LHS June 2012 Algebra 1 Final Exam

Transcription

1 Teacher: (circle one) Mrs. Gordon Mr. Normile E-block Mr. Normile F-block LHS June 2012 Algebra 1 Final Exam Multiple Choice + Short Answer = /65 Part I Multiple Choice 33 questions 33 points This is a 90-minute exam, but you will be allowed to work for up to 120 minutes. Calculator use is permitted for the entire exam. You are allowed to use the green reference sheet provided during this exam. Circle the choice that best completes the statement or answers the question. 1. What equation models the data in the table if d = number of days and c = cost? Days Cost a. d = 22c b. c = 22d c. c = d + 22d d. c = d Evaluate 4 w for w = 7. a. 3 c. 11 b. 11 d One winter day, the temperature ranged from a high of 40ºF to a low of 5ºF. By how many degrees did the temperature change? a. 45ºF c. 25ºF b. 35ºF d. 55ºF 4. Simplify by combining like terms. 3x 3 + 9z + 2x 3 + 5z + 6x 2 a. x 3 + 4z + 6x 2 c. 6x z + 6x 2 b. 5x z + 6x 2 d. 11x z A

2 5. The range of a set of scores is 27, and the lowest score is 39. Write and solve an equation to find the highest score. (Hint: In a data set, the range is the difference between the highest and the lowest values.) a. h + 27 = 39 The highest score is 12. b. h 39 = 2 27 The highest score is 93. c. h + 39 = 27 The highest score is 12. d. h 39 = 27 The highest score is Which number is a solution of the inequality? 4x 15 3 a. 2 b. 9 2 c. 3 4 d Tina can type at least 60 words per minute. Write and graph an inequality to model this situation. a. t< 60 c. t> 60 b. t 60 d. t Solve the inequality. Then graph your solution. 2w < 18 a. w > 9 c. w < 9 b. w < 16 d. w > 16 page 2

3 9. Solve the inequality. Then graph your solution. 2 < 4x 10 < 6 a. 4 < x < 12 c. 16 < x < 8 b. 3 < x < 1 d. 2 < x < Give the domain and range of the relation. Tell whether the relation is a function. x y a. D: { 3, 2, 1, 4}; R: {0, 1, 2} The relation is a function. b. D: {0, 1, 2}; R: { 3, 2, 1, 4} The relation is not a function. c. D: { 3, 2, 1, 4}; R: {0, 1, 2} The relation is not a function. d. D: {0, 1, 2}; R: { 3, 2, 1, 4} The relation is a function. 11. Determine a relationship between the x- and y-values. Write an equation. x y a. y = x + 4 c. y = x + 3 b. y = 3x + 1 d. y = x Choose the compound inequaltity for: all real numbers that are greater than 6 but less than 6 a. 6 x 6 c. 6 < x < 6 b. 6 < x < 6 d. 6 < x 6 page 3

4 13. Find the slope of the line. a. 0 c. b. undefined d Tell whether the slope of the line is positive, negative, zero, or undefined. a. negative c. undefined b. positive d. zero page 4

5 15. Find the slope of the line. a. 3 5 c. b. 2 3 d Use the graph. Which plant was the tallest at the beginning? Which plant had the greatest rate of change over the 6 weeks? a. Tallest: plant 2; Greatest rate of change: plant 3 b. Tallest: plant 2; Greatest rate of change: plant 1 c. Tallest: plant 3; Greatest rate of change: plant 3 d. Tallest: plant 1; Greatest rate of change:plant 2 page 5

6 17. Match the equation with its graph. 7x + 7y = 49 a. c. b. d. page 6

7 18. Graph the equations y = 3x 2 and y = 2x + 3 on the same coordinate plane. Then, find the point where both lines intersect. a. c. Intersection: (1, 1) Intersection: ( 1, 1) b. d. Intersection: ( 1, 1) Intersection: (1, 1) page 7

8 19. Which of the following graphs is a function? HINT - there is a test you can use. a. c. b. d. 20. Evaluate mn m + n when m = 10 and n = 11. a b c d Simplify: 3 + 3( 4 + 5) 3 a b. 149 c d. 19,686 page 8

9 22. The cost of renting a canoe is $7.50, plus $0.75 per hour for the time that the canoe is out. Which equation could be used to find C, the cost in dollars for using the canoe for H hours? a. C H = 7.50 c. C = H b. C = ( )H d. C = H 23. Simplify 4(x 4) a. 4x 4 b. 4x + 16 c. 4x 16 d. 4x Simplify 3x + 1 4x + 4 a. 7x 3 b. 7x + 5 c. x + 5 d. x Solve the equation. x 5 = 15 a. 75 b. 75 c. 3 d Write an equation in slope-intercept form of the graph. a. y = 11 5 x 7 b. y = 5 11 x 7 c. y = 5 11 x 7 d. y = 11 5 x 7 page 9

10 27. Determine which relation is a function. a. Input b. c. d. Output Input Output Input Output Input Output For the sequence in the table, write a rule in words and the expression for the nth term. Term number n Term a. Multiply the term number by 2 and add 7; 2n + 7 b. Multiply the term number by 7 and add 2; 7n + 2 c. Multiply the term number by 7 and subtract 2; 7n 2 d. Multiply the term number by 2 and subtract 7; 7n Jamilla runs an international trading business. Below is a table of the cost (c) of items and Jamilla's selling price (p). Jamilla's cost of item (c) $17 $16 $15 $14 Selling price of item (p) $51 $48 $45? What is the selling price for an item that costs $14? a. $14 b. $42 c. $43 d. $56 page 10

11 30. Temperature changes throughout the hours of a day. Early in the morning, temperature increases slowly. At noon, the temperature rises sharply. During the afternoon, the temperature stays the same for several hours. As night falls, the temperature decreases slightly. Choose the graph that best represents this situation. a. c. b. d. 31. Find the x- and y-intercepts of x + 2y = 8. a. x-intercept: 11, y-intercept: 4 c. x-intercept: 8, y-intercept: 3 b. x-intercept: 11, y-intercept: 3 d. x-intercept: 8, y-intercept: Find the slope and y intercept of the line given by the equation y = 4 3 x 3 a. slope 3; b. slope 3; c. slope 3 4 ; d. slope 4 3 ; y intercept 4 3 y intercept 4 3 y intercept 3 y intercept 3 page 11

12 33. A student finds the slope of the line between (14, 1) and (18, 17) She writes. What mistake did she make? 17 1 a. She should have added the values, not subtracted them. Ê run ˆ b. She used y-values where she should have used x-values. ËÁ rise c. She did not keep the order of the points the same in the numerator and denimonator. Part II Short Answer points each part; 11 questions 32 points total reminder - Calculator use is permitted for the entire exam. reminder - You are allowed to use the green reference sheet provided during this exam. Except for questions #35 and 42 you are required to show your work for full credit for all questions partial credit can be earned. 34. The solid line below is the graph of the equation y = 3x 1. The dashed line is the result of changing just one of the numbers, 3 or 1, in the equation for the solid line. Which number was changed and what was it changed to? The was changed to. page 12

13 35. You are planning on buying a sailboat that costs $650. If you plan to save $50 per month, how long will you have to save in order to purchase the sailboat? WORK: ANSWER: 36. Solve the equation 2x 2 = 7 WORK: ANSWER:. 37. Is x = 4 a solution of the inequality 2x 2 7? WORK: ANSWER: page 13

14 38. Solve the equation. 6x 2 =2x + 22 WORK: ANSWER: CHECK: 39. Graph the line with the slope 3 and y-intercept 6. 2 page 14

15 40. Write an equation of the line with slope 1 3 and y-intercept Find the x-intercept of the line with the equation 3x 4y = 12. WORK: ANSWER: 42. Find the y-intercept of the line with the equation 3x 4y = 12. WORK: ANSWER: page 15

16 43. Plot the points (3, 5) and (5, 4) and find the slope of the line through the points. a) using the slope triangle (show on graph) b) using the slope formula - show your work! WORK: Slope is: Slope is: page 16

17 44. Norma is in the business of repairing home computers. She charges a base fee of $45 for each visit and $25 per hour for her labor. a. Write a function rule for the total cost c(x) for a home visit and x hours of labor. b. Use your rule from part a., to make a table of values and a graph. x c(x) c. How many hours did she work for a bill of $145? page 17

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