Free Pre-Algebra Lesson 57! page 1

Transcription

1 Free Pre-Algebra Lesson 57! page 1 Lesson 57: Review for Final Exam Section I. The Natural Numbers Comprehensive Practice Lessons 1-6 Lesson 1: Counting, Estimating, and Rounding Skill: Estimate the size of a crowd HW1B #3. Estimate the number of cars in the photo. Skill: Use place value to read and write numbers. HW1B #1a. Write the group names as if reading the number aloud. 7,005,000,010 7, 5, 10 1b. Write the number 25 million, 5 thousand, 38 using digits. Skill: Round to a given place value, number of significant figures, or using your judgment in context. HW1B #4b Round 525,119 to the hundred thousands place. HW1B #6 Round using your judgment. In January of 2009, Facebook had 42,089,200 U.S. users; by January 2010 that had grown to 103,085,520 users and 471,447,000 users worldwide. HW1B #5b Round 311,267 kg. to four significant figures. Lesson 2: Measuring Length Skill: Measure length to the nearest inch. Measure the line to the nearest inch using the inch ruler provided. Skill: Measure length to the nearest centimeter. Measure the line to the nearest centimeter using the centimeter ruler provided.

2 Free Pre-Algebra Lesson 57! page 2 Lesson 3: Perimeter and Area Skill: Count perimeter and area for figures on a grid. Use appropriate units. HW3A #6. Find the perimeter and area of the figure. The grid is square centimeters. Skill: Use a memorized formula to find the perimeter of a rectangle, given the length and width. Write the answer with appropriate linear units. HW3A #11a. Find the perimeter of a rectangle with length 18 cm. and width 22 cm. Perimeter: Area: Skill: Use a memorized formula to find the area of a rectangle, given the length and width. Write the answer with appropriate square units. HW3A #12 b. Find the area of a rectangle with length 25 feet and width 30 feet. Expanded Skill HW7A #2. A rectangle has length 23 inches. The width is twice as much as the length. a. What is the width? b. What is the perimeter? c. What is the area? Lesson 4: Exponents and Volume Skill: Write multiplications with exponents. Write exponential notation as multiplications. Evaluate exponential expressions with a calculator. Write using an exponent, and evaluate. Skill: Use exponential abbreviations for square and cubic units. Write using an exponential abbreviation for the units. 23 square cm! 30 cubic cm! HW4A: #11a. Write out 5 8 as a multiplication, and evaluate. HW4A #2c. Evaluate 10 9, then write the number in words. Skill: Use a memorized formula to find the volume of a rectangular box. HW4A #12a. Find the volume of a box with length 22 inches, width 18 inches, and height 4 inches.

3 Free Pre-Algebra Lesson 57! page 3 Lesson 5: Arithmetic Operations and Precedence Skill: Write the related addition/subtraction problems for a set of numbers. HW5A #6a. Write the four related addition/subtraction equations using the numbers 4, 7, and 11. Skill: Write the related multiplication/division problems for a set of numbers. HW5A #6b. Write the four related multiplication/division equations using the numbers 4, 7, and 28. Skill: Refuse to divide by zero. Divide zero by other numbers and obtain zero as the answer. Differentiate between 0 as a number and answer and the situation with no possible answer. Divide, if possible. If not, write undefined. a. 6 0 b. 0 0 c. 0 6 Skill: Evaluate an expression in natural numbers using the correct order of operations. Skill: Use the vocabulary sum, difference, product, and quotient. HW6A #3. Match the operation to the name for the result: addition subtraction multiplication division quotient product sum HW5A #7 f. (22 4) 2 + (18 3) 2 difference HW5A #7 e HW6A #7d e. 45 (3 2 5)

4 Free Pre-Algebra Lesson 57! page 4 Lesson 6: More About Formulas Skill: Write an algebraic expression with variables and evaluate in a given situation. HW7A #8. The cost formula for a manufacturing business (per month) is Total Cost equals Fixed Costs plus Cost per Item times Number of Items Produced. Write the formula in algebraic notation. Skill: Write an algebraic expression with variables and evaluate in a given situation. L6Worksheet #5. Write a formula in algebraic notation for finding the amount of your paycheck. Amount of Paycheck is Hours Worked times Hourly Rate, minus Deductions. Find the cost (per month) for a business that has fixed costs of $2,485, and manufactured 9,244 items at a cost of $2 per item. Use the formula to find the amount of your paycheck when you have worked 32 hours at $14 per hour and have $96 deducted from the check. Skill: Use a memorized formula for distance-rate-time to solve a problem. HW6A #9. A hawk dived on its prey at a rate of 45 feet per second. The dive took 2 seconds. What distance was traveled? Skill: Use the given formula for Celsius-Fahrenheit conversions to solve a problem. HW6A #10. Mercury boils at about 355ºC. What temperature would this be in the Fahrenheit scale? Use the formula F = 9C/ !

5 Free Pre-Algebra Lesson 57! page 1a Lesson 57: Review for Final Exam Section I. The Natural Numbers Comprehensive Practice Lessons 1-6 Answers Lesson 1: Counting, Estimating, and Rounding Skill: Estimate the size of a crowd HW1B #3. Estimate the number of cars in the photo. Skill: Use place value to read and write numbers. HW1B #1a. Write the group names as if reading the number aloud. 7,005,000,010 7 billion, 5 million, 10 HW1B #1b. Write the number 25 million, 5 thousand, 38 using digits. 25,005,038 Skill: Round to a given place value, number of significant figures, or using your judgment in context. HW1B #4b Round 525,119 to the hundred thousands place. 525,119 rounds to 500,000 HW1B #5b Round 311,267 kg. to four significant figures. 311,267 rounds to 311,300 HW1B #6 Round using your judgment. In January of 2009, Facebook had 42,089,200 U.S. users; by January 2010 that had grown to 103,085,520 users and 471,447,000 users worldwide. 42 million; 103 million;, 471 million Lesson 2: Measuring Length Skill: Measure length to the nearest inch. Measure the line to the nearest inch using the inch ruler provided. Skill: Measure length to the nearest centimeter. Measure the line to the nearest centimeter using the centimeter ruler provided. The line is about 2 inches. It is a little over 2 inches. The line is about 5 cm. It is a little under 5 cm.

6 Free Pre-Algebra Lesson 57! page 2a Lesson 3: Perimeter and Area Skill: Count perimeter and area for figures on a grid. Use appropriate units. HW3A #6. Find the perimeter and area of the figure. The grid is square centimeters. Skill: Use a memorized formula to find the perimeter of a rectangle, given the length and width. Write the answer with appropriate linear units. HW3A #11a. Find the perimeter of a rectangle with length 18 cm. and width 22 cm. P = 2(L + W) P = 2(18 cm + 22 cm) P = 2(40 cm) P = 80 cm Perimeter: 22 cm Area: 20 cm Skill: Use a memorized formula to find the area of a rectangle, given the length and width. Write the answer with appropriate square units. HW3A #12 b. Find the area of a rectangle with length 25 feet and width 30 feet. A = LW A = (25 feet)(30 feet) A = 750 square feet Expanded Skill HW7A #2. A rectangle has length 23 inches. The width is twice as much as the length. a. What is the width? W = 2(23 inches) = 46 inches b. What is the perimeter? c. What is the area? P = 2( ) = 138 inches A = (23)(46) = 1058 square inches Lesson 4: Exponents and Volume Skill: Write multiplications with exponents. Write exponential notation as multiplications. Evaluate exponential expressions with a calculator. Write using an exponent, and evaluate. 8 5 = 32,768 HW4A: #11a. Write out 5 8 as a multiplication, and evaluate = 390,625 HW4A #2c. Evaluate 10 9, then write the number in words. 1,000,000,000 one billion Skill: Use exponential abbreviations for square and cubic units. Write using an exponential abbreviation for the units. 23 square cm! 23 cm 2 ; 30 cubic cm! 30 cm 3 Skill: Use a memorized formula to find the volume of a rectangular box. HW4A #12a. Find the volume of a box with length 22 inches, width 18 inches, and height 4 inches. V = (22 in)(18 in)(4 in) = 1584 in 3

7 Free Pre-Algebra Lesson 57! page 3a Lesson 5: Arithmetic Operations and Precedence Skill: Write the related addition/subtraction problems for a set of numbers. HW5A #6a. Write the four related addition/subtraction equations using the numbers 4, 7, and = = = = 7 Skill: Write the related multiplication/division problems for a set of numbers. HW5A #6b. Write the four related multiplication/division equations using the numbers 4, 7, and = = = = 7 Skill: Refuse to divide by zero. Divide zero by other numbers and obtain zero as the answer. Differentiate between 0 as a number and answer and the situation with no possible answer. Divide, if possible. If not, write undefined. a. 6 0 undefined b. 0 0 undefined c. 0 6 = 0 Skill: Evaluate an expression in natural numbers using the correct order of operations. HW5A #7 e = = = = 24 9 = 15 HW6A #7d = = 5 5 = 25 Skill: Use the vocabulary sum, difference, product, and quotient. HW6A #3. Match the operation to the name for the result: HW5A #7 f. (22 4) 2 + (18 3) 2 (22 4) 2 + (18 3) 2 = (18) 2 + (18-3) 2 = (18) 2 + (15) 2 = (15) 2 = = 549 HW6A #7e. 45 (3 2 5) 45 (3 2 5) = 45 (9 5) = 45 (45) = 1

8 Free Pre-Algebra Lesson 57! page 4a Lesson 6: More About Formulas Skill: Write an algebraic expression with variables and evaluate in a given situation. HW7A #8. The cost formula for a manufacturing business (per month) is Total Cost equals Fixed Costs plus Cost per Item times Number of Items Produced. Write the formula in algebraic notation. T = F + CN Find the cost (per month) for a business that has fixed costs of $2,485, and manufactured 9,244 items at a cost of $2 per item. T = (2485) + (2)(9244) = The total cost is $20,973 Skill: Use a memorized formula for distance-rate-time to solve a problem. HW6A #9. A hawk dived on its prey at a rate of 45 feet per second. The dive took 2 seconds. What distance was traveled? d = rt d = (45)(2) = 90 The distance was 90 feet. Skill: Write an algebraic expression with variables and evaluate in a given situation. L6Worksheet #5. Write a formula in algebraic notation for finding the amount of your paycheck. Amount of Paycheck is Hours Worked times Hourly Rate, minus Deductions. P = HR D Use the formula to find the amount of your paycheck when you have worked 32 hours at $14 per hour and have $96 deducted from the check. P = HR D P = (32)(14) 96 = 352 Your paycheck will be $352. Skill: Use the given formula for Celsius-Fahrenheit conversions to solve a problem. HW6A #10. Mercury boils at about 355ºC. What temperature would this be in the Fahrenheit scale? Use the formula F = 9C/ F = 9C/ F = 9(355)/ = 671 The Fahrenheit temperature is 671º.!

9 Free Pre-Algebra Lesson 57! page 5 Lesson 57: Review for Final Exam Section II. Fractions, Part 1 Comprehensive Practice Lessons 7-12 Lesson 7: Measuring Fractions of an Inch Skill: Measure lines to the nearest sixteenth of an inch. Write the measurement as a mixed number in lowest terms. HW7A #9 b. Measure the length of the line. Skill: Draw a line of a given length in fractions of an inch. HW7A #10 Draw a line of the given length. c. A line 2 1 / 4 inches long: Lesson 8: Factor Pairs Skill: Use division to find all factor pairs of a given number. Use the method of squares to make the most efficient factor pair table. Use divisibility shortcuts to increase efficiency. Lesson 9: Prime Factorization Skill: Determine if a number is prime or composite. Find the prime factorization of a composite number. Is the number 31 prime or composite? Worksheet 8 #3. Find all the factor pairs that have the given number as product Lesson 9 page 4: Find the prime factorization of 60.

10 Free Pre-Algebra Lesson 57! page 6 Lesson 10: Equivalent Fractions Skill: Use a model to visualize equivalent fractions. HW10A #8b. Write two names for the fraction of the rectangle that is shaded. Skill: Simplify a fraction to lowest terms. Lesson 10 page 5: Simplify 7/21 to lowest terms. HW10A #9. Use the rectangle to show that 3 4 = 6 8. Skill: Generate a list of equivalent fractions. HW10A #10a. Write 4 fractions equivalent to 5 7. Lesson 11: Mixed Numbers and Improper Fractions Skill: Relate mixed number and improper fraction notation to models. Worksheet 11 #5. Write an improper fraction for the number of blue rectangles. Each rectangle is 1 whole. Skill: Write an improper fraction as a whole or mixed number. HW11A #10. Write the improper fractions as mixed numbers Write a mixed number for this amount. 93 3

11 Free Pre-Algebra Lesson 57! page 7 Skill: Write a whole or mixed number as an improper fraction. HW11A #9. Write the mixed number as an improper fraction. Skill: Use and interpret notation N/N, N/1, 0/N, and N/0 correctly. Evaluate: HW11A #8. Write the whole number as an improper fraction using the given denominator. 3 = Lesson 12: Multiplying Fractions Skill: Understand fraction multiplication in models. HW12A #9. Use the picture to answer the questions. Skill: Multiply whole numbers with proper and improper fractions. Worksheet 12 #4. Multiply a a. What is 1/2 of 12? b. What is 1/3 of 12? c. What is 1/4 of 12? d. What is 1/6 of 12? e. What is 1/12 of 12? Skill: Multiply proper and improper fractions. Worksheet 12 #7c. Mulltiply the fractions. Use crosscancelling if possible. Do not convert answers to mixed numbers Skill: Multiply mixed numbers by converting to improper fractions. Worksheet 12 #8c. Convert the mixed numbers to improper fractions before multiplying. Write the answer as a mixed number !

12 Free Pre-Algebra Lesson 57! page 5a Lesson 57: Review for Final Exam Section II. Fractions, Part 1 Comprehensive Practice Lessons 7-12 Answers Lesson 7: Measuring Fractions of an Inch Skill: Measure lines to the nearest sixteenth of an inch. Write the measurement as a mixed number in lowest terms. HW7A #9 b. Measure the length of the line. 1 1/8 inches Skill: Draw a line of a given length in fractions of an inch. HW7A #10 Draw a line of the given length. c. A line 2 1 / 4 inches long: Lesson 8: Factor Pairs Skill: Use division to find all factor pairs of a given number. Use the method of squares to make the most efficient factor pair table. Use divisibility shortcuts to increase efficiency. Worksheet 8 #3. Find all the factor pairs that have the given number as product. Lesson 9: Prime Factorization Skill: Determine if a number is prime or composite. Find the prime factorization of a composite number. Is the number 31 prime or composite? Since 31 has no factors other than itself and 1, 31 is a prime number.. Lesson 9 page 4: Find the prime factorization of 60. Scratch Work: Method 1 Method The prime factorization of 60 is

13 Free Pre-Algebra Lesson 57! page 6a Lesson 10: Equivalent Fractions Skill: Use a model to visualize equivalent fractions. HW10A #8b. Write two names for the fraction of the rectangle that is shaded. 5/6 or 10/12 HW10A #9. Use the rectangle to show that 3 4 = 6 8. Skill: Simplify a fraction to lowest terms. Lesson 10 page 5: Simplify 7/21 to lowest terms. Method 1: GCF The GCF of 7 and 21 is = 1 3 Method 2: Prime Factorization = = 1 3 Skill: Generate a list of equivalent fractions. HW10A #10a. Write 4 fractions equivalent to = = = = Lesson 11: Mixed Numbers and Improper Fractions Skill: Relate mixed number and improper fraction notation to models. Worksheet 11 #5. Write an improper fraction for the number of blue rectangles. Each rectangle is 1 whole. 25/6 Skill: Write an improper fraction as a whole or mixed number. HW11A #10. Write the improper fractions as mixed numbers = 9r = Write a mixed number for this amount. 4 1/ = 31r = 31

14 Free Pre-Algebra Skill: Write a whole or mixed number as an improper fraction. HW11A #9. Write the mixed number as an improper fraction = = 22 3 HW11A #8. Write the whole number as an improper fraction using the given denominator. Lesson 57! page 7a Skill: Use and interpret notation N/N, N/1, 0/N, and N/0 correctly. Evaluate: 7 7 = = = undefined 3 = = 12 Lesson 12: Multiplying Fractions Skill: Understand fraction multiplication in models. HW12A #9. Use the picture to answer the questions. Skill: Multiply whole numbers with proper and improper fractions. Worksheet 12 #4. Multiply a a. What is 1/2 of 12? 6 b. What is 1/3 of 12? 4 c. What is 1/4 of 12? 3 d. What is 1/6 of 12? 2 e. What is 1/12 of 12? = = 6 1 = 6 Skill: Multiply proper and improper fractions. Worksheet 12 #7c. Mulltiply the fractions. Use crosscancelling if possible. Do not convert answers to mixed numbers = = 4 1 = 4 Skill: Multiply mixed numbers by converting to improper fractions. Worksheet 12 #8c. Convert the mixed numbers to improper fractions before multiplying. Write the answer as a mixed number = = = = 35 3 = 112 3!

15 Free Pre-Algebra Lesson 57! page 8 Lesson 57: Review for Final Exam Section III. Algebra, Part 1 Comprehensive Practice Lessons Lesson 13: More Cancelling Skill: Simplify fractions with variables in the numerator and or denominator. HW13A #8c. Simplify 4xy 6xy 2 Skill: Interpret the fraction bar as a division symbol in the order of operations. HW 13A #9a. Simplify 18! Skill: Cancel units in distance-rate-time problems. HW13A #10b. Write the rate as a fraction and adapt the distance-rate-time formula to solve the problem. Show your units throughout. A copy machine can make 85 copies per minute. If the machine is busy for 34 minutes on a job, how many copies were made? Lesson 14: Solving Equations, Part 1 Skill: Solve single operation equations with correct algebraic technique. HW14A #9. Solve the equations. a. 7x = 161 Skill: Substitute numbers in a formula and solve the resulting equation. HW14A #10. Use a formula to write an equation. Solve the equation and write units with your answer. a. The length of a rectangle is 14 cm, and the area is 224 cm 2. Find the width. b. y 5 = 10 c. N + 29 = 107 b. A ship traveled 315 miles in 9 hours. Find the speed (rate) of the ship. d. M! 29 = 107

16 Free Pre-Algebra Lesson 57! page 9 Lesson 15: Simplifying Algebraic Expressions Skill: Multiply monomials. HW16A #2a. Multiply (14a)(3ab) Skill: Combine like terms. HW16A #2d. Combine like terms to simplify 10N + 5M + 6N + M Skill: Use the distributive property. HW16A #2e. Use the distributive property to simplify 9(2M + 1) Skill: Simplify using a combination of methods. HW16A #2. Simplify 3(3x + 3) + 5(5x + 4) Lesson 16: Solving Equations, Part 2 Skill: Solve multi-step equations. HW16A #3f. Solve the equation 17 = 2 + 3n Skill: Simplify expressions in equations before solving. HW17A #5b. Solve the equation 5a a = 26 Skill: Substitute numbers in a formula and solve the resulting equation. HW17A #6b. The perimeter of a rectangle is 780 cm. The width is 180 cm. What is the length? Skill: Write the answer to an equation as an improper fraction in lowest terms. Lesson 16 page 5: Solve 5x + 2 = 20.

17 Free Pre-Algebra Lesson 57! page 10 Lesson 17: Formulas for Triangles Skill: Find the perimeter of a triangle by measuring and adding the sides. HW18A #3. A triangle has the measurements shown. Skill: Find the area of a triangle using the memorized formula. HW18A #3. A triangle has the measurements shown. a. Find the perimeter. b. Find the area. Lesson 18: Word Problems Skill: Use a structure sentence to write a formula for a word problem. Solve the problem using the formula. HW18B #8. Use the structure sentence No. Boxes No. Items per Box = No. Items to write equations for the problems. Then solve. a. For our fundraiser we got 200 cases of candy bars. That s 5000 candy bars. How many candy bars in one case? Skill: Write an equation and solve to answer a word problem. HW18A #10. Write an equation and solve: The amusement park charges $55 for an adult and $40 for a child. The group took 24 children, and their cost for the day at the park was $1180. How many adults went along?!

18 Free Pre-Algebra Lesson 57! page 8a Lesson 57: Review for Final Exam Section III. Algebra, Part 1 Comprehensive Practice Lessons Answers Lesson 13: More Cancelling Skill: Simplify fractions with variables in the numerator and or denominator. HW13A #8c. Simplify 4xy 6xy = 2 2 x y x y y = 2 3y Skill: Interpret the fraction bar as a division symbol in the order of operations. HW 13A #9a. Simplify 1 18! = 18! = = 1 2 Skill: Cancel units in distance-rate-time problems. HW13A #10b. Write the rate as a fraction and adapt the distance-rate-time formula to solve the problem. Show your units throughout. A copy machine can make 85 copies per minute. If the machine is busy for 34 minutes on a job, how many copies were made? 85 copies 34 mins rt = 1 min 1 = 2890 copies Lesson 14: Solving Equations, Part 1 Skill: Solve single operation equations with correct algebraic technique. HW14A #9. Solve the equations. a. 7x = 161 b. y 5 = 10 5 y 5 c. N + 29 = 107 d. M! 29 = x 7 = x = 23 = 5 10 y = 50 N + 29 = 107!29 =!29 N = 78 M! 29 = = +29 M = 136 Skill: Substitute numbers in a formula and solve the resulting equation. HW14A #10. Use a formula to write an equation. Solve the equation and write units with your answer. a. The length of a rectangle is 14 cm, and the area is 224 cm 2. Find the width. A = LW 14W 14 = = 14W W = 16 cm b. A ship traveled 315 miles in 9 hours. Find the speed (rate) of the ship. d = rt 315 = r 9 9r 9 = r = 35 mph

19 Free Pre-Algebra Lesson 57! page 9a Lesson 15: Simplifying Algebraic Expressions Skill: Multiply monomials. HW16A #2a. Multiply (14a)(3ab) (14a)(3ab) = 14 3 a a b = 42a 2 b Skill: Combine like terms. HW16A #2d. Combine like terms to simplify 10N + 5M + 6N + M 16N + 6M Skill: Use the distributive property. HW16A #2e. Use the distributive property to simplify 9(2M + 1) 18M + 9 Skill: Simplify using a combination of methods. HW16A #2. Simplify 3(3x + 3) + 5(5x + 4) 9x x + 20 = 34x + 29 Lesson 16: Solving Equations, Part 2 Skill: Solve multi-step equations. HW16A #3f. Solve the equation 17 = 2 + 3n 3n + 2! 2 = 17! 2 3n = 15 3n / 3 = 15 / 3 n = 5 Skill: Simplify expressions in equations before solving. HW17A #5b. Solve the equation 5a a = 26 5a a = 26 8a + 2 = 26 8a + 2! 2 = 26! 2 8a = 24 8a / 8 = 24 / 8 a = 3 Skill: Substitute numbers in a formula and solve the resulting equation. HW17A #6b. The perimeter of a rectangle is 780 cm. The width is 180 cm. What is the length? P = 2L + 2W 780 = 2L + 2(180) 2L = 780 2L + 360! 360 = 780! 360 2L = 420 2L / 2 = 420 / 2 L = 210 cm Skill: Write the answer to an equation as an improper fraction in lowest terms. Lesson 16 page 5: Solve 5x + 2 = 20. 5x + 2 = 20 5x + 2! 2 = 20! 2 5x = 18 5x / 5 = 18 / 5 x = 18 5

20 Free Pre-Algebra Lesson 57! page 10a Lesson 17: Formulas for Triangles Skill: Find the perimeter of a triangle by measuring and adding the sides. HW18A #3. A triangle has the measurements shown. Skill: Find the area of a triangle using the memorized formula. HW18A #3. A triangle has the measurements shown. a. Find the perimeter. P = 7 in /2 in + 12 in = 27 1 /2 in. b. Find the area. A = bh 2 = (12 in.)( in.) = 36 in 2 Lesson 18: Word Problems Skill: Use a structure sentence to write a formula for a word problem. Solve the problem using the formula. HW18B #8. Use the structure sentence No. Boxes No. Items per Box = No. Items to write equations for the problems. Then solve. a. For our fundraiser we got 200 cases of candy bars. That s 5000 candy bars. How many candy bars in one case? 200N = N / 200 = 5000 / 200 N = 25 There are 25 candy bars per case. Skill: Write an equation and solve to answer a word problem. HW18A #10. Write an equation and solve: The amusement park charges $55 for an adult and $40 for a child. The group took 24 children, and their cost for the day at the park was $1180. How many adults went along? Cost for group = cost for adults + cost for children Cost for children: 24 $40 per child is = $960 Cost for adults: UNKNOWN number of adults (use the variable $55 per adult is $55A Equation: 1180 = 55A A = A + 960! 960 = 1180! A = A / 55 = 220 / 55 A = 4 Four adults went along.!