events, plus a chi-square table template. It also includes Hardy–Weinberg equilibrium equations: p^2 + 2pq + q^2 = 1 and p + q = 1 with allele frequency definitions.\"},{\"question\":\"What biological quantitative concepts are covered beyond statistics?\",\"answer\":\"It includes water potential relationships (pressure potential and solute potential) and the solute potential equation with ionization constant, concentration, gas constant, and temperature in Kelvin. It also provides growth-rate terms and Simpson’s diversity index.\"}]","AP® Biology - Equations and Formulas - Exam Reference Information | PDF",1789900651]