Chapter 1: Variables, Expressions, and Integers

Transcription

1 Name: Pre-Algebra Period: 8 Chapter 1: Variables, Expressions, and Integers Outline 1.1: p. 7 #12-15, 20-27, 32, 33, 34, 36 Date 1.2: p. 12 #16-20, 25-28, 30, 31, : p. 19 #10-18, 21-25, : p. 25 #18-23, 26-29, 34-37, 44, 46, 47 Ch. 1 Quiz 1 1.5: p. 32 #14-16, 24-32, : p. 36 #12-19, 24-31, 35, : p. 45 #12-23, 42, : p. 49 #8-15, Practice Test Ch. 1 Test 1.1 Expressions and Variables Numerical expression: Variable: Variable expression: Evaluate a variable expression: 1) Evaluate each expression when b = 90. a) 3 b b) 4 b + 5 2) Evaluate each expression when x = 8 and y = 4. a) x + y b) xy c) y x

2 Verbal model: 3) You have a 350-page manuscript that needs to be edited very quickly. You are going to divide the number of pages among several editors. You want to give the same number of pages to each editor. Use a verbal model to write a variable expression for the number of pages given to each editor if you know the number of editors. The word divide indicates Verbal model: Answer: Assignment: p. 7 #12-15, 20-27, 32, 33, 34, 36

3 1.2 Powers and Exponents Power: Base: Exponent: 1) Write the product using an exponent. a) = b) (0.4)(0.4)(0.4) = c) a a a a = 2) Using the above answers, write the power in words. a) b) c) 3) Evaluate the expression when n = 0.2. a) n 2 = b) n 4 =

4 Area and Volume Formulas Area A of a square A = Volume V of a cube V = 4) You are planning to put wall-to-wall carpeting in your room. To do this, you need to find the area of the square-shaped floor. A = s 2 Substitute for (replace) s: Answer: 5) Find the volume of a cube with a side length of 2 meters. V = s 3 Substitute: Answer: Assignment: p. 12 #16-20, 25-28, 30, 31, 36

5 1.3 Order of Operations Order of operations: Grouping symbols: Order of Operations 1. Evaluate expressions inside grouping symbols 2. Evaluate powers 3. Multiply and divide from left to right 4. Add and subtract from left to right 1) Evaluate each expression. a) b) c) ) Evaluate each expression. a) 5(14 3.8) b) c) 4 [35 (11 + 8)]

6 3) Evaluate each expression when x = 2 and y = 5. a) y(10 x 2 ) Substitute for x and y: Simplify: b) y(10 x) 2 Substitute for x and y: Simplify: c) 6y x + 1 Substitute for x and y: Simplify: Assignment: p. 19 #10-18, 21-25, 31

7 1.4 Comparing and Ordering Integers Integers: Negative integers: Positive integers: 1) Use the number line to order the integers from least to greatest: 0, 6, 2, 8, 7, 9, 3 From least to greatest: Absolute value: 2) State the absolute value of the number. a) 7 b) 5 Opposites: 3) State the absolute value and opposite of each number. a) 9 b) 12 Assignment: p. 25 #18-23, 26-29, 34-37, 44, 46, 47

8 Name CHAPTER 1 Practice Quiz 1 Lessons Evaluate the expression when x = 3, y = 1, and z = x 2. 8y Date Answers z y 4. y z 4. Write the power in words and as a repeated multiplication. Then evaluate the power (1.3) Evaluate the expression ( ) [(15 9) 2]

9 Complete the statement using < or > Answers State the absolute value and the opposite of the number Abs. Val. Opp. 14. Abs. Val. Opp. 15. You can evaluate the expression 6x to find the number of dollars a fund raising committee raises when x raffle tickets are sold for $6 each. Find the amount the committee receives when they sell 150 raffle tickets. 15.

10 1.5 Adding Integers Additive inverse: Additive inverse property: 1) Use a number line to find the sum. a) 7 + ( 10) = b) = Adding Integers 1. Same sign: = 6 + ( 4) = 2. Different signs: ( 8) = = 3. Opposites: ( 7) = 2) Find the sum. a) b) 7 + ( 41) + 32 c) 29 + ( 31) + 47 Assignment: p. 32 #14-16, 24-32, 33-35

11 1.6 Subtracting Integers To subtract an integer,. 1) Find the difference. a) 3 8 = = b) 2 9 = = c) 6 ( 3) = = 2) Evaluate the expression when y = 12. a) y 6 b) 7 y Substitute for y: Add the opposite: Simplify: Substitute for y: Add the opposite: Simplify: 3) Write a verbal model to find the change in temperature given the start temperature and the end temperature. Use the model to find the change in temperature from 5 F to 12 F. Verbal model: = Substitute: Add the opposite: Simplify: a) Find the change from 15 C to 2 C. Assignment: p. 36 #12-19, 24-31, 35, 36

12 1.7 Multiplying and Dividing Integers When multiplying sign, the answer is signs, the answer is The product of an integer and 0 is 1) Find the product. a) 7( 12) b) 9( 5) c) 250(0) d) 4(11) When dividing sign, the answer is signs, the answer is The quotient of 0 and any nonzero integer is 2) Find the quotient. a) 0 ( 43) b) 32 ( 4) c) 28 7 d) 38 ( 19) You can use a tic-tac-toe board to help you remember your signs when multiplying and dividing. x = = Assignment: p. 45 #12-23, 42, 46

13 1.8 The Coordinate Plane Coordinate plane: x-axis: y-axis: Origin: Quadrant: Ordered pair: x-coordinate: y-coordinate:

14 1) Give the coordinates of the point. a) C = Start at the Move first this is the Then move this is the b) D = c) E = 2) Plot the point in the coordinate plane. Describe the location of the point. a) A(2, 3) b) B( 4, 0) c) C(1, 3) Assignment: p. 49 #8-15, 17-24

15 Name CHAPTER 1 Practice Test Date Evaluate the expression when x = x 2. x x x 5. You can use the expression 10n to determine the amount of money you have, in cents, when you have n dimes. Find the amount of money you have, in cents, when you have 13 dimes. Write the product using an exponent (7)(7)(7)(7)(7)(7) 8. m m m m Evaluate the expression when n = n n 4 Evaluate the expression (4 + 9)

16 CHAPTER 1 Practice Test Evaluate the expression when t = t (t 7) t (t + 4) Order the integers from least to greatest: 7, 11, 6, 2, 0, 6 State the absolute value and the opposite of the number Evaluate the expression when c = c 23. c Find the sum, difference, product, or quotient ( 4) 25. ( 6)( 10) ( 11)

17 Find the change in temperature. 27. From 4 C to 10 C 28. From 15 F to 4 F Give the coordinates of the point. 29. U _(, )_ 30. V _(, )_ 31. W 32. X 33. Y 34. Z Plot the point in the coordinate plane. Describe the location of the point. 35. P(3, 3) 36. Q(4, 1)