Equations
I won’t bore you by presenting a giant list of equations here, as one is available at the end of the module. Instead, we will look into how to memorize equations effectively and how to apply the 5-step general strategy to the same calculation we already solved using units.
Memorizing Equations
Equations are an abstract collection of symbols and numbers, as such our minds tend to have a hard time remembering them. This difficulty is further compounded by the sheer number (90+) of potential equations we have to remember. However, we can make our lives easier by grouping equations so that we have a conceptual framework to “hold” on to and make them stick.
For instance, we can group all of the energy equations that have a similar form and remember what type of energy they are used to calculate.
[latexpage]
\[KE_{motion}= \frac{1}{2}mv^2\]
\[KE_{fluids}=\frac{1}{2} \rho v^2\]
\[PE_{spring}=\frac{1}{2}kx^2\]
\[PE_{capacitor}=\frac{1}{2}CV^2\]
In this way, we can remember the general form of the equation, realize that it has multiple different applications, and essentially get four equations for the price of one.
The equation sheet in the resources section will be organized topically as most equation sheets are and will have an additional grouped page to help you get a better handle on memorizing equations. Additionally, the accompanying Anki cards will always list similar equations in the notes section to help you strengthen the connection and remember equations with ease.
Knowing Variables is Key
A giant list of memorized equations isn’t very useful if we don’t know how to use them. This is especially true on the MCAT since calculations will often require you to combine multiple equations in order to solve a question.
However, if we know the variables that make up equations and are able to deduce a variable’s identity from both units and context it is much easier to determine, which equation to use.
Here is a short list of some of the variables and the context in which they will come up (the full downloadable list is available at the end of this module):
| Variable(s) | Represents | Context | Units |
| Force (F) | Force | N | |
| Torque (t) | Rotational Forces | J | |
| Work (W) | Energy | J, eV | |
| Energy (E) | Energy | Photon/Light Energy | J, eV |
| Kinetic Energy (KE) | Energy | Motion | J, eV |
| Potential Energy (PE) | Energy | Static | J, eV |
Using Equations
Now, let’s look at the question we already solved using units to exemplify the strategy.
A train must generate 500N of force to overcome friction and maintain a constant velocity of 30m/s. How much power does the train generate and how much energy does it consume in a 10-minute period?
A. 15,000 W; 6,000,000 J
B. 15,000 W; 9,000,000 J
C. 90,000 W; 1,500,000 J
D. 90,000 W; 9,000,000 J
- Answer’s variables: Power (
P) and Energy/Work (
W)
- Variables units: Velocity (
V), Force (
F), and Time (
t)
- Generate equations:
P = F∙v, P = W/t, and W = F∙d
- Triangulation: Not passage based
- Arrange and Solve Equations Style
To begin our arrange step we will want to determine if we need to re-arrange our equations to solve for the answer variable as such:
Or nest equations as shown below:
In this case we probably don’t want to nest any equations as it incorporates more variables that we haven’t been given.
The rearrangement step is useful however and we will stick with it since it contains the set of variables, we have in step 1 and step 2. This leaves us with:
Now we can plug and chug making sure we are using the proper units for time by converting the minutes to seconds.