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Hey everyone!
Here are three MCAT math tricks.
1. The first one is for when you have the concentration of H+ ions and you want to find the pH.
So lets say the hydrogen ion concentration is 3.5 e -5 M and you want to find the pH.
pH = - log [ 3.5 e -5 ]
The first step is to make sure the concentration is in scientific notation (which it is). The next step is to take the 5 that is part of the exponent and subtract it from 0.35, which is the coefficient divided by 10, to get 4.65.
5 - 0.35 = 4.65
This is the estimate value for the -log of 3.5 e -5.
If you do this out in a calculator you get 4.45.
Doing calculations this way will usually get a number that of off by 0.1 or 0.2 and in this case our estimate is off by 0.2.
2. The second trick is to find the hydrogen ion concentration given the pH.
Lets say the pH is 4.22 and we want to know what the hydrogen ion concentration is.
First you need to go up to the next whole number of what ever the pH is. So because we have 4.22 the next whole number would be 5.00
Next you would take that number and subtract is from the pH plus 0.15 to get 4.37.
This will give you 5.00 - 4.37, which is equal to 0.63.
Next you multiply that number by 10 to get 6.3 and the last step is to take the number 5.00 that you rounded up to and make that the exponent of 6.3 to get 6.3 e -5.
This is an estimate value and the actual answer is 6.3 -5.
Lots of students will sometimes as where the 0.15 came from. The 0.15 comes from doing the problem in reverse (the first math trick I went over). Doing calculations that will get a number that is off by 0.1 or 0.2 so 0.15 is just the average of those two.
3. The third trick is to find cos, sin, and tan
If you take your left hand and make your thumb 0 degrees, your pointer 30 degrees, your middle finger 45 degrees, your ring finger 60 degrees, and your pinky 90 degrees you can pick which degrees you want by picking the finger with the corresponding degrees.
For example, let say you want the sin of 60 degrees. 60 degrees is your ring finger and if you want sin then you count the number of fingers to the right of your ring finger which would be 3, so you take the sqrt 3 and you always divide by 2.
Therefore, the sin of 60 is sqrt 3 / 2. If you want cos then you count the number of fingers to the left.
Here are three MCAT math tricks.
1. The first one is for when you have the concentration of H+ ions and you want to find the pH.
So lets say the hydrogen ion concentration is 3.5 e -5 M and you want to find the pH.
pH = - log [ 3.5 e -5 ]
The first step is to make sure the concentration is in scientific notation (which it is). The next step is to take the 5 that is part of the exponent and subtract it from 0.35, which is the coefficient divided by 10, to get 4.65.
5 - 0.35 = 4.65
This is the estimate value for the -log of 3.5 e -5.
If you do this out in a calculator you get 4.45.
Doing calculations this way will usually get a number that of off by 0.1 or 0.2 and in this case our estimate is off by 0.2.
2. The second trick is to find the hydrogen ion concentration given the pH.
Lets say the pH is 4.22 and we want to know what the hydrogen ion concentration is.
First you need to go up to the next whole number of what ever the pH is. So because we have 4.22 the next whole number would be 5.00
Next you would take that number and subtract is from the pH plus 0.15 to get 4.37.
This will give you 5.00 - 4.37, which is equal to 0.63.
Next you multiply that number by 10 to get 6.3 and the last step is to take the number 5.00 that you rounded up to and make that the exponent of 6.3 to get 6.3 e -5.
This is an estimate value and the actual answer is 6.3 -5.
Lots of students will sometimes as where the 0.15 came from. The 0.15 comes from doing the problem in reverse (the first math trick I went over). Doing calculations that will get a number that is off by 0.1 or 0.2 so 0.15 is just the average of those two.
3. The third trick is to find cos, sin, and tan
If you take your left hand and make your thumb 0 degrees, your pointer 30 degrees, your middle finger 45 degrees, your ring finger 60 degrees, and your pinky 90 degrees you can pick which degrees you want by picking the finger with the corresponding degrees.
For example, let say you want the sin of 60 degrees. 60 degrees is your ring finger and if you want sin then you count the number of fingers to the right of your ring finger which would be 3, so you take the sqrt 3 and you always divide by 2.
Therefore, the sin of 60 is sqrt 3 / 2. If you want cos then you count the number of fingers to the left.
