Name_________________________________________Period_____Assignment #_____

AP Biology Math Review

Lab 00 Mendelian GeneticsWhat is the null hypothesis (H0) in a genetic cross?

You null hypothesis for a genetic cross will always be the difference between the observed and expected ratio is due to chance. If the chi square statistic (χ2) is less than or equal to a p-value of 0.05 than the difference is significant and we reject the null hypothesis and accept the alternative hypothesis (HA). The alternative hypothesis is always some other mode of inheritance is causing the inheritance pattern. If we reject the null hypothesis, we are saying that the probability of getting the results we did by chance is 5% or less.

You don’t need to memorize how to calculate the chi square statistic (χ2), but you need to be able to state a null hypothesis, calculate the chi square statistic, and interpret the results in terms of p-value. You also may be given a p-value form a t-test of some other statistical test, but all you need to do is use the same logic for your interpretation.

1) In cattle, roan coat color (mixed red and white hairs) occurs in the heterozygous (Rr) offspring of red (RR) and white (rr) homozygotes. What parental genotypes would produce the following results? 893 red, 1,856 roan, and 813 white. Test you answer with a Chi square test and support your answer with a discussion of the resulting p-value.

See What determines sex ratio? Lab, Lab #12 (Virtual Animal Behavior), and Lecture #153

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2) Yellow seed color is dominant to green seed color and smooth seed coat are dominant to yellow seed color and wrinkled seed coat. A test cross was conducted between a plant with an unknown genotype. The following phenotypes of the offspring were counted: 451 yellow/smooth, 501 yellow/wrinkled, 401 green/smooth, and 425 green/wrinkled. What is the genotype of the unknown plant? Test you answer with a Chi square test and support your answer with a discussion of the resulting p-value.

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3) The genotype of F1 individuals in a tetrahybrid cross is AaBbCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes? Show your work.

See lecture #153

a. Aabbccdd

b. AaBbCcDd

c. AABBCCDD

d. AaBBccDd

e. AaBBCCdd

4) Phenolketonuria (PKU) is an inherited disease caused by a recessive allele. If a woman and her husband, who are both carriers, have three children, what is the probability of each of the following?

a. All three children are of normal phenotype

b. One or more of the three children have the disease.

c. All three children have the disease.

d. At least one child is phenotypically normal.

5) Red/green color blindness is an X-linked trait. What is the probability of a having a child that is male or having a color blind child if the mother is heterozygous and the father sees color?

See lecture #’s 153 and 156

6) Red/green color blindness is an X-linked trait. What is the probability of a having a child that is male and color blind child if the mother is heterozygous and the father sees color?

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7) In 1981, a stray black cat with unusual rounded, curled-back ears was adopted by a family in California, Hundreds of descendants of the cat have since been born, and cat fanciers hope to develop the curl cat into a show breed. Suppose you owned the first curl cat and wanted to develop a true-breeding variety.

How would you determine whether the curl allele is dominant or recessive?

How would you obtain true-breeding curl cats?

8) Imagine that you are a genetic counsel, and a couple planning to start a family comes to you for information. Charles was married once before, and he and his first wife had a child with cystic fibrosis. The brother of his current wife, Elaine, died of cystic fibrosis. What is the probability that Charles and Elaine will have a baby with cystic fibrosis? (Neither Charles, Elaine, nor their parents have cystic fibrosis.) Show your work!

A planet is inhabited by creatures that reproduce with the same hereditary patterns seen in humans. Three phenotypic characters are height (T = tall, t = dwarf), head appendages (A = antennae, a = no antennae), and nose

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morphology (S = upturned snout, s = downturned snout). Amoral Earth scientists do some controlled breeding experiments using various heterozygotes in testcrosses.

See Lecture #157

9) For heterozygotes that are tall/antennae, the offspring were tall/antennae, 46; dwarf/antennae, 7; dwarf/no antennae, 42; and tall/no antennae, 5. Calculate the recombination frequency.

10) For heterozygotes with upturned snout/antennae, the offspring were upturned snout/antennae, 47; downturned snout/antennae, 6; upturned snout/no antennae, 5; and downturned snout/no antennae 48. Calculate the recombination frequency for the experiment.

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11) They do another testcross using a heterozygote for height and nose morphology. The offspring are tall/upturned snout, 55; dwarf/upturned snout, 17; dwarf/downturned snout, 50; and tall/downturned snout, 13. Calculate the recombination frequency from this data.

12) Using your testcross data above, determine the genetic map for height, antennae, and nose morphology.

Lab 01 Artificial Selection

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Lab 02 Population Genetics

For the problems below assume the population is in Hardy-Weinberg equilibrium, all genes have only two alleles, and there is a simple dominant recessive relationship. Show your work!

See Lab #2 (Virtual Hardy-Weinberg)

13) If 98 out of 200 individuals in a population express the recessive phenotype, what percent of the population would you predict would be heterozygotes?

14) Lets say that brown fur coloring is dominant to gray fur coloring in mice. If you have 168 brown mice in a population of 200 mice what is the percent heterozygous?

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15) If 81% of a population is homozygous recessive for a given trait what is the frequency of the dominant allele?

16) If 51% of the population carries at least one copy of the recessive allele what is the percent homozygous dominant?

Lab 03 Comparing DNA Sequences Using BLAST

Lab 04 Diffusion and Osmosis17) The molar concentration of a sugar solution in an open beaker has been

determined to be 0.2M. Calculate the solute potential at 73 C. Round your ̊ answer to the nearest hundredth.

See lecture #45, Lab #4 Diffusion and Osmosis, and Lab #4 Virtual Diffusion and Osmosis

18) If the water potential is -3 bars and the solute potential is -5 bars, what is the pressure potential?

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19) If a cell is in equilibrium with its surrounding environment, and the solute potential on the outside of the cell is -8, what is the pressure potential?

20) At 36°C, a cell with ΨP of 9 bars is in equilibrium with the surrounding 0.35M solution of sucrose in an open beaker. What is the molar concentration in the cell?

21) Use the graph below to answer the following questions. It shows the percent change in mass of potato cores in different concentrations of sucrose.

22) What it the molarity of the potato cells?

23) Why did the potato cells gain mass at 0.2 and 0.4 molarity?

24) Why didn’t the potato cells gain more mass in a 0.2 molar solution than they did in the 0.4 molar solution?

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Lab 05 Photosynthesis25) Calculate the Rf values for all of the pigments shown in the chromatograph

See Lab #5 Virtual Photosynthesis

Rf= Distancemoved by pigmentDistance solvent moved ¿

sample ¿

If DPIP is in an oxidized state, it will be blue, and the percentage of light transmitted will be low. If, on the other hand, chlorophyll's electrons have been excited and move on to reduce the DPIP, the sample will become progressively paler, allowing more light energy to pass through the sample. We can measure this change over time until the sample has been completely reduced, is almost colorless, and the percentage of transmittance is very high.

26) Compare the rate of photosynthesis at 5 minutes to the rate at 10 minutes

27) What can be said about the rate of photosynthesis at 25 minutes?

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Lab 06 Cellular Respiration

28) What is the DIFFERENCE in respiration rate for germinating corn at 22°C and germinating corn at 1 C22 2 ̊

See Lab #6 Virtual Cellular Respiration

Lab 07 Mitosis and Meiosis29) You observe 20 onion root tip cells in interphase, 10 in prophase, 3 in metaphase, 2 in anaphase, and 1 in

telophase. If the cell cycle of an onion root tip can be completed in 24 hours, how long does the cell spend in each phase? How much time does mitosis require? Show your work!

See Lab #7 Virtual Mitosis and Meiosis

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Lab 08 Transformation30) After doing a transformation and incubating the pate for 48 hours, Billy is excited to see if the transformation

worked. He counts 120 glowing colonies on his plate. He knows that the concentration of the plasmid DNA provided was 0.3 µg/µL. In the protocol he followed, he used 200 µL of calcium chloride, 10 µL of plasmid, and 250 µL of LB broth. He spread 75 µL of cells on the LB ampicillin agar plate. Calculate Billy’s transformation efficiency.

TE=Number of transformed colonieson LBampicillin plateMass∈μgof plasmid DNAused

Mass∈μg of plasmid DNAused=Mass∈μg of plasmid added ¿ themicrotube X Fractionof tube volume spreadon plate

Mass∈μg of plasmid added ¿ themicrotube=Plasmid∈ μgμL

X volume of plasmid∈μL

Fractionof tube volumespread on plate= volume spread on plate∈μLtotal volume∈tube∈μL

See lab #8 Transformation

31) If a particular experiment were known to have a transformation efficiency of 4 X 102 bacteria/µg of plasmid DNA, how many transformant colonies would be expected to grow on the LB amp plate? You can assume that the concentration of plasmid DNA, the volume of plasmid DNA, and the fraction of cells spread on the LB amp agar are the same as in previous question.

Lab 09 ElectrophoresisSee lab 9 Electrophoresis and lab 9 Virtual Restriction Enzyme Analysis

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Lane 1 base pair lengths (6751, 3652, 2827, 1568, 1118, 825, 630)

32) Lane 2 base pair length

33) Lane 3 base pair lengths

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Use the standard curve to determine the fragment lengths of the bands in lane 3

Use the standard curve to determine the fragment length of the band in lane 2

This is the standard ladder. Use this lane to plot your standard curve on the semi log graph below.

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Lab 10 Energy Dynamics34) List the data you would need to collect to determine the amount of energy lost to respiration by a primary

consumer (herbivore)? Explain why you would need each bit of data.See lab 10 Energy Dynamics Dry Lab and lab 10 Virtual Energy Dynamics

35) Imagine we run an experiment on a marine diatom (a type of algae). We place equal amounts of the diatom species in light and dark settings, and measure their starting weight (using an identical third sample) and dry it out. After one week, we end up with the following data.

What is the percent moisture of the samples, and the NPP, respiration, and GPP of the species of diatom? Express your answer in grams per bottle.

Week Wet weight (g) Dry weight (g)Start 14 9.0One week later 18 11.7 (light bottle)One week later 11 7.15 (dark bottle)

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36) Eleven cabbage butterfly larvae were grown on mustard plants. The wet mass of a mustard plants on day 1 was 1016.6g. On day 5 the wet mass was 552.6g. The dry mass was 138.8g on day 5. The wet mass of the cabbage butterfly larvae was 1.4g on day 1 and 6.8g on day 5. The dry mass of the larvae was 1.3g. The frass mass (waste produced by the larvae) was 1.8g. The mustard plants contain 4.35 kcal/g, the larvae contain 5.5 kcal/g, and the fass contains 4.75 kcal/g. How much energy was lost to cellular respiration per larva?

37) On average, how much energy is transferred from one trophic level to the next?

See lecture #12

38) How much phytoplankton mass does it take for a blue whale to gain 358 pounds.

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39) Suppose a killer whale has 2,718,000 kcal of energy. What is the minimum energy from primary productivity consumed by the killer whale?

40) How much blue whale mass can be made from 1000 pounds of phytoplankton mass?

41) How much killer whale mass can be made from 1000 pounds of phytoplankton mass?

See lab #10 Virtual Energy Dynamics

42) What is the % oxygen saturation of water with 8ppm (parts per million) at 18°C?

43) What is the % oxygen saturation of water with 8ppm (parts per million) at 27°C?

44) How would you measure respiration rate using BOD bottles (biological oxygen demand bottles)?

45) How would you measure gross productivity rate using BOD bottles (biological oxygen demand bottles)?

46) How would you measure net productivity rate using BOD bottles (biological oxygen demand bottles)?17

47) Calculate the carbon fixed at 50% light

48) Calculate the carbon fixed if the net productivity is 4.5 mg O2/L

49) How much oxygen was consumed for cellular respiration in plants grown at 75% light?

Lab 11 Transpiration 50) The shamrock to the right is on 1cm X cm grid paper. What is its surface area?

See Lab 11 Transpiration and Lab 11 Virtual Transpiration

51) The leaf from the previous question was placed in a photometer for 45 minutes. The water in the photometer decreased by 15mL. Calculate the water loss in mL/cm2/hour

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Population Ecology

52) There are 115 deer in a 32km X 3km sector. There is no immigration or emigration. If 34 deer die and 15 are born in one month, what is the population density at the end of the month?

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In a population of 550 squirrels, the per capita birth rate in a particular period is 0.04 and the per capita death rate is 0.18.

53) What is the per capita growth rate of the population?

54) What is the number of squirrels that die during this particular period?

55) What is the actual number of squirrels that are born during this period?

Suppose that 180 rats of a cohort within a colony where born in January. At the start of March, 170 are still alive, and 90 are still alive at the start of May.

56) What is the survivorship rate up to the start of March?

57) What is the mortality rate from the beginning of March to the beginning of May?

58) If the survivorship during May is 0.25, how many rats died during that month of May?

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59) A population of 215 swans was introduced to Circle Lake. The population’s birth rate is 0.3 swans/year per capita, and the death rate is 0.25 swans/year per capita. What is the rate of population growth per capita, and is it increasing or decreasing?

60) A population has a carrying capacity of 1,750 individuals and an rmax of 0.5/year. What is the population growth after one year with a starting population of 1,500?

61) A population has a carrying capacity of 1,750 individuals and an rmax of 0.5/year. What is the population growth after one year with a starting population of 1,750?

62) A population has a carrying capacity of 1,750 individuals and an rmax of 0.5/year. What is the population growth after one year with a starting population of 2,050?

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