Algebra Basics Needed for PreCalculus
The basics of precalculus consist of reviewing number systems, properties of the number systems, order of operations, notation, and some essential formulas used in coordinate graphs. Vocabulary is important in mathematics because you have to relate a number or process to its exact description.
For precalculus, you’ll work with simplifying algebraic expressions and writing answers in the following ways:

Identifying which are whole numbers, integers, and rational and irrational numbers

Applying the commutative, associative, distributive, inverse, and identity properties

Computing correctly using the order of operations (parentheses, exponents/powers and roots, multiplication and division, and then addition and subtraction)

Graphing inequalities for the full solution

Using formulas for slope, distance, and midpoint

Applying coordinate system formulas to characterize geometric figures
Don’t let common mistakes trip you up; keep in mind that when working with simplifying expressions and communicating answers, your challenges will be

Distributing the factor over every term in the parentheses

Changing the signs of all the terms when distributing a negative factor

Working from left to right when applying operations at the same level

Assigning points to the number line in the correct order

Placing the change in y over the change in x when using the slope formula

Satisfying the correct geometric properties when characterizing figures
Practice problems

Identify which property of numbers the equation illustrates. If x = 3 and y = x, then y = 3.
Answer: transitive
The transitive property says that if one value is equal to both a second value and a third, then the second and third values are equal to one another.

Find the midpoint of the segment between the points (−5, 2) and (7, −8).
Answer: (1, ‒3)
Use the midpoint formula,
and the given points: