AP Biology: Math for Dummies

1. AP Biology: Math for Dummies

2. Big Idea 1 The Process of Evolution Drives the Diversity and Unity of Life Change in the genetic makeup of a population over time is evolution. Organisms are linked by lines of descent from common ancestry. Life continues to evolve within a changing environment. The origin of living systems is explained by natural processes. Hardy-Weinberg Equations Probabilities

3. Big Idea 2 Biological Systems Utilize Free Energy and Molecular Building Blocks to Grow, Reproduce and Maintain Dynamic Homeostasis Growth, reproduction & maintenance of the organization of living systems require free energy & matter. Growth, reproduction & dynamic homeostasis require that cells create & maintain internal environments that are different from their external environments. Organisms use feedback mechanisms to regulate growth & reproduction & to maintain dynamic homeostasis. Growth & dynamic homeostasis f a biological system are influenced by changes in the system’s environment.. Many biological processes involved in growth, reproduction & dynamic homeostasis include temporal regulation & coordination. Water Potential Gibb’s Free Energy

4. Big Idea 3 Living Systems Store, Retrieve, Transmit and Respond to Information Essential to Life Processes Heritable information provides for continuity of life. Expression of genetic information involves cellular & molecular mechanisms. The processing of genetic information is imperfect & is a source of genetic variation. Cells communicate by generating, transmitting & receiving chemical signals. Transmission of information results in changes within and between biological systems. Chi square Gene Linkage

5. Big Idea 4 Biological Systems Interact and These Systems and Their Interactions Possess Complex Properties Interactions within biological systems lead to complex properties. Competition & cooperation are important aspects of biological systems. Naturally occurring diversity among & between components within biological systems affect interactions within the systems. Population Growth Energy Transfer Primary Productivity

6. 1. On the AP Biology Exam, you probably won’t have to do the actual count and identification; you will be given a data table and asked questions, like- From the data, calculate the percentage of time a cell spends in interphase Calculate the percentage of time a cell spends in mitosis

7. 2. Step 1- count the total # of cells 72 Step 2- divide 52/72 x 100 to get % of time spent in interphase 72% Step 3- Subtract 72% from 100% to get time spent in mitosis 28%

8. A Cellular Biologist wants to double check that statement that cells spend 90 percent of their time in Interphase as compared to the various stages of Mitosis. She grows some Allium in her laboratory. She then takes one of the plants, cuts off the root tips, stains the DNA in the cells so as to be able to see the stages of the cell cycle. Her hypothesis states “If cells spend 90 percent of their time in Interphase, then she should be able to calculate the relative time existing between Interphase and Mitosis based upon the cells counted in her specimen.” She counted 1000 cells from her preserved specimen under the microscope. Her data are shown below. Calculate the X2 to the nearest hundredth.

10. 3. To measure the population density of monarch butterflies occupying a particular park, 100 butterflies are captured, marked with a small dot on a wing and then released. The next day, another 100 butterflies are captured, including the recapture of 20 marked butterflies. What would you estimate the population to be? NOTE- this is not on your formula sheet! (100 x 100)/ 20 = 500

11. 4. Study this age structure diagram that shows the human population for India. What percent of the population is under 20?

12. 5. 2 x 2 = 4 6 x 4 = 24

13. The ability to taste PTC is due to a single dominant allele (A). 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? AA, Aa, aa 65/216 = .3 = q2 q = .55 p = .45 (.45)(.45) = .2 = 20% 20% x 215 = 43 AA 2(.45)(.55) = .495 = 50% 50% x 215 = 107 Aa

14. 7. 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, 64 show the dominant phenotype. What is the frequency of the recessive allele? .6 64 show the dominant phenotype, So 36 show the recessive phenotype. Since this is a population of 100, 36% Show the recessive phenotype .36 = q2 .6 = q

15. 8. Atmospheric pressure is the combined partial pressures of all of the gases that make up the atmosphere. At the summit of a high mountain, the atmospheric pressure is 380mm/Hg. The partial pressure of oxygen is 69mm/Hg. What percentage Of the atmosphere is made up of oxygen at this altitude? 18% 69/380 = .18 = 18% (the average partial pressure of oxygen at sea level is 21%)

16. 9. Cytosine makes up 12% of the nucleotides in a sample of DNA from an organism. Approximately, what percentage of the nucleotides in this sample will be thymine? 38% Remember Chargaff’s Law? Amount of A = T and C=G If 12% is cytosine, then 12% is guanine 76% is made up of adenine and thymine; divided equally between them

17. H2O HO H HO H HO H • 10. How many oxygen atoms would be in the polysaccharide that results from 100 glucose molecules being linked together by dehydration synthesis? 100 C6H1206 would give you 600 oxygen atoms 99 water molecules would be produced by dehydration synthesis Each water molecule contains one oxygen atom 600 - 99 = 501

18. 11. 1st 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)

19. 12.

20. 13. Geneticists working in an agriculture lab wanted to develop a crop that combines the disease resistance of rye grain with the high crop yielding capacity of wheat grain. Rye grain has a diploid chromosome number (2n) of 14 and wheat grain has a diploid chromosome number of 42. The resulting grain is called triticale and is an alloploidy plant. How many chromosomes are found in the pollen grain of triticale? Alloploidy results when two different plant species combine their diploid genome to make new and unique species. That would mean that this particular species would have 56 chromosomes. The cells in a pollen grain of would be haploid so the resulting number is 28.

21. 14. What is the water potential of a cell with a solute potential of -0.67 MPa and a pressure potential of 0.43 MPa? -.24MPa -0.67 + 0.43

22. How many naked ladies to you see in this picture?

23. 15. You measure the total water potential of a cell and find it to be -0.24 MPa. If the pressure potential of the same cell is 0.46 MPa, what is the solute potential of that cell? Since water potential is equal to the solute potential + the pressure potential, -0.24 MPa = 0.46 MPa + X. Solve for x= -0.7

24. 16. A wind blown pollen grain with a solute potential of -3.0 MPa has dried out somewhat after blowing around in the wind. This has caused its turgor pressure to go to zero. It lands on a flower stigma whose cells have a solute potential of -3.0 Mpa and a pressure potential of +1 Mpa. Which way will water flow? From the pollen grain to the stigma or the stigma to the pollen grain? Show how you deduced your answer.

25. 17. From the Osmosis/Diffusion Lab. Once the molar concentration of a sucrose solution has been determined, how would you determine the water potential of that sucrose solution? Work one to show how. Assume room temperature (22C). .4 -(1)(.4)(.0831)(295) = -9.8 Since this was done in an Open container, your pressure potential is 0, so the water potential is the same as the solute potential

26. 18. Use the Station 1 data to calculate the Primary Productivity of a water sample. Report your answer in units of mg Carbon fixed/Liter Station 1 4.2 mg O2/L  0.698 = 2.9 mL O2/L 2.9 mL O2/L  0.536= 1.6 mg Carbon fixed/L

27. 19. What is the mean rate of growth per day between day 5 and day 25? Record your answer to the nearest hundredth of a cm. If this same rate of growth continues, how tall will the plant be on day 50? Record your answer to the nearest hundredth of a cm. 18-3 = 15 15/20 days = .75 cm .75 x 25 = 18.75 18.75 + 18 = 36.75

28. A population of ground squirrels has an annual per capita birth rate of 0.06 and an annual per capital death rate of 0.02. Estimate the number of individuals added to (or lost from) a population of 1,000 individuals in one year. dN/dt = B-D Change in population size/time = Birth rate – Death rate 0.06 – 0.02 = 0.04 x 1000 = 40 individuals added per year

29. 21. In 2005, the United States had a population of approximately 295,000,000 people. If the birth rate was 13 births for every 1,000 people, approximately how many births occurred in the United States in 2005? 295,000,000/1,000 = 295,000 295,000 x 13 = 3,835,000

30. 22. A population of June beetles is estimated to be 3,000. Over the course of a month, there are 400 births and 150 deaths. Estimate r and calculate what the population size is predicted to be at the end of the month. Predict the population at the end of the second month. Birth rate = 400/3000 = 0.1333 births Death rate = 150/3000 = 0.0500 deaths r = birth rate – death rate = 0.1333 – 0.0500 = 0.0833 3000 x 0.0833 = 250 250 + 3000 = 3250 3250 x 0.0833= 271 271 + 3250 = 3521

31. A population of frogs exhibits logistic growth. If the carrying capacity is 500 frogsand r = 0.1 individuals (per month), what is the maximum population growth rate for this population? (Maximum population growth rate occurs when N = K/2) 12.5 K/2 = 500/2 = 250= N dN = rN(K-N) dT K 0.1 x 250 (0.5) = 12.5 individuals/month

32. 24. What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125? Find the mean Find the difference between the mean and each number (some will be + and some will be –) Square each difference (now they’re all +) Add them together Take the square root Bam! That’s it. Raise your hand if you need help.

33. I hate standard deviations.

35. 25. How many unique gametes could be produced through independent assortment by an individual with the genotype AaBbCCDdEE? Aa and Bb and Dd can each make 2. CC and EE can only make 1. 2 x 2 x 1 x 2 x 1 = 8

36. Assuming the genotype of F1 individuals in a tetrahybrid cross is AaBbCcDd. independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes? • aabbccdd • AaBbCcDd • AABBCCDD • AaBBccDd • AaBBCCdd AaBbCcDd x AaBbCcDd ¼ AA ½ Aa ¼ aa ¼ BB ½ Bb ¼ bb ¼ CC ½ Cc ¼ cc ¼ DD ½ Dd ¼ dd ¼ x ¼ x ¼ x ¼= 1/256 ½ x ½ x ½ x ½ = 1/16 ¼ x ¼ x ¼ x ¼= 1/256 ½ x ¼ x ¼ x ½ = 1/64 ½ x ¼ x ¼ x ¼ = 1/128

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38. Science Practices- The student can: -use representations & models to communicate scientific phenomenon & solve scientific problems. -use mathematics appropriately. -engage in scientific questioning to extend thinking or to guide investigations within the context of the AP course. -plan & implement data collection strategies appropriate to a scientific question. 5. -perform data analysis & evaluation of evidence. 6. -work with scientific explanations & theories. 7. -is able to connect & relate knowledge across various scales, concepts & representations in and across domains.

39. Experimental Design Pose scientific questions Refine scientific questions Evaluate scientific questions

40. Put your enzyme stuff here-

42. Justify the selection of the kind of data needed to answer a particular scientific question. Design a plan for collecting data to answer a particular scientific question. Collect data to answer a particular scientific question. Evaluate sources of data to answer a particular scientific question.

43. Analyze data to identify patterns or relationships. Refine observations and measurements based on data analysis. Evaluate the evidence provided by data sets in relation to a particular scientific question.

44. Science Practices- The student can: -use representations & models to communicate scientific phenomenon & solve scientific problems. -use mathematics appropriately. -engage in scientific questioning to extend thinking or to guide investigations within the context of the AP course. -plan & implement data collection strategies appropriate to a scientific question. 5. -perform data analysis & evaluation of evidence. 6. -work with scientific explanations & theories. 7. -is able to connect & relate knowledge across various scales, concepts & representations in and across domains.

45. Models & Representations 1. Create a model

46. 2. Describe what is taking place Specifically, describe the relationship between colony growth and sucrose concentration.

47. 3. Refine Model Using the model, calculate the water potential of the potato cores.

48. 4. Use and Apply The purpose of a particular investigation was to see the effects of varying salt concentrations of nutrient agar and its effect on colony formation. Below are the results Determine the mean for each treatment and graph the results.

50. What might you be asked to do with this graph? Describe the relationship between the salt concentration and colony growth 2. Predict the salt concentration that would allow no colony growth. Justify your answer.