Download AP Biology Semester 1 Math Review Name: Statistics A study was

AP Biology Semester 1 Math Review
Name:
A. Statistics
1. 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.
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.
2. In a certain species of flowering plant, the purple allele P is dominant to the yellow allele p.
A student performed a cross between a purple-flowered plant and a yellow-flowered plant. When planted, the
146 seeds that were produced from the cross matured into 87 plants with purple flowers and 59 plants with
yellow flowers. Calculate the chi-squared value for the null hypothesis that the purple flowered parent was
heterozygous for the flower-color gene. Give your answer to the nearest tenth.
3. Grasshoppers in Madagascar show variation in their back-leg length. Given the following data, determine the
standard deviation for this data: Length(cm): 2.0, 2.2, 2.2, 2.1, 2.0, 2.4 and 2.5. Round the answer to the nearest
hundredth.
B. Hardy Weinberg:
4. 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.
What is the frequency of the dominant allele?
What is the frequency of the recessive allele?
How many individuals would you expect to be heterozygous for the trait?
5. 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?
6. Some people have the ability to taste a bitter chemical called phenylthiocarbamide (PTC). The ability to taste PTC
is due to the presence of at least one dominant allele for the PTC tast gene. The incidence of nontasters in North
America is approximately 45%. Assuming the population is in Hardy-Weinberg equilibrium, what percent of the
North American population is homozygous dominant for the ability to taste PTC? Provide your answer as a
number between 0 and 1 to the nearest hundredth.
Combine Hardy-Weinberg expectations with Chi Square Analysis
7. In a certain species of flowering plant, the red allele R is dominant to the white allele, r. A student carried out a
cross between a red flowered plant and a white flowered plant. When planted, the 158 seeds that were
produced from the cross matured into 92 plants with red flowers and 66 plants with white flowers. Calculate the
chi squared value for the null hypothesis that the red flowered parent was a hybrid for the flower color gene.
Give your answer to the nearest tenth.
red
white
Total
Observed
92
66
158
Expected
158
O-E
(O-E)2
(O-E)2/E
(O-E)2/E
8. 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.
Observed
Expected
O-E
(O-E)2
(O-E)2/E
black
78
blue
206
white
116
Total
(O-E)2/E
C. Genetics
9. An XxYYZZ parent mated with an xxYyZz parent. Assuming independent assortment of these three genes, what is
the chance for the offspring to be xxYyZZ?
10. A certain species of plant has four unlinked genetic loci, W, X, Y, and Z. Each genetic locaus has one dominant
allele and one recessive allele. For a plant with the genotype WwXxYyZz, what is the probability that one plant will
produce a gamete with a haploid genotype of Wxyz? Give your answer as a fraction or as a value between 0 and
1, to four decimal places.
11. In fruit flies, long wings (A) and gray bodies (B) are dominant to vestigial wings and black bodies. In a cross of
AaBb x aabb, the following results are obtained. Calculate the cross over value (recombination frequency) for the
offspring of the test cross.
123 long wing, gray body
21 long wing, black body
27 vestigial wing, gray body
129 vestigial wing, black body
D. Q10
12. Data taken to determine the effect of temperature on the rate of respiration in a goldfish is given in the table
below. Calculate Q10 for this data. Round to the nearest whole number.
Temperature (C)
Respiration Rate (Min)
16
16
21
22
E. Molarity
13. If a culture medium requires 3% sucrose, how many grams of sucrose would you need to use to make 100 ml of
this solution?
14. How many grams of sucrose do you need to make 250 mL of a 0.1 M solution? Molar mass of sucrose = 342.3
g/mol. Round to nearest hundredth.
15. Joe has a 2 g/L solution. He dilutes it and creates 3 L of a 1 g/L solution. How much of the original solution did he
dilute? Round to the nearest tenths.
16. If you dilute 174 ml of a 1.6 M solution of LiCl to 1 L, what is the new concentration of the solution?
F. Slope
17. Based on the data shown, calculate the average rate of increase in
oxygen consumption for animals acclimated to 5oC as the temperature
increases from 10oC to 30oC. Give the answer in mL O2/g/h/oC to the nearest
tenth.
18. The enzyme phosphofructokinase (PFK) is an allosterically regulated enzyme that catalyzes the following reaction.
Fructose-6-phosphate + ATP  Fructose-1,6-bisphosphate + ADP
The graph below shows that at certain concentrations ATP inhibits the enzyme, whereas AMP activates it.
According to the information presented in the graph, when the concentration of fructose-6-phosphate is 0.5 mM,
how many times more active is PFK in cells with 1 mM ATP + 0.1 mM AMP than in cells with 5 mM ATP?
Express your answer to the nearest whole number.
19. Use the graph above to calculate the mean rate of population growth (individuals per day) between day 3 and day
5. Give your answer to the nearest whole number.
20. 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
hundreds.
Time (mins)
Amount of O2
produced (mL)
1
2.3
2
3.6
3
4.2
4
5.5
5
5.9
G. Surface Area
21. In the Diffusion Lab, agar cubes are used to illustrate the relationship of surface area/volume/diffusion rate. Fill in
the values missing in the table
Block
cm x cm
Surface
Volume
Surface Area:Volume Ratio
Area cm ml
A
2x2
B
3x3
C
4x4
22. A typical human lymphocyte has a radius of about 10 μm, while a typical bacterium (e.g., S. pneumoniae) has a
radius of about 1 μm. Assuming that both cell types are perfectly spherical, how many times larger is the surface
area of a typical human lymphocyte compared to the surface area of a typical bacterium?
H. Gibbs Free Energy
23. An experiment determined that when a protein unfolds to its denatured (D) state from the original folded (F)
state, the change in Enthalpy is ΔH = H(D) – H(F) = 46,000 joules/mol. Also the change in Entropy is ΔS = S(D) – S(F)
= 178 joules/mol. At a temperature of 20⁰C, calculate the change in Free Energy ΔG, in j/mol, when the protein
unfolds from its folded state.
24. The following graph shows the effect of an enzyme on activation energy. Plot A is the progress of the reaction
without an enzyme, and plot B is the same reaction with an enzyme. Determine the Gibbs free energy change
(∆G) for the reaction. Express your answer to the nearest whole number.