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Equation Practice The following problems test your ability to use math to solve biology problems and analyze data. You will need to use your AP Biology Equations and Formulas sheet (Appendix
B in Curriculum Framework) to help you solve each problem.
1. In corn seedlings, the seedlings can be green (dominant) or albino (recessive). A green parent (GG) is crossed with an albino parent. All of the F1 offspring are green. The F1’s are mated to produce F2’s.
(a) Show the Punnett square for this cross in the space below.

(b) The results of the F1 cross are 72 green F2 seedlings and 12 albino seedlings. Using the table below, calculate the Chi­square for the results of the F1 cross. Phenotype Genotype

# Observed

# Expected (e)

(o­e)

2
(o­e)

2
(o­e)
/e

Green

GG or Gg

72

Albino

gg

12

2
2
χ = ∑(o­e)
/e
(c) Using your formula sheet, find the critical value for this Chi­square. What is the probability of these results? Are the results acceptable? Explain

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2. An investigator observes that when pure­breeding long­wing
Drosophila are mated with pure­breeding short­wing flies, the F1 offspring have an intermediate wing length. When several intermediate wing length flies are allowed to interbreed, the following results are obtained. Observed
230 long wings
510 intermediate wings
260 short wings
(a) Write a hypothesis describing the mode of inheritance of wing length in
Drosophila
(this is your null hypothesis).

(b) Complete the table below using the data above. (o­e)

2
(o­e)

2
(o­e)
/ e Phenotype

Genotype # Observed

# Expected (e)

2
2
χ = ∑(o­e)
/e

(c) Using your formula sheet, find the critical value for this Chi­square. How many degrees of freedom are there? What is the probability value (p) for these data? According to the analysis, can you accept or reject your null hypothesis? Explain

3. As a result of photosynthesis, a plant cell becomes saturated with glucose at a concentration of 0.1 moles/Liter. Glucose does not ionize in water (ionization constant of 1).
Because of the plant cell’s wall, however, water pressure builds up at 3.2 bars at a temperature of 20º Celsius. is Calculate the water potential of this cell. Show your work below.

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4. In the guard cells of a leaf, potassium chloride, KCl, is an essential solute that dissolves into two ions, K+ and Cl­. The K+ ions lower the water potential of the the vacuole which drives the opening of the stoma. Calculate the water potential of a guard cell with a KCl concentration of 0.3M, a temperature of 18º C (assume no measurable water pressure).

5. A mammalian intestinal cell has a square column shape with the following dimensions: length:
16 μm width:
12 μm height:
12 μm
An alveolus from the same mammal has a spherical shape with a radius of 4 um.
(a) Which cell type has the greater surface area? How many times greater is that cell’s surface area compared with the other cell?

(b) What is the surface area:volume ratio of each cell type?

6. You are monitoring a population of wild lupine plants in an area above the foothills. After one year of mapping, tagging and sampling the population, you obtain the data listed below.
Initial number of plants (N): 500 Number of new seedlings established: 100 Number of the initial plants that died: 20
(a) Calculate the B (birth rate) by dividing the number of births from the initial population: (b) Calculate the D (death rate) by dividing the number of deaths from the initial population: (c) Calculate r
(rate of growth) by B­D (subtract the death rate from the birth rate): max (d) To estimate the population size N after growth (dN), add 1 + r: (e) Using your r and assuming exponential growth, what would the population of