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AP Biology Math Review 2014

AP Biology Math Review 2014. Get an APPROVED calculator and formula sheet. 2) Pick a grid sheet. You will solve each problem and grid in the answer. Tips. Grid LEFT to right Use the formula sheet Don’t round until the end Look at HOW the answer should be given “round to nearest…”

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AP Biology Math Review 2014

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  1. AP Biology Math Review 2014 Get an APPROVED calculator and formula sheet. 2) Pick a grid sheet. You will solve each problem and grid in the answer.

  2. Tips • Grid LEFT to right • Use the formula sheet • Don’t round until the end • Look at HOW the answer should be given “round to nearest…” Ex: answer = .123

  3. Q1: Laws of Probability • Calculate the probability of tossing three coins simultaneously and obtaining three heads. • Express your answer as a fraction.

  4. Q1: Probability Answer

  5. Q2: Surface Area and Volume • What is the SA/V ratio for this cell? Round your answer to the nearest hundredths.

  6. Q2: SA / Volume Ratio Answer SA = (equation) = Volume of a sphere = (equation) = SA/V ratio=

  7. Reminder: • Fluids must touch the membrane of the cell to diffuse in. • Cells need a large SA to Vol ratio so that fluids move in quickly enough to all parts to keep the cell alive. • Cells are small due to metabolic demands.

  8. Q3: Metric Conversions • Convert 158 centigrams to milligrams. • Convert 12 centimeters to meters.

  9. Q3: Metric Conversions Answer K H D basic unit D C M (king hector died _ drinking chocolate milk) Every step is 10X greater (right) or smaller (left). • Convert 158 centigrams to milligrams. = • Convert 12 centimeters to meters. =

  10. Q4: Acids/Bases - pH • What is the hydrogen ion concentration of a solution with a pH 3? • What is the pH of a solution with an [OH-] of 10-9 Remember: pH scale is a -log 10 scale

  11. Q4: pH Answers pH 3 = [H+] = [OH-] = [H+] as a decimal = [OH-] of 10-9 [H+] = = pH

  12. Remember: Acids (pH 0-6) release H+ into solutions so they have high [H+] ex. HCl Bases (pH 8-14) remove H+ or add OH- to solutions so they have a low [H+] ex. NaOH

  13. Q5: Mean, Median and Mode • Grasshoppers in Madagascar show variation in their back-leg length. • Given the following data, determine the mean, median and mode values. • Round the answer to the nearest tenths Length(cm): 2.0, 2.2, 2.2, 2.1, 1.9, 1.8, 2.5

  14. Q5: Mean, Median and Mode Answer • Order the data: • Mean (average) = • Median = • Mode =

  15. Q6:Standard Deviation • Using the previous data, determine the standard deviation. Round the answer to the nearest hundredths. STANDARD DEVIATION describes how much variation there is in your sample around your mean value. If the value is high it means that individual data points in your sample vary a lot from your mean - this is bad as it reflects poor precision in your experiment. Length(cm): 2.0, 2.2, 2.2, 2.1, 1.9, 1.8, 2.5

  16. Q6: Standard Deviation Answer Data: 2.0, 2.2, 2.2, 2.1, 1.9, 1.8, 2.5 • Mean (Avg) = 2.1 • Dev = • Dev Squared = • Sum of the deviations squared =

  17. Q7: Hardy Weinberg Question • In a population of 250 peas, 84% have smooth skin which is the dominant phenotype. • How many peas have wrinkled skin (recessive phenotype)? • How many of the total alleles in the population are dominant?

  18. Hardy Weinberg Strategy • Figure out where the data you are given fits in the equation. • Allele frequency (p or q) = top row • Genotypes/phenotypes (p2, 2pq, q2) = bottom row • Figure out what you are solving for ---- • Always answer in decimals.

  19. Q7: HW Answer 250 peas: 84% dominant, _______recessive Homozygous recessive q2 = 250 * ______= ________are wrinkled q = q =p+q = 1 p = _____________of alleles are dominant

  20. Q8: Rate of a Reaction Hydrogen peroxide is broken down to water and oxygen by the enzyme catalase. The following data were taken over 5 minutes. What is the rate of enzymatic reaction in mL/min from 2 to 4 minutes? Round to the nearest hundredths Remember: 1st column in a data table = X axis (independent variable)

  21. Q8: Rate of Reaction Answer Rate = slope! (x2-x1 / y2-y1) • Rise/run = rate =

  22. Q9: Population Growth N = total number in pop r = rate of growth rmax = max growth rate of population • There are 2,000 mice living in a field. • If 1,000 mice are born each month and 200 mice die each month, what is the per capita growth rate of mice over a month? • Round to the nearest tenths.

  23. Q9: Population Growth Answer • N = 2000 1000 born, 200 die/month • b = • m= • rmax= (rate)

  24. Population Growth Q#2 • In 2009, the US had a population of about 307 million people. If there were 14 births and 8 deaths per 1000 people, what was the country’s net population growth that year (ignoring immigration/emmigration)?

  25. Population Growth Q2 Answer • 307 million people 14 born, 8 die/1000 b = m = Growth rate = 307million * ____________________ = increase of __________________________ people

  26. Q10: Chi Square Analysis • A heterozygous red eyed female was crossed with a red eyed male. The results are shown below. Red eyes are sex-linked dominant to white eyes, determine the chi square value. Round to the nearest hundredths.

  27. Chi Square Strategy • Given= what is observed • You have to figure out expected. Usually to do a Punnett square to figure this out. • Plug in data + +

  28. Expected: Q10: Chi Square Answer Observed: 134 red eyes, 66 white eyes = 200 total red white XR Xr + XR XR XR Xr XR XR Xr Y Y Y + _________ expected ratio 134+ 66 = 200 total flies _____ red expected _____ white expected

  29. Chi Square Q#2 • In pea plants, smooth seeds are dominant to wrinkled seeds, and purple flowers are dominant to whiteflowers. • In a dihybrid cross where a 9:3:3:1 ratio is expected, the following data was collected. Smooth and Purple= 223 Smooth and White= 84 Wrinkled and Purple= 89 Wrinkled and White= 33 • Determine the chi-square value.

  30. Chi Square #2 Answer Observed 223 84 89 33 = 429 Expected Do the math… X2 = df= n-1 = Critical value = Explain if you accept or reject your null hypothesis:

  31. Q11: Solute Potential Solute potential= –i CRT • i = The number of particles the molecule will make in water; for NaCl = 2; for sucrose or glucose = 1 • C = Molar concentration (from your experimental data) • R = Pressure constant = 0.0831 liter bar/mole K • T = Temperature in degrees Kelvin = 273 + °C of solution Sample Problem • The molar concentration of a sugar solution in an open beaker has been determined to be 0.3M. Calculate the solute potential at 27C. Round your answer to the nearest tenths.

  32. Q11: Solute Potential Answer Solute potential= – i CRT -i = C = R = pressure constant = T= Solute concentration=

  33. Q12: Water Potential • Scientists are trying to determine under what conditions a plant can survive. They collect data and would like to know the water potential of the plant cell. Solute potential = -0.6 MPa Pressure potential is -1.0MPa. What is the water potential?

  34. Remember: • Water potential = pressure potential + solute potential (always a neg. #) • Water potential is potential for water to move. Water moves hypo-hyper or from areas of high water potential (more water) to low water potential (less water).

  35. Q12: Water Potential Answer • Water potential = * If placed in pure water (0MPa) the water would move ________________ the plant cell.

  36. Q13: Temp Coefficient Q10 • Data collected to determine the effect of temperature on the rate of respiration in a goldfish are given in the table below. • Calculate the temperature coefficient Q10 for this data. Round to the nearest whole number.

  37. What is Q10? • The Q10 temperature coefficient is a measure of the rate of change of a biological system as a consequence of increasing the temperature by 10°C. • For most biological systems, the Q10 value is ~ 2 to 3

  38. Q13: Temp Coefficient Answer Calculate the temperature coefficient Q10for this data. Round to the nearest whole number. Q10=

  39. Q14: Dilution of Solutions • Dilution - used to create a dilute solution from a concentrated stock solution CiVi= CfVf C = concentration of solute i = initial (starting) f = final (desired) V = volume of solution

  40. Q14: Dilution of Solutions • Joe has a 2g/L solution. He dilutes it and creates 3L of a 1g/L solution. How much of the original solution did he dilute? Round to the nearest tenths.

  41. Q14: Dilution Answer Joe has a 2g/L solution. He dilutes it and creates 3L of a 1g/L solution. CiVi = CfVf C = concentration of solute i = initial (starting) f = final (desired) V = volume of solution

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