Mary Jane Sterling - Pre-Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

Trigonometry basics and solving trig identities ( Chapters 7through 11)

Complex numbers, polar coordinates, and conic sections ( Chapters 12through 13)

Systems of equations, sequences, and series ( Chapters 14and 15)

Limits and continuity ( Chapter 16)

Chapter 1

The basics of pre-calculus 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. The problems in this chapter reacquaint you with many old friends from previous mathematics courses.

In this chapter, you’ll work with simplifying 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

1–10Identify which number doesn’t belong to the number system.

1. Which is not a rational number?

2. Which is not a rational number?

3. Which is not a natural number?

4. Which is not a natural number?

5. Which is not an integer?

6. Which is not an integer?

7. Which is not an irrational number?

8. Which is not an irrational number?

9. Which is not an imaginary number?

10. Which is not an imaginary number?

11–20Identify which property of numbers the equation illustrates.

11.

12.

13.

14.

15.

16.

17.

18.

19. If x = 3 and y = x , then y = 3.

20.

21–30Simplify the expression by using the order of operations.

21.

22.

23.

24.