# Practice as you will perform

To get top marks on quantitative tests, you need to practice the course content until it becomes automatic. For most students, this means doing **a lot** of problems, often many more than were assigned. Here are some tips on how to get the most out of your practice sessions.

## Practice without looking up the answer

Solving problems, while peeking at the answer key or using your notes, is often the first step. Don’t stop there though. Making it through the first step doesn’t mean you know how to solve an unfamiliar problem in test-like conditions. As you work through your assigned problems, you should be using fewer and fewer aids.

If you can’t solve questions start to finish without consulting the answer, your notes, the textbook, or another resource, you aren’t ready for the test. You need to do more problems.

## Practice struggling

Most people feel anxiety when they don’t know how to solve a problem. It’s an unpleasant feeling.

Students who always relieve this anxiety by immediately looking up the solution or giving up don’t get to practice other ways of getting un-stuck. If the high pressure setting of the test is the first time you try to solve problems without looking at the answer key, your anxiety can quickly become paralyzing.

Reduce the chances you will freeze on the test by regularly studying without looking up hints. Embrace the anxiety that comes with hard problems. Practice getting un-stuck by trying another problem, taking a short meditation/deep breathing break, looking for hints in other questions, brainstorming solutions, etc. The more often you practice the skill of getting yourself un-stuck without looking at your textbook/notes, the better you’ll be able to perform on the test.

## The problems done in class are usually the ‘easy’ ones!

They may not feel easy, but lecture problems are an introduction to a topic, not the full scope of what will be tested. There will almost certainly be questions on the test that are harder, different and backwards from those demonstrated in class.

Most of your study time should be spent on the hardest of the assigned problems (usually the last third of the assignment).

## Practice with hard problems

Solving hard, unfamiliar problems is the best possible practice for tests. Hard problems are usually difficult in one of these ways. Use this table as a guide when trying to work through a problem you are finding difficult. Also, develop practice problems of each of these types to help yourself prepare for the test.

Hidden knowns |
Required data is not stated in the problem (ex: there are 365 days in a year, gravity is 9.8 m/s2). |

‘Dummy’ variables |
Required value is not given in the problem, but cancels out later in the solution. |

Red herrings |
Data is stated but not needed. |

Work backwards |
A problem that needs to be solved backwards from ‘typical’ problems. |

Letters only |
Word problems with variables instead of names (ex: ‘solution A’ instead of ‘HClO4’). |

Multipart – same concept |
Solution requires same operation to be repeated. |

Multipart – different concepts |
Solution requires several different operations. Often the solution to the first step is required as input for the second step. |

Multipart – simultaneous equations |
Solution requires different operations. Partial solution to first step is input for the second step. Neither step can be solved completely from the beginning. |

(Source: Fleet, J. Goodchild F. and R. Zajchowski. (2006). Learning for Success: Effective Strategies for Students. (4th Ed.) Toronto: Thomson Nelson.)

## Start a study group

Write **very, very hard problems** for each other. At first, work as a team to figure them out. Then move towards being able to solve similar problems without your group members’ help.

## Study as you will be tested

Make sure you do some problems sitting at a quiet desk, with nothing in front of you but the problems and blank paper. Maybe even give yourself a time limit to get through a set number of problems.

Listening to music, talking to yourself, pacing while you work, working with classmates, snacking, and other common study habits can be effective in keeping you on task while you study, but the test shouldn’t be the first time you try to work in test-like conditions.

This is part 3 in the A Better Approach to Quantitative Courses series. Part 1 covers how to distill lecture and readings into concept summaries. Part 2 covers how to use practice problems to deepen your understanding.