Assigning the same sign to quantities with opposite directions
Assigning opposing signs to quantities with the same directions
Failing to include relationships to cardinal directions when given cardinal direction information
Falsely referring to cardinal directions, or to a horizontal or to a vertical line when the intended angle is measured in reference to something else.
Using the magnitude of a vector quantity in place of one of its components
Precision:
Failure to use proper significant figures
Careless calculator use:
Failure to switch between radian and degree mode or vice versa
Failure to group powers of 10 with their associated coefficient. (Often solved through proper use of the EE key.)
Careless algebra:
Asymmetric application of a function to the equation (applying it to one side but not the other, or applying the inverse function to one side in lieu of the actual function)
Substituting multiplication for division or vice versa when reconciling fractions on either side of an equation.
Substituting addition for multiplication when reconciling fractions on either side of an equation
Adding to one side rather than subtracting, or vice versa
Dropping a term from one line to the next
Inverting a known relationship eg: average velocity = change in time/displacement instead of average velocity = displacement/change in time
Sign error
Careless Trigonometry
Using the wrong trigonometric function
Substituting the inverse trigonometric function for the trigonometric function or vice versa
Units:
Omitting units
Using improper units
Using units that are dimensionally inappropriate (can be caught through dimensional analysis)
Using a value that would be correct for the quantity but with an incorrect set of units eg: km/year instead of m/s. (can be caught through factor labeling)
Graphing:
Failure to use either graph paper or a computer printout.
Omitting labels of quantities or of units on axes
Incorrect labels of quantities or of units on axes
Graphing the wrong quantities on the wrong axes
Switching which quantity should be plotted on the x vs. on the y axes.
Declaration of any curving relationship as exponential when a function of the form y = Aexp(bx)+C does not yield the best fit.
Descriptions
Recursive definitions – using the same term or a variation of the same term to describe or define that term.
Vague language:
Using the phrase “constant motion” when “constant velocity” is meant.
Using the term “rate” when “velocity” or “rate of change of position with respect to time” or some other specific rate is meant.