Free Pre-Algebra Practice Cumulative Final Exam! page 1

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1 Free Pre-Algebra Practice Cumulative Final Exam! page 1 Cumulative, Excluding Optional Sections Practice Final Exam Your instructor may choose a different selection of course topics to emphasize in your class final exam. 1. Write the number using digits. a. ninety-two million, forty-seven 2. Round the numbers as indicated. a. Round 78,951,876 to the nearest million. b. twenty-two thousandths b. Round meters to two significant figures. c billion c. Round to the nearest hundredth. d x d. Round to three decimal places. 3. Find the length of the line shown. a. to the nearest centimeter 4. Write the related problems. a. Write the related addition/subtraction problems for the numbers 8, 3, and 11. b. to the nearest sixteenth of an inch b. Write the related multiplication/division problems for the numbers 8, 3, and 24. c. Write the related square and square root problems for Find the perimeter and area of the figure. The grid is square centimeters. 6. Find the perimeter and area of a rectangle with length 43 meters and width 2 meters less than the length. Length: 43 meters Width: Perimeter: Area: Perimeter: Area:

2 Free Pre-Algebra Practice Cumulative Final Exam! page 2 7. Find the perimeter and area of a triangle with the measurements shown. 8. Find the radius, circumference, and area of a circle with the measurements shown. Round to the nearest hundredth. Perimeter: Area: 9. If a rectangular box has length 22 inches, width 24 inches, and volume 8448 cubic inches, what is the height? Radius: Circumference: Area: 10. A rectangle has perimeter 64 cm. The width is 4 cm more than the length. Write the equation and solve to find the length and width of the rectangle. 11. Find the area of the figure with the measurements shown. 12. Find the side not marked. Round to the nearest tenth. 13. The diagonal is 34 inches. Is the angle a right angle?

3 Free Pre-Algebra Practice Cumulative Final Exam! page Evaluate (22! 4) 2! 7! Evaluate 6 3! 5(!20)!10 2! 5(!20) 16. Convert 16.4º C to Fahrenheit. F = 9C An object is tossed up from a 48 foot balcony. The height at time t seconds after it was tossed is given by the equation h =!16t 2 + 8t Find the height after 1.1 seconds. 18. Simplify to lowest terms. 28a 2 b 42ab Write as an improper fraction. 20. What is two-thirds of a group of 48 people? 21. Divide 20w w. 22. Find equivalent fractions with a common denominator Add ! 24. Simplify x + 11 $ # " 12 & % 25. Solve 7 8 x =!

4 Free Pre-Algebra Practice Cumulative Final Exam! page A plane traveled 1820 miles in 3 1 / 2 hours. What was the plane s rate? 27. How many cups are in 5 1 / 4 gallons? (4 cups = 1 quart, 4 quarts = 1 gallon) 28. Vera is constructing a 1:36 scale model of a home design for her architecture class. The east wall of the home will measure 27 feet. How long is the east wall in the model? 29. Find the unit prices. Planet Ultra Laundry Detergent 100 fl oz. 4 pack for $51.15 Seventh Generation Laundry Detergent 150 fl oz. for $ Fill in the table. FRACTION DECIMAL PERCENT 3/4 1/ % 3% 34. If sales tax is 9.25% and the item cost $80, what is the tax? 29. Jackson uses a bedroom measuring 174 square feet for a home office. His home is 1568 square feet. What percent of his home is used for an office? 35. After her 5% raise, Chelsea was making $14.70 per hour. How much did she make before the raise? 36. The number of students who graduated decreased from 834 to 816. What was the percent decrease? 37. $50,000 is split between two investments. $21,000 is invested at 3% and the rest at 4% annual interest. Find the combined interest earned in the two accounts.

5 Free Pre-Algebra Practice Cumulative Final Exam! page Compare the foods as requested. 100 g serving Nonfat Frozen Yogurt Ice Cream calories carbs 19.7 g 28.2 g fat 0.8 g 11.0 g protein 4.4 g 3.8 g a. Compare the calories in ice cream to those in nonfat frozen yogurt using a ratio. Ice cream has about times the calories as nonfat frozen yogurt. b. Compare the carbs using a difference. Ice cream has g more carbs than nonfat frozen yogurt. 39. Simplify a. x! 2x b. 3( 5x! 6)! 8x + 13! 7x 40. Evaluate a.!9 b.! 9 c. (!3) 2 d Solve the equation.!16 = x! Solve the equation. 4n 18! 9 18 = Solve the equation. 5k! 7 = A child s ticket to the play costs $5, and an adult ticket costs $15. A group paid $75 for their tickets. Three of the group were adults. How many were children? Write an equation and solve. 45. Answer true or false, and give a reason for your answer. a. The number! is not a real number. b. The number 2 is irrational. c. All integers are rational numbers.

6 Free Pre-Algebra Practice Cumulative Final Exam! page 1a Cumulative, Excluding Optional Sections Practice Final Exam Answers Your instructor may choose a different selection of course topics to emphasize in your class final exam. 1. Write the number using digits. a. ninety-two million, forty-seven 92,000,047 b. twenty-two thousandths c billion 19,500,000,000 d x ,000,000, Round the numbers as indicated. a. Round 78,951,876 to the nearest million. 79,000,000 b. Round meters to two significant figures. 890 meters c. Round to the nearest hundredth d. Round to three decimal places Find the length of the line shown. a. to the nearest centimeter a little over 4 cm. b. to the nearest sixteenth of an inch 1 and 7/16 inch. 4. Write the related problems. a. Write the related addition/subtraction problems for the numbers 8, 3, and = 11 11! 3 = = 11 11! 8 = 3 b. Write the related multiplication/division problems for the numbers 8, 3, and = = = = 3 c. Write the related square and square root problems for Find the perimeter and area of the figure. The grid is square centimeters. 8 2 = = 8 6. Find the perimeter and area of a rectangle with length 43 meters and width 2 meters less than the length. Length: 43 meters Width: 43 2 = 41 meters Perimeter: P = 2(L + W) = 2(43 m + 41 m) = 2(84 m) = 168 meters Area: A = LW = (43 m)(41 m) = 1763 m 2 Perimeter: 26 cm Area: 19 cm 2

7 Free Pre-Algebra Practice Cumulative Final Exam! page 2a 7. Find the perimeter and area of a triangle with the measurements shown. 8. Find the radius, circumference, and area of a circle with the measurements shown. Round to the nearest hundredth. Perimeter: P = 80 cm + 50 cm + 78 cm = 208 cm Area: A = bh/2 = (78 cm)(48 cm)/2 = 1872 cm 2 9. If a rectangular box has length 22 inches, width 24 inches, and volume 8448 cubic inches, what is the height? V = LWH 8448 in 3 = (22 in)(24 in)(x in) 528x = x / 528 = 8448 / 528 x = 16 The height is 16 inches. 11. Find the area of the figure with the measurements shown. 12. Find the side not marked. Round to the nearest tenth. a 2 + b 2 = c b 2 = b 2 = b 2 = ! = b = " The side is about 11.8 cm Radius: r = d/2 = 9.36 / 2 = 4.68 in. Circumference: C =!d =!(9.36 in.)! in. Area: A =!r 2 =!(4.68 in) 2! in A rectangle has perimeter 64 cm. The width is 4 cm more than the length. Write the equation and solve to find the length and width of the rectangle. 64 = 2L + 2(L + 4) 4L + 8 = 64 4L = L = 56 4L / 4 = 56 / 4 L = 14, W = L + 4 = 18 The length is 14 cm and the width is 18 cm. Figure is rectangle plus two triangles. Area of rectangle is (40 cm)(20 cm) = 800 cm 2 Area of one triangle is (20 cm)(20 cm) / 2 = 200 cm 2 area of rectangle + 2 triangle = 800 cm 2 + 2(200 cm 2 ) = 1200 cm 2 The figure is 1200 cm The diagonal is 34 inches. Is the angle a right angle? = c 2 c 2 = 1156 c = 1156 = 34 Yes, since a 2 + b 2 = c 2, the angle is right.

8 Free Pre-Algebra Practice Cumulative Final Exam! page 3a 14. Evaluate (22! 4) 2! 7! 14 2 = (18) 2! 7! 14 2 = 324! 7! 196 = 121 = Convert 16.4º C to Fahrenheit. F = 9C F = 9(!16.4) + 32 = 2.48ºF Evaluate 6 3! 5(!20)!10 2! 5(!20) = ! = No answer is possible. 17. An object is tossed up from a 48 foot balcony. The height at time t seconds after it was tossed is given by the equation h =!16t 2 + 8t Find the height after 1.1 seconds. h =!16(1.1) 2 + 8(1.1) + 48 = feet 18. Simplify to lowest terms. 28a 2 b 42ab 2 = a a b a b b = 2a 3b 19. Write as an improper fraction = = What is two-thirds of a group of 48 people? 2! 16 $ 3 48 = 32 people " # % & 22. Find equivalent fractions with a common denominator. 7 8 = = = = 22 24! 24. Simplify x + 11 $ # " 12 & % 21. Divide 20w w. = w 12 w Add = = = 16w 2 3 ( ) + 21 = = = Solve 7 8 x =! ! $ # " 24 & % 3 = 24 2! 7 # " 8 x $ & % + 24 = 21x + 22! 11 $ # & " 12 % x =! x =! 3 13

9 Free Pre-Algebra Practice Cumulative Final Exam! page 4a 26. A plane traveled 1820 miles in 3 1 / 2 hours. What was the plane s rate? d = rt 3.5r = r / 3.5 = 1820 / 3.5 r = 520 mph 28. Vera is constructing a 1:36 scale model of a home design for her architecture class. The east wall of the home will measure 27 feet. How long is the east wall in the model? 28. Fill in the table. 27 feet = 324 inches 1 36 = x = 36x 36x / 36 = 324 / 36 x = 9 inches FRACTION DECIMAL PERCENT 3/ % 1/ % 2/ % 1 1 / % 2/ % 3/ % 34. If sales tax is 9.25% and the item cost $80, what is the tax? $80 = $ The number of students who graduated decreased from 834 to 816. What was the percent decrease? difference is = / 834 = about a 2% decrease 27. How many cups are in 5 1 / 4 gallons? (4 cups = 1 quart, 4 quarts = 1 gallon) gal Find the unit prices. 4 qt 1 gal 4 cups = 84 cups 1 qt Planet Ultra Laundry Detergent 100 fl oz. 4 pack for $51.15 $51.15! $0.13 per oz. 400 fl oz Seventh Generation Laundry Detergent 150 fl oz. for $20.89 $20.89! $0.14 per oz. 150 fl oz 29. Jackson uses a bedroom measuring 174 square feet for a home office. His home is 1568 square feet. What percent of his home is used for an office? 174 / 1568 = about 11% 35. After her 5% raise, Chelsea was making $14.70 per hour. How much did she make before the raise? 1.05x = x / 105 = 14.7 / 105 x = 14 Her previous wage was $14.00 per hour. 37. $50,000 is split between two investments. $21,000 is invested at 3% and the rest at 4% annual interest. Find the combined interest earned in the two accounts. 0.02(21,000) (50,000 21,000) = = 1580 $1580 interest

10 Free Pre-Algebra 38. Compare the foods as requested. 100 g serving Nonfat Frozen Yogurt Ice Cream calories carbs 19.7 g 28.2 g fat 0.8 g 11.0 g protein 4.4 g 3.8 g 39. Simplify a. x! 2x =!1x =!x b. 3( 5x! 6)! 8x + 13! 7x 41. Solve the equation.!16 = x! 5 2 = 15x! 18! 8x + 13! 7x = 0x! 5 =!5 x! 5 2 =!16 2 x! 5 2 =!16 2 x! 5 =!32 x! =! x =! Solve the equation. 5k! 7 = 0 5k! 7 = 0 5k! = k = 7 5k / 5 = 7 / 5 k = 7 5 Practice Cumulative Final Exam! page 5a a. Compare the calories in ice cream to those in nonfat frozen yogurt using a ratio. 216 / 107 = Ice cream has about _2_times the calories as nonfat frozen yogurt. b. Compare the carbs using a difference g 19.7 g = 8.5 g Ice cream has _8.5_g more carbs than nonfat frozen yogurt. 40. Evaluate a.!9 not a real number b.! 9 =!3 c. (!3) 2 = 3 d. 3 2 = Solve the equation. 4n 18! 9 18 = n! 9 = 11 4n! = n = 20 4n / 4 = 20 / 5 n = A child s ticket to the play costs $5, and an adult ticket costs $15. A group paid $75 for their tickets. Three of the group were adults. How many were children? Write an equation and solve. 5c + 15(3) = 75 5c + 45 = 75 5c = c = 30 5c / 5 = 30 / 5 c = 6 There were 6 children. 45. Answer true or false, and give a reason for your answer. a. The number! is not a real number. False.! is on the number line and is a real number. b. The number 2 is irrational. True. There is no fraction exactly equal to 2. c. All integers are rational numbers. True. Any integer is the answer a division problem with integers.