Algebra Intro Quarter 4 - Benchmark Review Packet

Transcription

1 Class: Date: Algebra Intro Quarter 4 - Benchmark Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the graph that displays the speed of a baseball being pitched and then hit by the batter. a. c. b. d. 1

2 2. Identify the graph that displays the depth of water in a swimming pool after the drain is opened. a. c. b. d. Short Answer Write an equation of the line that passes through the pair of points. 3. Ë Á 5, 2 ˆ, 3, 1 ˆ 4. Ë Á 5, 8 ˆ, 3, 8 ˆ Solve the equation or formula for the variable specified. 5. df + 10h = 3 for d 6. 3qr + 9t = 7u for r The formula for the perimeter, P, of a rectangle is P = 2 + 2w, where is the length and w is the width. 7. Solve the formula for the perimeter of a rectangle for w. 2

3 Write each equation in standard form. 8. y + 6 = (x + 4) 9. y + 3 = 2/5(x + 9) Find the slope of the line that passes through the pair of points. 10. ( 3, 2), (5, 4) 11. (2, 3), ( 5, 1) Write an equation of the line with the given slope and y-intercept 12. slope: 2/7, y-intercept: 3 Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle. 13. Write an equation for the total cost C of renting a bicycle and riding for m miles. 14. Graph the equation needed to represent the cost at Beach Bike Rentals. Use the graph below to determine the number of solutions the system has. 15. x = 4 y = x x = 4 y = x 1 3

4 17. 2x = 2y 6 y = x + 3 Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. 18. y = x + 5 y = 6x 2 Use the method of your choice to solve the following systems For the word problems, set up a system of equations, then solve algebraically. 19. y = x + 1 8x 4y = x 10y = 10 3x + 10y = x + 8y = 8 8x + 4y = x 2y = 5 7x + 6y = x 6y = 6 7x + 9y = The sum of two numbers is 90. Their difference is 12. What are the numbers? 25. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $ Sabrina bought 9 CDs and spent a total of $ How many $12.00 CDs did she purchase? 26. Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan? 27. Dakota s math test grade was 7 points less than his science test grade. The sum of the grades was 183%. What did Dakota get on his math test? 28. Isaac downloaded 7 ringtones. Each polyphonic ringtone costs $3.25, and each standard ringtone costs $1.50. If he spends a total of $21 on ringtones, find the number of polyphonic and standard ringtones he downloaded. 29. Christie has a total of 15 pieces of fruit, all bananas and apples, worth $1.59. Bananas are 13 cents each and apples are 7 cents each. How many bananas and how many apples does she have? 4

5 30. Dylan has 15 marbles. Some are red and some are white. The number of red marbles is three more than six times the number of the white marbles. Write a system of equations that can be used to find the number of white marbles, x, and the number of red marbles, y. 31. Sam s test score is 12.5 more than Nicole s score. The sum of twice Sam s score and three times Nicole s score is 195. What are Sam and Nicole s test scores? Use double or triple distribution to simplify 32. ( r 8) ( r + 5) 33. ( 6t 4v) ( 7t 4v) 34. ( 6k + 4) 7k 2 ˆ + 2k m 2 ˆ 6m + 4 4m 2 2m 7 ˆ 36. ( 6c + 6) 2 Translate the sentence into an equation. 37. Four less than the product of eight and the number g is equal to ten more than g. Write a verbal expression for the algebraic expression. 38. x 3 y y 2 3 Translate the equation into a verbal sentence y + 8 = 32 Evaluate the expression (9 3) ( 3) 2 ( 6) Evaluate the following expression if a = 12, b = 5, and c = 9. 3c + bc 2a 45. Evaluate the following expression if x = 1 2, and y = 1 4 4xy y 5

6 46. Evaluate the following expression if x = -12, y = 6, and z =8. x 2 y 2z 4 Evaluate the expression. Show each step ˆ ( ) Solve the equation a = ( ) 9 8 ( 2) + 8 Simplify the expression x + 4 ( x + 9) Simplify the expression. If not possible, write simplified ( 6m + 11c 2c) 52. Solve the equation. Then check your solution. 7 9 m = x 12 = a = 2 z 30 = m 3.9 = z = Solve the equation. Then check your solution x = 9x = 2 ( 4x + 9) 60. 9( 38u 69) = 63(3u 52) 61. 1/4( a) = a 4 6

7 Simplfy completely a 4a 2 ˆ + ( 5 + 6a) 63. 5a 3b 2 ˆ a + b 3 + 8a 2 ˆ 64. 4a 4a 2 ˆ ( 8a 4) 65. 2s 3 t 3 7s 5 t 5 5st 3 ˆ 3t 66. 2r 3 2r 2 ˆ 4r x 2 2x 2 ˆ 4x 3 x 3x 3 ˆ Solve the equation x( x 3) = 2 2x 2 ˆ y y 3 ˆ + 5 = 3 y 2 ˆ 2y 2y 70. 2n ( n + 4) + n ( n 2) 15 = 3n ( n + 1) + 2n ( 4x + 4) = 2 ( 5x + 9) p Ë Á 3p 8 ˆ 8 = 9p p 3 ˆ The table below shows the yearly sales of a CD player in a particular store. Year Sales Find an equation in function notation for the relation. 74. The table below shows the cost of cartons of milk. Number of cartons Cost ($) Graph the data. 7

8 The following table shows car sales at a local car dealership for the first seven days of October. Day Sales Draw a graph to show car sales for the first seven days of October. 8

9 Algebra Intro Quarter 4 - Benchmark Review Packet Answer Section MULTIPLE CHOICE 1. A 2. B SHORT ANSWER 3. y = 1/8x 11/8 4. y = 8x d = 3 10h f 6. r = 7u 9t 3q 7. w = P x y = x 5y = / /7 12. y = 2/7x C = m one 16. one 17. infinitely many 1

10 18. one solution; (1, 4) 19. (1, 2) 20. (0, 1) 21. ( 3, 4) 22. (7, 8) 23. ( 18, 13) and % polyphonic, 1 standard bananas, 6 apples 30. x + y = 15 y = 6x Sam s score: 46.5; Nicole s score: r 2 3r t tv + 16v k 3 40k k m m 3 53m m c c g 4 = 10 + g 38. x cubed times y to the fifth power 39. the quotient of 8 times y squared and Three times a number y plus 8 equals

11 ˆ + 4 = ( 16 16) + 4 = ( 0) + 4 = = ( ) + 1 = 2 + 4(19 9) + 1 = 2 + 4(10) + 1 = = x m + 54c 52. 0/9/ a 2 + 9a a 2 3b 2 + 4a + b a a s 8 t s 4 t 6 + 6s 3 t r 5 + 8r r x x 3 + 6x 2 + 3x f( x) = 45x

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