How to Avoid Losing Marks For No Reason

• Make your solution easy to read.

Make your solution neat and readable. Write in complete English sentences, not in some weird mathematical shorthand you've invented. Be clear what questions you are answering, and be clear in your answer. If I can't understand your answer, I may just decide that you don't, either; you will lose marks.
 
• Pay attention to the small stuff.

Disappearing negative signs or brackets, misreading numbers (in the question or your solution), forgetting units, etc. will lose you minor marks, but they might also turn a simple problem into a gorilla. If you can't tell the difference between a "+" and a "t," change your handwriting. Watch the details.
 
• Use proper math form.

Remember that 15-20% of your final mark is based on communication, and a significant part of the communication mark comes from math form. Watch your use of the equals sign: only one per line and don't use it when you really mean "and the next step is..." (Why?) Start with the formula. Look at the posted solutions to see how to set up a solution properly.
 
• Please answer the questions.

It is heartbreaking: many students lose marks simply because they don't answer a question. This usually happens because 1) you ran out of time because a harder question came first 2) you don't know how to do the question or 3) you don't know how to do part (a), but you need part (a) to do part (b).

For 1), the solution is to read through the entire test first, then answer the easier questions first. Don't worry about answering them out of order. Your goal is to get as many marks as you can. An "easy" question worth 4 marks has just as much weight as a "hard" question worth 4 marks. Do the easy questions first!

In the case of 3), here's what you do: make up an answer for part (a) and use that answer for part (b). Trust me on this; it's how I got through 2A Calculus at U(W).

Never never never leave a question blank if you know how to do even part of it. Remember, the marks aren't all or nothing. You know something about the problem. Write it down. The worst that will happen is that you will get no marks. The best that will happen is that you will figure out how to solve the problem and get full marks. What will usually happen is that you will get part marks.
 
• Please answer the specific question.

I rarely ask you to state definitions. I am always more interested in seeing if you know how to use the concept than if you can regurgitate a definition. So when I ask "what does this mean?" I am almost always asking to you to tell me what it means in the context of the problem I have given you. For example, when I ask "What does this y-intercept tell you/mean/represent?" I want an answer like "It tells me that the start-up cost is $100." Similarly, "What do the residuals tell you about this curve of best fit and why?" is begging you to tell me that you know that the quadratic model is good because the residuals are small and have no pattern. Don't tell me what the residuals could tell you about. Tell me what they are telling you, right now. When I want just the definition, you'll see "State the definition of ..."
 
• Highlight your answers to computational questions.

Put the answer in a box, or underline it in red ink, or something. If the answer has three parts, put them all in one place; don't just leave them scattered about the page.

Remember: If I can't find your answer, then you will not get a mark for it.
 

• Math: Express numbers algebraically.

Unless otherwise specified, use fractions and roots -- not decimal expansions --to express numerical values in a math course. An expression involving a fraction or a root, even if it looks "incomplete" to you, is actually far more precise than a decimal expansion. For example,
• "1/3" is far more precise than "0.333333..." could ever be.
• "π" is far more precise than "3.14159265358979323846264338..."
• "_/2" is more precise than "1.4142136..."

Furthermore, an algebraic expression encodes the meaning of the number; a decimal expansion does not. The expression "π/2" is has immediate meaning to a mathematician, and tells her many things; this expression must involve circles or trigonometric concepts, and specifically, probably involves a quarter angle somewhere. On the other hand, the decimal expansion "1.5707963..." communicates nothing
 
• Physics: Express your answers using the proper number of significant digits and with the proper unit and direction, if applicable.

I'll always spend some time at the beginning of the course reviewing significant digits, and an answer without a unit (or the wrong unit) is an incorrect answer. An answer that needs a direction and is missing one (or shouldn't have a direction but has one) is the wrong answer. Don't lose marks this way.
 
• Express answers in simplest form.

Rationalise denominators, and simplify fractions, please. No negative vectors. If your answer is expressed in some complicated, byzantine format, I can't tell if it is equal to the correct answer or not.
 
• Try to communicate your ideas clearly.

Communicating a complex and subtle idea is hard work. It is also the most important skill you will ever learn. A mathematics course gives you ample opportunity to hone this skill; indeed, this is one of the chief purposes of such a course. Incidentally, this is one of the reasons law, medical, and business schools love math and physics students. True story. (See How to communicate mathematical ideas clearly.)
 
• Justify your solutions.

The main reason for justifying your answer is to show me that you know what you're talking about.  The clearer your solution is, the less likely you will lose marks.  If you jump from one thing to the next without saying what you are doing and you do it incorrectly, you will lose many more marks than if you said:  "This is what I'm trying to do here."  General rule: if I can't follow your solution, it will be marked as incorrect (even if you get the right answer at the end).   Getting the right answer is not as important as showing that you know how to get the right answer, and it is possible to get a correct answer using incorrect methods.  Example: 

 

• Please put the assignment questions in order.

(Assignments only) I will be looking for the answer to a certain question at a certain specific place in the assignment. If it's somewhere else instead, I might not find it, and then you might not get marks.

Note that it is much easier to put the questions in order if each question appears on a separate piece of paper. (see "Wasting Paper")
 

• Do not hand in a rough draft; do not hand in "random walk" solutions.

Often, finding a solution is a long and difficult process, involving many false starts, dead ends, blind alleys, etc. You may find that you get three quarters of the way through five versions of a solution, only to quit each time, realising that your "great idea" wasn't so great. Don't get demoralised; it happens to everyone.

However, your assignment should not reflect this process. Your assignment should contain a clear, concise explanation of the final solution you found; it shouldn't contain five false starts or dead-end arguments. Putting this much "false" mathematics in an assignment is almost certainly going to convince me that you don't understand what you're talking about.

Think of it this way: would you hand in an English essay with paragraphs crossed out or three different theses for which you couldn't quite find supporting arguments?  No!  So don't do it with math.
 

For a really good exposition on common mistakes made in math, check out Common mistakes in undergraduate mathematics -- the mistake noted here will also lose you marks in high school.