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Chapter 1

Chapter 1. Variables, Function Patterns, and Graphs. Lesson 1-1 Variables, Patterns, and Graphs. Check Skills You’ll Need. (For help, go to the skills handbook page 75.). Estimate to find whether each answer is reasonable. 2. 478.23. 1. $154.38. – 199.30. 22.45. 378.93. 276.12.

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Chapter 1

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  1. Chapter 1 Variables, Function Patterns, and Graphs

  2. Lesson 1-1Variables, Patterns, and Graphs Check Skills You’ll Need (For help, go to the skills handbook page 75.) Estimate to find whether each answer is reasonable. 2. 478.23 1. $154.38 – 199.30 22.45 378.93 276.12 + 28.98 $481.93 4. $316.24 3. 76.425 – 48.76 18.94 $267.48 182.6 + 54.769 232.729

  3. Lesson 1-1Variables, Patterns, and Graphs

  4. Lesson 1-1Variables, Patterns, and Graphs Key Concepts A variableis An algebraic expressionis Examples: An equationis An open sentenceis

  5. Lesson 1-1Variables, Patterns, and Graphs Write an algebraic expression for each phrase. Example 1 a. the sum of nand 8 b. six less than b

  6. Lesson 1-1Variables, Patterns, and Graphs Define a variable and write an algebraic expression for each phrase. Example 2 a. “ten more than twice a number.” b. “three times a number minus six.”

  7. Lesson 1-1Variables, Patterns, and Graphs Write an equation to show the total income from selling tickets to a school play for $5 each. Example 3

  8. Gallons Miles Lesson 1-1Variables, Patterns, and Graphs Write an equation for the data in the table. Example 4 4 6 8 10 80 120 160 200

  9. Lesson 1-1Variables, Patterns, and Graphs Lesson Quiz Write an algebraic expression for each phrase. 1. 7 less than 9 2. the product of 8 and p 3. 4 more than twice c Define variables and write an equation to model each situation. 4. The total cost is the number of sandwiches times $3.50. 5. The perimeter of a regular hexagon is 6 times the length of one side.

  10. Lesson 1-1Variables, Patterns, and Graphs Homework Pages 6 – 8; 1 – 24, 48 – 56

  11. Lesson 1-2Exponents and Order of Operations Check Skills You’ll Need (For help, go to the skills handbook page 755.) Find the greatest common factor of each set of numbers. 1. 4 and 8 2. 12 and 15 3. 5 and 7 4. 8 and 12 5. 14 and 21 6. 12 and 20 Find the least common multiple of each set of numbers. 7. 4 and 8 8. 12 and 15 9. 5 and 7 10. 3 and 9 11. 6 and 9 12. 9 and 12

  12. Lesson 1-2Exponents and Order of Operations

  13. Lesson 1-2Exponents and Order of Operations Key Concepts To simplify a numerical expression, You evaluate an algebraic expression by

  14. Lesson 1-2Exponents and Order of Operations Key Concepts An exponentis A power has two parts, a ________ and an ___________.

  15. Lesson 1-2Exponents and Order of Operations Simplify 32 + 62 – 14 • 3. Example 1

  16. Lesson 1-2Exponents and Order of Operations Evaluate 5x + 32 ÷ p for x = 2 and p = 3. Example 2

  17. Lesson 1-2Exponents and Order of Operations Find the total cost of a pair of jeans if the price is $32 and the sales tax rate is 8%. Example 3

  18. Lesson 1-2Exponents and Order of Operations Simplify 3(8 + 6) ÷ (42 – 10). Example 4

  19. Lesson 1-2Exponents and Order of Operations Evaluate each expression for x = 11 and z = 16. Example 5 a. (xz)2 b.xz2

  20. Lesson 1-2Exponents and Order of Operations Simplify 4[(2 • 9) + (15 ÷ 3)2]. Example 6

  21. Lesson 1-2Exponents and Order of Operations Lesson Quiz Evaluate each expression. 4. 4x + 3y for x = 2 and y = 4 5. 2 • p2 + 3s for p = 3 and s = 11 6.xy2 + z for x = 3, y = 6 and z = 4 Simplify each expression. 1. 50 – 4 • 3 + 6 2. 3(6 + 22) – 5 3. 2[(1 + 5)2 – (18 ÷ 3)]

  22. Lesson 1-2Exponents and Order of Operations Homework Pages 12 – 13 2 – 58 even, 63,73

  23. 2 5 Lesson 1-3Exploring Real Numbers Check Skills You’ll Need (For help, go to the skills handbook page 762.) • Write each decimal as a fraction and each fraction • as a decimal. • 0.52. 0.053. 3.254. 0.325 • 5.6.7.8. 3 3 8 2 3 5 9

  24. Lesson 1-3 Exploring Real Numbers

  25. Lesson 1-3 Exploring Real Numbers Natural numbers: Counting numbers {1, 2, 3, . . .} Key Concepts Whole numbers: Natural numbers and zero {0, 1, 2, 3, . . .} Integers: Negative numbers, zero, positive numbers {. . . , -2, -1, 0, 1, 2, . . .}

  26. Lesson 1-3 Exploring Real Numbers Key Concepts A rational number in decimal form is either terminating, such as 3.27 or repeating, such as 8.232323…, which can be written as . All integers are rational numbers because you can write any integer n as . Rational numbers: any number that can be written in the form , where a and b are integers and b ≠ 0.

  27. Lesson 1-3 Exploring Real Numbers Key Concepts Irrational numbers: any number that cannot be written in the form , where a and b are integers. An irrational number in decimal form does not terminate or repeat.

  28. Lesson 1-3 Exploring Real Numbers Key Concepts Together, rational numbers and irrational numbers form the set of real numbers.

  29. 21 43 c. Lesson 1-3 Exploring Real Numbers Name the set(s) of numbers to which each number belongs. Example 1 a.–17 b.5.46 d.89

  30. Lesson 1-3 Exploring Real Numbers Which set of numbers is most reasonable for each situation? Example 2 a.the number of available tables at a restaurant b.the length of a dollar bill c. the outdoor temperature

  31. Lesson 1-3 Exploring Real Numbers Determine whether the statement is true or false. If it is false, give a counterexample. Example 3 All negative numbers are integers.

  32. Lesson 1-3 Exploring Real Numbers Key Concepts An inequality is a When you compare two real numbers, only one of these can be true: a < b a = b a > b is less than is equal to is greater than There are three other symbols that compare two values. a ≤ b a ≠ b a ≥ b is less than is not equal to is greater than or equal to or equal to

  33. Lesson 1-3 Exploring Real Numbers Key Concepts Two numbers that are the same distance from zero on a number line but lie in opposite directions are opposites. The absolute value of a number is

  34. Lesson 1-3 Exploring Real Numbers Write , , and , in order from least to greatest. Example 4

  35. Lesson 1-3 Exploring Real Numbers Find each absolute value. Example 5 a.|–5| b.|3.2|

  36. Lesson 1-3 Exploring Real Numbers Lesson Quiz Name the set(s) of numbers to which each given number belongs. 1.–7.22.3.11 Use <, =, or > to compare. 4.5. _ _ 6. Find 3 4 5 8 3 4 5 8

  37. Lesson 1-3 Exploring Real Numbers Homework Page 20 – 21 2 – 62 even Quiz 1-1 through 1-3

  38. Lesson 1-4 Patterns and Functions Check Skills You’ll Need (For help, go to Lesson 1-1.) Write an algebraic expression for each phrase. 1. 10 more than twice a number 2. a number divided by 4 3. 8 minus six times a number 4. twice a number subtracted from 7

  39. Lesson 1-4 Patterns and Functions

  40. Lesson 1-4 Patterns and Functions Key Concepts A function is A function rulesuch as C = p + 0.06p,

  41. Lesson 1-4 Patterns and Functions Key Concepts The value of the dependent variable depends on the value of the independent variable. The possible values for the input, or independent variable, of a function are the __________of the function. The possible values of the output, or the dependent variable, of a function are the __________of the function.

  42. Lesson 1-4 Patterns and Functions Suppose you are buying apples from a vending machine. Use the table to write a function rule. Example 1

  43. Lesson 1-4 Patterns and Functions Suppose you want to find out how much gas a trip will take, in a car that uses one gallon of gas to go about 18 miles. What are the independent quantity and the dependent quantity for this situation? Example 2

  44. Lesson 1-4 Patterns and Functions Ken burns 425 calories per hour when he bikes. He bikes from 3 to 7 hours each weekend. Identify the independent and dependent quantities for this situation and find reasonable domain and range values. Example 3

  45. Lesson 1-4 Patterns and Functions Lesson Quiz Copy and complete each table. Then write a function rule for each relationship. 1. 2.

  46. Lesson 1-4 Patterns and Functions Lesson Quiz Identify the independent and dependent quantity in each situation and find reasonable domain and range values. 3. Gerald rents 2 movies for each day of the 3-day holiday weekend. Each rental costs between $2.50 and $5. The weight of each kitten in the litter of 5 is between 10 and 12 ounces. Jill chooses a basket that can support the total weight of the litter. 4.

  47. Lesson 1-4 Patterns and Functions Homework Pages 29 – 30 1 – 10 Quiz 1-4

  48. Lesson 1-5 Scatter Plots Check Skills You’ll Need (For help, go to Review Page 24.) Graph each point on the same coordinate grid. 1. (6, 4) 2. (–5, 1) 3.4. (0, –1)

  49. Lesson 1-5 Scatter Plots

  50. Lesson 1-5 Scatter Plots Key Concepts • A scatter plot is • To make a scatter plot, plot the two groups of data as ordered pairs. • Most scatter plots are in the first quadrant of a coordinate plane, because the data are usually positive numbers.

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