Basic Concepts

1. Chapter 1 Basic Concepts

2. Chapter Sections 1.1 – Study Skills for Success in Mathematics, and Using a Calculator 1.2 – Sets and Other Basic Concepts 1.3 – Properties of and Operations with Real Numbers 1.4 – Order of Operations 1.5 – Exponents 1.6 – Scientific Notation

3. Evaluate Exponential Expressions • Factors are the numbers or expressions that are multiplied. • The quantity 32 is called an exponential expression. In the expression, the 3 is called the base and the 2 is called the exponent. Example a.) -62 = -(6 · 6) = -36 b.) (-6)2 = (-6)(-6)= 36

4. Evaluate Square and Higher Roots • The symbol used to indicate a root, √ , is called a radical sign. • The number or expression inside the radical sign is called the radicand. Example a.) , since 5 · 5 = 25

5. Order of Operations To evaluate mathematical expressions, use the following order: First, evaluate the expressions within grouping symbols, including parentheses, ( ), brackets , braces , and absolute value, | |. If the expression contains nested groupingsymbols (one pair of grouping symbols within another pair), evaluate the expression in the innermost grouping symbols first. Continued.

6. Order of Operations Next, evaluate all terms containing exponents and radicals. Next, evaluate all multiplicationsor divisionsin the order in which they occur, working from left to right. Finally, evaluate all additionsor subtractionsin the order in which they occur, working from left to right.

7. Order of Operations Evaluate: 6 + 3 · 52 – 17 = Steps Taken 6 + 3 · 25 – 17 = exponent 6 + 75 - 17= multiplication 81 – 17 = addition 64 subtraction

8. Order of Operations parentheses subtraction exponent addition

9. Expressions Containing Variables Evaluate: -x3 –xy – y2 when x = -2 and y =5