Lesson 2: Introduction to Variables

Transcription

1 In this lesson we begin our study of algebra by introducing the concept of a variable as an unknown or varying quantity in an algebraic expression. We then take a closer look at algebraic expressions to learn about their structure, and introduce methods of working with and simplifying them. Lesson Topics Section 2.1: Evaluating Algebraic Expressions Section 2.2: Some Vocabulary Variable Term Coefficient Constant Term Factor Section 2.3: Like Terms Identifying Like Terms Combining Like Terms Section 2.4: The Distributive Property Section 2.5: Simplifying Algebraic Expressions Page 23

2 Lesson 2 Notes Page 24

3 Name: Date: 2 Section 2.1: Evaluating Algebraic Expressions Evaluate the algebraic expression. Use your calculator to CHECK your answer. Example 1: Evaluate a 2 b 2 given a = 5 and b = 3 Example 2: Evaluate a 2 (b c) given a = 5, b = 4, and c = 2 Application Example 3: The maximum heart rate is the highest heart rate achieved during maximal exercise. In general, you get the most benefits and reduce the risks when you exercise within your target heart rate zone. Usually this is when your exercise heart rate (pulse) is about 80 percent of your maximum heart rate. The formula M = 0.8(220 A), gives the recommended maximum heart rate, M, in beats per minute, for a person who is A years of age. What is the recommended maximum heart rate for a person who is 40 years old? GIVEN: GOAL: STRATEGY: SOLUTION: CHECK: FINAL RESULT AS A COMPLETE SENTENCE: Page 25

4 You Try 1. Evaluate b 2 4ac given a = 5, b = 1, c = A golfer strikes a golf ball. The height, H (in feet), of the ball above the ground after t seconds is given by the equation H = 16t t. Determine the height of the ball after 3 seconds. GIVEN: GOAL: STRATEGY: SOLUTION: CHECK: FINAL RESULT AS A COMPLETE SENTENCE: Page 26

5 Section 2.2: Some Vocabulary Definitions Terms: Parts of an algebraic expression separated by addition or subtraction (+ or ) symbols. Constant Term: A number with no variable factors. A term whose value never changes. Example 1: Consider the algebraic expression 4x 5 + 3x 4 22x 2 x + 17 a. List the terms. b. Identify the constant term. Factors: Numbers or variables that are multiplied together Coefficient: The number that multiplies the variable. Example 2: Complete the table below. 4m x 1 2 bh 2r 5 List the Factors Identify the Coefficient Example 3: Consider the algebraic expression y 5y 8y y 7 4 a. How many terms are there? b. Identify the constant term. c. What is the coefficient of the first term? d. What is the coefficient of the second term? e. What is the coefficient of the third term? f. List the factors of the fourth term. Page 27

6 You Try 3. Consider the algebraic expression 2m 3 + m 2 2m 8 a. How many terms are there? b. Identify the constant term. c. What is the coefficient of the first term? d. What is the coefficient of the second term? e. List the factors of the third term. Page 28

7 Section 2.3: Like Terms Terms whose variable factors (letters and exponents) are exactly the same are called LIKE TERMS. Identify the Like Terms Example 1: Identify the like terms in each of the following expressions 3a 6a + 10a a 5x 10y + 6z 3x 7n + 3n 2 2n 3 + 8n 2 + n n 3 Example 2: Combine the like terms 3a 6a + 10a a = Combine Like Terms 5x 10y + 6z 3x = 7n + 3n 2 2n 3 + 8n 2 + n n 3 = Page 29

8 4. Combine the like terms. You Try a. 3x 4x + x 8x = b a² 4a + a² + 7 = Page 30

9 Section 2.4: The Distributive Property a(b + c) = ab + ac Use the Distributive Property to Expand Each of the Following Expressions Example 1: 5(2x + 4) = Example 2: 3(x 2 2x + 7) = Example 3: (5x 4 8) = Example 4: 2 x 1 = Page 31

10 You Try 5. Use the Distributive Property to expand the algebraic expression a. 5(3x 2 2x + 8) = 2 1 b. 6x 3 2 Page 32

11 Section 2.5: Simplifying Algebraic Expressions Step 1: Simplify within parentheses Step 2: Use distributive property to eliminate parentheses Step 3: Combine like terms. Simplify Completely Example 1: Simplify the following algebraic expressions. Show all possible steps. x b. 3 2 x 5 4x 10 a. 3(2 4) (3x 8) c. 8 5x 2 = d. 9 3(2x 5) = 6 Page 33

12 You Try Simplify completely. Show all steps. 6. 2(7x 2 + 3x +2) (8x 2 7) 7. 2( x 6) 8 2 Page 34