Biology Problem of the Week: Plant Cells versus Animal Cells

One of the most common kinds of questions on standardized biology tests (such as the SAT Subject Test) are ones that ask the student to recognize the difference between plant and animal cells. Here are the diagrams for both kind of cells. The question is, which one is the plant cell and which one the animal cell?

Although both cells have mitochondria, rough endoplasmic reticulum and other structures in common, there are some key differences as follows:

1. The plant cell has a cell wall whereas the animal cell does not.

2. The plant cell has chloroplasts (for photosynthesis) while the animal cell does not (which makes plants autotrophs and plants heterotrophs).

3. The animal cell has lysosomes whereas the plant cell lacks them.

4. The animal cell has centrosomes but the plant cell does not.

5. Plant cells can have very large vacuoles whereas animal cells do not.

Thus, the first cell is a plant cell and the second an animal cell.

Chemistry Problem of the Week: Calculating the pH of a Solution of a Weak Acid

One of the more intimidating problems you may encounter in your chemistry course or AP test is one where you need to calculate a pH for a weak acid. Typically, you are given a weak acid, which partially dissociates. An example follows:

Given that acetic acid has an acid dissociation constant (Ka) of 1.8 · 10^-5, calculate the pH of a 0.10 M solution.

To solve this, first start with the equilibrium one would expect for the weak acid, in this case, acetic acid.

HA(aq) ↔ H+(aq) + A-(aq)

Note that you can use the ICE method (Initial, Change, Equilibrium) to calculate the equilibrium concentration of H+.

   HA(aq)      ↔      H+(aq)      +      A-(aq)

I                                                0.10 M                    0                        0

C                                                  - x                       +x                     +x

E                                              (0.10 - x)                  x                       x

Therefore, since Ka = ([H+][A-]) / [HA], then we set up the calculation as

1.8 · 10^-5 = (x^2) / (0.10 - x)

This can be solved as a very time-consuming quadratic. An easier method is to approximate by noting x will be very small compared to 0.10 in the denominator (in red). Thus, the following approximation is valid:

1.8 · 10^-5 = (x^2) / (0.10)   (the -x term in the denominator was removed)

Solving for x, we get x = [H+] = 0.0013 M. Recalling pH = -log[H+], we get

  pH = 2.9

Physics Problem of the Week: Calculating Power Required to Lift an Object

Problem: If a mass of 10.0 kg needs to be lifted 10.0 meters upwards in 5.00 seconds, what will be the average power required?

Solution: Two formulas are needed here. The first is the formula for power:

P(av) = ∆W / ∆t    (W = work and t = time)

But to calculate the average power we will need to calculate the amount of work done. Noting that:

∆W = F · ∆s  (where s = displacement)

we conclude that the work done (since displacement is vertical) is used to overcome the weight of the object, therefore the gravitational potential energy change is equal to the work done!

∆W = m · g · ∆h (where m = mass, g = 9.81 m/s^2, and h = height) 

Thus, ∆W = (10.0 kg)(9.81 m/s^2)(10.0 m) = 981 Joules

Using this energy in the average power equation above, we see

P(av) = (981 J) / (5.00 s) = 196 J / s = 196 Watts 

For a video similar to this topic, see

https://www.youtube.com/watch?v=zt1noaXrJ14

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Math Tip of the Week: Learning Geometry by Working with GeoGebra

Geometry is one of the toughest subjects for many students, as indicated by the groans and eye-rolling you often see when asking them about their geometry class. A good tutor can help you become really comfortable with this subject, but a great complementary way to learn geometry is by using a software suite called GeoGebra. It can be downloaded here: http://www.geogebra.org/cms/en/

For example, suppose you would like confirmation the following statement is true:

If two chords intersect on the circumference of the circle to form perpendicular line segments, then the chord which connects their other endpoints must be a diameter of the circle.

Try using GeoGebra to confirm this. First draw circle A with perpendicular chords BC and CD (note, the angle can be constrained to be exactly 90 degrees but 89.97 degrees drawn freehand will be close enough!)

Now draw chord BD to connect their other endpoints and you will notice it passes right through the center of the circle at point A and thus BD is a diameter.

Therefore a right triangle is revealed, which should be the case since angle BCD should intercept an arc of twice its angular measure, or 180 degrees.

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Test Taking Tips: Use This Logic Trick to Narrow Down Your Answer Choices

   We've all taken standardized tests before where we have encountered questions we just may not be able to answer. Are there any tips to narrow down your answer choices so that you may be able to take an educated guess on two possibilities instead of five? You may be able to use the following trick. The following question and answers demonstrate this.

   Suppose the question you encounter is "Which of the following is true about euglena?"

(a) They are incapable of generating ATP due to modifications of their mitochondrial membranes early in their life cycle
(b) They are almost always multicellular with few exceptions
(c) They are considered protists
(d) They are considered plants
(e) They are exclusively heterotrophic


   At first glance, you have no idea how to solve this problem, but then you recall your studies of taxonomy. You remember with 100% certainty they are not considered animals nor fungi and they are not prokaryotic. Based on taxonomic classifications, then, they must be either plants or protists; these are the only possibilities. Therefore, you can immediately narrow down the choices to (c) or (d), because logic dictates "If A or B, and not A, then B". In other words, it must be the case that euglena are either plants or protists, and since you know this to be true, none of the other answer choices can be correct.


(a) They are incapable of generating ATP due to modifications of their mitochondrial membranes early in their life cycle
(b) They are almost always multicellular with few exceptions
(c) They are considered protists
(d) They are considered plants
(e) They are exclusively heterotrophic

   Whereas previously you had effectively a 1 in 5 chance of answering the question, you now have a 1 in 2 chance of answering the question! The correct answer, by the way, is (c).

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