Math review 2014


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

  • Hardy Weinberg
  • Chi 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 microns

Problem #2 Submitted by Orna
Water Potential

In a U shaped tube, the two arms are separated by a membrane permeable to water. One side of the tube contains a solution with a solute potential of -.28, and the other side contains water with a solute potential of zero. There is positive pressure of .40 on the side with the solution.Find the water potential of each side of the U shaped tube.

Problem #4 (submitted by Allie Pannoni)
Concept 1.A.1: Natural Selection is a major mechanism of evolution.

Within a population of butterflies, the color brown (B) is dominant over the color white (b) and 40% of all butterflies are white. Given this information, calculate the frequency of the recessive allele, the frequency of the dominant allele, and the percentage of the heterozygous genotype.

Problem #3 Submitted by Kelsey
Concept 3.14
Chi Square
In a plant, pink flowers (P) are dominant over yellow (p) flowers, and short plants (S) are dominant over tall (s) plants. When two double heterozygote (PpSs) plants were crossed, these were the resulting phenotypes:
Pink, short- 206
yellow, short- 83
Pink, tall- 65
Yellow, tall- 30

Perform a chi square analysis to determine if the predicted phenotype is correct

Phenotype
Observed (O)
Expected (E)
O-E
(O-E)^2
(O-E)^2/E
























Totals


X
X


Problem #5 (Submitted by Tara)
Probability

In a cross between RrWwYy x RRwwYy, what is the probability of getting the offspring RrWwYY?

Problem #6 (Submitted by Maddie)
Hardy Weinberg

Assuming that there are:
  1. No mutations
  2. Random mating
  3. No natural selection
  4. Extremely large population size
  5. No gene flow
determine the following:
Brown fur is dominant to gray fur in mice. If you have 120 brown mice in a population of 200, what is the predicted frequencies of heterozygotes.
Helpful equations:
  • p2+2pq+q2=1
  • p+q=1


Problem #7 (Submitted by Tory)

Solute Potential
A cell is in equilibrium with a surrounding sucrose solution of 0.6 M at room temperature ( 293°K). Calculate the solute potential of the surrounding solution. (Use 0.00831 liter Pa/mole °K as the pressure constant)
Solute potential () = –(iCRT) where:
i= ionization constant
C= molar concentration
R= pressure constant
T= temperature

Problem #8 (Submitted by Jess)
water potential
If a cell’s pressure potential is 3 bars and its solute potential is -4 bars, what is the resulting water
potential?
Ψ = ΨS + ΨP

Problem #9 (submitted by Sophia)
Population growth
There were 5,000 squirrels living in the park in 2013. If there were 50 births and 25 deaths per 1,000 squirrels, what is the park's net population growth for that year?
Δ N/ Δ t = bN- dN

Problem #10 (Submitted by Katherine)
Statistics

Concept 2.A.2 Organisms capture and store free energy for use in biological processes (applicable to this specific problem)

Learning Objective 4.19 The student is able to use data analysis to refine observations and measurements.

To measure the rate of photosynthesis, one lab group conducted an experiment that utilized the floating leaf disk technique. The time it took each disk to rise was observed and recorded. What is the mode, median, mean, and range of the data collected?

Time It Took For Disk to Rise (Minutes):
12 18 22 8 16 15 19 25 7 12

Mode:

Median:

Mean:

Range:



Problem #11 (Submitted by Erin)
Population Growth

In a population with a size of 100, there were 20 births and 5 deaths in one year. Determine the:
Birth Rate:
Death Rate:
And using the population growth equation, calculate the:
Population Growth Rate as a number between 0 and 1.