AP Biology Math Review-Answers

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1 AP Biology Math Review-Answers There are many basic math skills that you must be able to do to work the more complex math problems in AP Biology. Use this as a review, to sharpen your skills, and gain some comfort in working with math and biology. Working with decimals, ratios, fractions and percentages Convert scientific notation to standard numbers Calculating rates or slopes Report your answer with the number of significant figures that the question requires 1. In a monohybrid cross, two heterozygotes are crossed and produce 345 offspring: You are supposed to know the ratio of a monohybrid cross; the problem probably won t tell you. a. What is your expected phenotypic ratio? 3:1 b. How many individuals are expected to have the dominant phenotype? 345 x.75 = 259 c. How many individuals are expected to have the recessive phenotype? 345 x.25 = In this genetic cross Aa x aa there are 714 offspring: Make a Punnett square to help you determine the ratio. a. How many individuals are expected to have the dominant phenotype? 714 x.5 = 357 b. How many individuals are expected to have the recessive phenotype? 714 x.5 = In a dihybrid cross between two heterozygotes, if you have 360 offspring, how many of each of the following? Make a Punnett square or understand that the ratio of any dihybrid cross is 9:3:3:1 a. Both dominant phenotypes 9/16 =.56 = 56%, 360 x.56 = 202 b. One dominant; one recessive 3/16 =.19 = 19%, 360 x.19 = 68 c. One recessive; one dominant 3/16 =.19 = 19%, 360 x.19 = 68 d. Both recessive phenotypes 1/16 =.06 = 6%, 360 x.06 = The following data was observed; fill in the missing values. Stage of the Cell Cycle Number of Cells in each stage % of Cells in each stage Interphase 62 62/117 = 53% Prophase 31 31/117 = 26% Metaphase 12 12/117 = 10% Anaphase 8 8/117 = 7% Telophase 4 4/117 = 3% 5. What percentage of the cells listed above are in mitosis? 47% (or 46% because of rounding) On the AP Biology exam, you will only be allowed to use a four function calculator. You will not be able to enter numbers using scientific notation. You must convert to standard numbers, then simply add or subtract (and maybe convert to percentages) to get the correct answer. Use the Energy flow diagram below. AP BIOLOGY EXAM REVIEW - KRABATH 1

2 6. What percentage of the biomass in the forest community is tied up in the grass layer? Give your answer to the nearest whole number. 9% see description below 1 st Law of Thermodynamics- energy cannot be created or destroyed, but it can change form: 18,000 energy accumulated as biomass; 12,000 going to the tree layer; 4,400 going to the shrub layer; 1,600 left, to go to the grass layer. 1,600 is 9% of 18,000 (1,600/18,000 x 100) NOTE: The question asked that you give your answer as a whole number. When you do the calculation, you probably got What percent of country 1 is under the age of 20? 55% The answer range is 45% - 55% which is determined by looking at the population pyramid. 8. Use the graph to the left to calculate the mean rate of population growth (individuals per hour) between hours 6 and 9. Give your answer in the nearest whole number. 12 per hour = 36 (Population change) /3-hour time change 36/3 = 12. The word mean in this question confuses some students AP BIOLOGY EXAM REVIEW - KRABATH 2

3 9. The graph shows the growth in cm of a pea plant over a period of 5 weeks. What was the mean growth rate per day between week 1 and week 3? Give your answer to the nearest tenth. 3.6 days = 50 height change)/ 14 days are in 2 weeks 50/14 = 3.6 days Use the graph on Atmospheric Carbon Dioxide levels to: 10. Calculate the rate of increase in CO 2 production from 1974 to Record your answer to the nearest tenth. 1.7 ppm/year; see below for explanation 11. What will be the approximate CO 2 concentration in 2100? Record your answer to the nearest whole number. 154 ppm; see below for explanation AP BIOLOGY EXAM REVIEW - KRABATH 3

4 Hardy-Weinberg Problems: 12. The allele for the hair pattern called widow s peak is dominant over the allele for no widow s peak. In a population of 100 individuals, 91 show the dominant phenotype. 91 have a widow s peak & 9 don t (don t miss this step!!) 9 =.09% = q2 q =.3 p =.7 a. What is the frequency of the dominant allele?.3 b. What is the frequency of the recessive allele?.7 c. How many individuals would you expect to be heterozygous for the trait? 2(.3)(.7) =.42 = 42% = The ability to taste PTC is due to a single dominant allele (T). You sampled 215 individuals in biology and determined that 150 could taste PTC and 65 could not. How many individuals in this population show the following genotype? Give your answer to the nearest whole number. a. TT 44 Of the 150, some are TT and some are Tt. b. Tt 106 The answer to tt is given in the problem, it is 65 c. tt 65 65/215 =.30 (students will skip this step!) 3 = q2; q =.55 p =.45 Check your answer by seeing if this adds up to In a population of robins in which the allele for dark head plumage is dominant to the allele for light head plumage, a cold winter leads to the selection against lighter head plumage. When the winter is over, 8% of the remaining birds exhibit light head plumage. If the population is now in Hardy-Weinberg equilibrium, what will be the frequency of the light head plumage in the next generation? Give your answer to the nearest tenth..3 8% =.08 = q2 q = In a certain population of deer on Fire Island, NY, the allele for a black spot behind the eye is dominant to the allele for no spot. After the hunting season, the percent of deer with no black spot is 17% and the population is in Hardy-Weinberg Equilibrium. What is the frequency for the allele for having no black spot, to the hundredths?.41 17% =.17 = q2 q =.41 Combine Hardy-Weinberg expectations with Chi Square Analysis: 16. In poultry, the autosomal gene FB produces feathers black in color and another allele, FW, produces white feathers. The heterozygous condition produces feathers of blue color. When a population of white hens was mated to black roosters, the resulting offspring were all blue. These blue offspring were mated with one another. The F2 generation yielded 78 black, 206 blue, and 116 white chickens. Determine the frequency of each allele in the F2 population. Determine if the population is in Hardy-Weinberg equilibrium by calculating the chi-squared value. Give your answer for χ2 to the nearest hundredth. FB =.45 and FW =.55 AP BIOLOGY EXAM REVIEW - KRABATH 4

5 Sample FRQs: 17. A study was conducted on the island of Daphne Major in the Galapagos Islands by Peter and Rosemary Grant. This study lasted over 20 years. The study investigated how the type of seeds available to the finches impacted the depth of their beaks. In years when rain and water were plentiful, the available seeds were smaller and easy to crack. In years experiencing drought, fewer seeds were produced, and the finches had to eat the larger, leftover seeds produced from previous years. During years of drought, birds with a greater beak depth had a selective advantage. a. Use the data above to determine the increase in the mean of the depth of the beak between the wet and dry years. Give your answer to the nearest hundredth of a millimeter mm AP BIOLOGY EXAM REVIEW - KRABATH 5

6 18. How much carbon (g/m 2 ) is released into the atmosphere as a result of the metabolic activity of herbivores? Give your answer to the nearest whole number. 42 g/m2 100 going to Herbivores; subtract 58 which is the total leaving, 8 to predators and 50 to decomposers. 19. A large population of laboratory animals has been allowed to breed randomly for a number of generations. After several generations, 36% of the animals display a recessive trait (aa), the same percentage as at the beginning of the breeding program. The rest of the animals show the dominant phenotype, with heterozygotes indistinguishable from the homozygous dominants. What is the estimated frequency of allele a in the gene pool? Record your answer to the nearest hundredth..36 = q2 so q = In a hypothetical population of 1,000 people, tests of blood-type genes show that 160 have the genotype AA, 480 have the genotype AB, and 360 have the genotype BB. What is the frequency of the A allele? p2 = 160/1000 =.16 there for p =.4 What percentage of the population has type O blood? 0% The o allele is not shown the population If there are 4,000 children born to this generation, how many would be expected to have AB blood under the conditions of Hardy-Weinberg equilibrium? p =.4 then q =.6 so 2pq = 2(.4)(.6) =.48.48(4000) = 1, Upon chemical analysis, a particular protein was found to contain 556 amino acids. How many peptide bonds are present in this protein? Starting with a fertilized egg (zygote), a series of five cell divisions would produce an early embryo with how many cells? Cytosine makes up 38% of the nucleotides in a sample of DNA from an organism. Approximately, what percentage of the nucleotides in this sample will be thymine? 12% remember Chargaff s rule that the percentage of A = T and the percentage of C = G. Also the total of each must equal 100%. Therefore, G =38% C =38% A = 12 % and T =12%12% 24. A population of ground squirrels has an annual per capita birth rate of 0.06 and an annual per capita death rate of Estimate the number of individuals added to (or lost from) a population of 1,000 individuals in one year. Birthrate of 0.06 death rate of.02 =.04 therefore.04 x 1,000 = 40 added ,000 kcal of producer would support approximately kcal of tertiary consumer. 10 kcal Draw a trophic diagram and apply the 10% rule AP BIOLOGY EXAM REVIEW - KRABATH 6