Math+Review+2013

= Math Review 2013 =

Choose from the following types of problems. Make sure to include associated biological concept.


 * Hardy Weinberg
 * Ch Square
 * Population Growth
 * Surface Area and Volume
 * Water Potential
 * Solute potential
 * Gibbs Free Energy
 * Probability
 * Statistics (Mean, range, etc.)
 * Dilution

Problem #1 (submitted by Mrs. McLoughlin)

Concept 2A.3: Surface area to volume ratios affect a biological system's ability to obtain necessary resources or eliminate wastes.

Compare the following two cells. Which cell would be more successful in obtaining nutrients? Justify your answer and show all work Cell #1 (a cube) = 4 X 4 X 4 microns Cell #2 (a rectangle) = 1 X 4 X 16 micron

Hardy Weinberg - Gabriela Christian 4.C.3, c: Allelic variation within a population can be modeled by the Hardy Weinberg equation(s).

In a certain plant population, the allele for white flowers is dominant over the allele for purple flowers. In a population of 200 individuals, 16% show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait?

Dilutions - Emily Bernardi This is more of a Chemistry subject but I thought it would be an interesting topic to review considering it is a basic knowledge needed for Biology.

How much 2.0 Molar of NaCl solution would be needed to make 250 mL of 0.20 Molar NaCl solution?

Brian Millham Water Potential Calculate the water potential when the molarity of sucrose is 1.5 Mol/Liter. Sucrose's ionization constant is 1. The Temperature of the experiment was 20 degrees celcius and the pressure constant was 0.0831 liter bars/mole K.

Statistics- Christina Dykas Appendix A Big Idea 4 Letter f

In an environment, temperatures were recorded at 8 am for 10 days in a row. The recorded temperatures were 22, 27, 25, 22, 18, 24, 25, 21, 20, and 20 degrees. What is the range of the temperatures, the mean of the temperatures, and the mode of the data?

Chi Square- Kenna Garrison In flies, a solid body is dominant over a striped body and green eyes are dominant over blue eyes. A heterozygous solid bodied green eyed fly is crossed with a striped bodied blue eyed fly. The resulting offspring are 231 solid body/green eyes, 35 solid body/blue eyes, 228 striped body/blue eyes, and 41 striped body/green eyes. Using a chi square analysis, determine if the results are statistically significantly different from what a punnett square based on the law of independent assortment would predict.

Hardy Weinberg - Kayla Kaufmann 4.C.3, c: Allelic variation within a population can be modeled by the Hardy Weinberg equation(s).

Imagine in a plant population that red flowers (R) are dominant to white flowers (r). In a popluation of 500 individuals, 25% show the recessive phenotype. How many individuals would be expected to be homozygous dominant and heterozygous for this trait?

Population Growth (Page 1181) by Jake Barry Essential Knowledge 4.a.5. Communities are composed of populations of organisms that interact in complex ways.

Populations have the potential to expand greatly if sufficient resources are available. The formul is exponential because if every individual in a population reproduces, then there will be at least an equal amount of individuals in the next generation. For each additional child that an individual has will add an extra (more than the first generation) to the second generation. This will continue over the next generations as well, cause the population to increase exponentially.

t}} =N 0 *e (r*t)N t =N 0 *e (r*t)
This is the model. N0 is the origional amount in the population. K is the rate, and T is the time. Practice:

In 1950, the world's population was 2,555,982,611. With a growth rate of approximately 1.68%, what was the population in 1955?

http://www.coolmath.com/algebra/17-exponentials-logarithms/06-population-exponential-growth-01.htm http://math.ucsd.edu/~wgarner/math4c/textbook/chapter4/expgrowthdecay.htm

Statistics - Amanda Vespermann The daily water consumption levels of two plants were recorded every day for one week. In mL, plant 1 consumed 2, 1, 0.7, 0.5, 1, 1.2 and 1.1. Plant 2 consumed 1.3, 2.1, 0.3, 0.4, 0.7, 1.1, and 1.2 mL. Which plant consumed the higher mean amount of water per day over the week interval?

Chi Square - Submitted by Maddy Harmon

The trait long ears is hypothesized to be autosomal dominant over short ears in a rabbits. Pure breeding long eared rabbits are crossed with short eared rabbits. In the F2 generation, the following offspring are observed-

long eared- 429 short eared- 151

Do the results support the hypothesis? Use Chi Sqare Analysis to determine.

Mariah Pennington Probability Let’s say that in rats the trait for black fur is dominant to gray and the trait for a long tail is dominant to a short one. If a female that is heterozygous for both traits is crossed with a homozygous recessive male, what is the probability that their offspring will have gray fur and a long tail? Use a Punnett square to support your answer.

Maggie Garrahan Solute Potential If the solute potential for a sucrose solution in a dialysis bag is -4.25 bars and it is placed in a cup of sucrose solution having a solute potential of -2.5 bars and if the pressure potential inside and outside the bag is zero, will the bag gain or lose mass? Explain your answer.

Statistics - Lea Adams Big idea 1 Letter b Three small aquatic organisms were discovered in many different depths of the ocean. To compare these organisms that are thought to be related, scientists sequenced their DNA and found differences between them. Scientists took chunks of the sequences and counted how many differences there were from the organism that they believed to be the original. The second organism had 16 differences in the first chunk, 47 in the second, 38 in the third, 68 in the fourth and 93 in the fifth. The third organism had 23 in the first chunk, 40 in the second, 32 in the third, 80 in the fourth and 98 in the fifth. By finding the average or mean number of differences, which organism contains less differences in DNA sequencing and is therefore more closely related to the original aquatic organism?

Grace Goodfellow Probability Blood type is a result of multiple alleles: IA, IB, and iO. A few simple rules of blood type genetics are: IA is dominant over iO. IB is dominant over iO. IAIB are co-dominant. Suppose two parents that are heterozygous for type A blood and carry the sickle cell trait have children. Complete a dihybrid Punnett square to determine the frequency of the different phenotypes of the offspring.

Kohl Romeiser Solute/Water Potential The molar concentration of a sugar solution in an open beaker is 0.3 Molars. Calculate the solute potential of the solution at 27 degrees Celsius. In addition to the solute potential, calculate the water potential

 Amanda Seale Statistics The water temperature of Nikki's swimming pool was recorded over the span of a week. The temperatures were recorded as followed: 65°,67°, 67°, 68°, 72°, 70 and 69°. Plot the data using a line graph. What is the average temperature of the pool during the week? What is the mode and the range of the data?

Bunyad Bhatti Population Growth

Overtime, populations grow in an exponential manner. Each individual reproduces ( say one child), which leads to the offspring producing more children in the next generation. The formula used for figuring out the population growth is:


 * 1. Exponential growth:** where resources are unlimited.

dN/dt = change in population size; r = intrinsic rate of increase (= per capita rate of increase and equals birth rate minus death rate); N = population size.
 * dN/dt = rN** where:


 * 2. Logistic Growth:** where resources are limited.

dN/dt = change in population size; r = intrinsic rate of increase; N = population size; K = carrying capacity (upper asymptote).
 * dN/dt = rN [K - N/K]** where:

Practice question:

An insect population has 1500 individuals, and is growing at a rate of 5%. What will be the population after 5 years? When will the population reach 10,000 individuals?

Owen Gaffney Concept 2A.3: Surface area to volume ratios affect a biological system's ability to obtain necessary resources or eliminate wastes. Imagine two cells, each having specific roles in the human body. One cell s found in the lungs and known for exchanging gasses; another is a simple epithelial cell of an outer epidermis. By being given the dimensions of each cell determine which functions where. Explain your reasoning and show all work. Give surface area to volume ratios. Cell 1- 2 x 2 x 2 microns Cell 2- 4 x 4 x 8 microns



Kylie Dolan Hardy-Weinberg If you sample a population, which the percentage of the homozygous recessive genotype (bb) is 49%. Calculate:

The frequency of the Bb genotype. The frequency of the b allele. The frequency of the B allele.

Kayla Kaufmann (Make-up work for missed math review day) Solute Potential

A cell is in equilibrium with its surroundings. The molarity of the surrounding solution is 0.5M. The temperature is 20 oC. To convert molarity to solute potential in MPa, use the formula: Y S = - ( i CRT )

i = ionization constant (assume that is 1) C= molar concentration R = pressure constant (R=0.00831 liter MPa/mole oK) T = temperature in Kelvin (273 + oC)

Answer since this is make up work -(1x0.5x.00831x293) = -1.22 MPa