I got the right answer, so why didn't I get full marks?
There is more to a correct math solution than just getting the right final answer. In fact, in many cases, the final answer may only be worth 1 mark, and it's the process that you took to arrive at it that gets you the rest of the marks. Mathematics is a language, so your answer has to be complete, correct, and easy to understand! You wouldn’t hand in an essay with no punctuation, or with words and sentence fragments scattered across a page and how you communicate in math shouldn’t be any different.
Make what You're Doing Clear
If you are evaluating a function, then writing
f(x) = x2
= 4
is horribly WRONG, even if someone can guess what you're doing. You must write:
f(x) = x2
f(2) = 4
Scattered Math
This is really bad! You should not have math calculations scattered all over the place, with no explanation of which calculation implies the next, or why you’re doing what you’re doing.
e.g., in the above example, simply writing
x2
4
is about as bad as notation gets and really makes no sense (and will lose you lots of marks as a result!!!)
Show Your Work
Unless you’re performing a really simple/obvious step, you should always show your work. Otherwise, you'll miss out on part marks if the answer is wrong, and your solution may be difficult to follow. Think of how hard it would be for you to read a solution without any work shown, so make sure your solution is easy to read for others. As part of this, include explanations in words, and finish off application problems with a concluding statement.
Rough Work
If you do rough work calculations that aren’t part of the formal solution, then these should be written to the side of the page, and clearly labelled as “Aside” or “Rough Work.”
Checking Your Work
If you finish your work early (e.g. quiz, midterm, final exam), then there is plenty of time for you to check your work before you go. Make you you clearly label this work as "check" to avoid confusion for the grader as to what you are doing.
Don't Forget the Units
Be careful about units during your calculations! If the formula uses hours while you’re interested in the population after 30 minutes, then you have to convert 30 minutes to 0.5 hours. If you just substitute 30 in directly, that would be the population after 30 hours!! Obviously, that makes a big difference! Also, include the units in your final answer.
Simplifying Your Work
At the very least, you must collect like terms; e.g., a final answer of 3y5z+9x+2x will not receive full marks. You should write 15yz+11x for this example.
Rounding
When performing calculations, you can round your final answer as instructed by your professor. In the context of an application problem, round according to what makes sense for the application (e.g., you shouldn’t have a population of 85.32). Finally, remember that you should NOT round intermediate results, as this introduces round-off error.
State Formulas
Whenever you use a formula (even if it's given), it is always a good idea to write the formula down before starting to substitute things into it.
