Scientific notation is used to write much larger or smaller numbers as a decimal number between 1 and 10, multiplied by 10 to some power. This allows for representation of small or large numbers in a compact form, and can ease order of magnitude estimations.

The significant figures of a number are the digits which contribute to its accuracy and precision. This includes all digits other than leading zeros, trailing zeros indicating the scale of a number, and any digits introduced beyond the amount of digits in the original number.

Dimensional analysis is an extremely powerful tool in checking your answers. Dimensional analysis differs from unit analysis in that while units differ between metric systems, dimensions never change. Any equation with physical meaning will have the same dimensions on either side, therefore along any line of physical reasoning, the dimensions should "check out".

Units of measurement provide a definite magnitude of a quantity, defined by convention, which establishes a standard for measurement of a quantity. Units are often expressed as multiples of other, more fundamental units, called derived units.

Algebra is a major prerequisite for introductory physics. Students will be manipulating equations both numerically and symbolically. Use the resources found below to brush up on your algebra skills and see your instructor if you're uncertain about your preparedness for these types of mathematical operations.

Mathematization involves translating physical description into a mathematically viable representation. That is, when someone describes a physical scenario, that scenario can be "mathematized" into something that can be solved using mathematical reasoning. Mathematization is the backbone of physics, and is arguably the most important and useful tool in a physicist's toolkit.

Graphical representation of physical phenomena helps us understand the situation we are dealing with. These basic functions will show up often in problems and being able to recognize their graphs and various functional forms will assist in making sense of these problems.

Proportional reasoning involves identifying how variables are changing with respect to each other. This is like asking, "If I turn this knob (change this variable), how will the machine (output of equation) respond? or how can I turn the rest of the knobs to compensate and retain the same answer?" This skill is useful for identifying causality in everyday life.

You have indubitably have encountered geometry and trigonometry before, and may have hoped to never see them again. SURPRISE! Geometry and trigonometry once again rear their heads in physics. You will often be working in two dimensions, in which case the Pythagorean theorem describes the shortest distance between points. In these cases, you will need to solve for the rest of the triangle using SOHCAHTOA.

Vectors! Anyone who has studied physics has dealt with vectors. A vector is a mathematical object with two (or more!) pieces of information. Any time something needs multiple quantities to describe it fully, you should use a vector. This can be position in two dimensions, the position and momentum of a ball, or even things like the location of a word in a book, which can be described <page number, location of word on page>.

Order of magnitude estimations are quick, back of the envelope estimations up to an order of 10. These can help check answers by making sure your solution is on the same order of magnitude as the variable values.