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ALGEBRA 1 EOC REVIEW 1 (LINEAR FUNCTIONS)

ALGEBRA 1 EOC REVIEW 1 (LINEAR FUNCTIONS). 1). Suppose that the function: f(x) = 3 x + 14 represents the cost to rent x video games from a local store. Jack has $ 19 in his wallet. How much more will he need in order to rent 5 video games this month?. f(x) = 3(5) + 14. money needed:

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ALGEBRA 1 EOC REVIEW 1 (LINEAR FUNCTIONS)

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  1. ALGEBRA 1 EOC REVIEW 1 (LINEAR FUNCTIONS)

  2. 1) Suppose that the function: f(x) = 3 x + 14 represents the cost to rent x video games from a local store. Jack has $ 19 in his wallet. How much more will he need in order to rent 5 video games this month? f(x) = 3(5) + 14 money needed: $ 29 – $ 19 = $ 10 f(x) = 15 + 14 f(x) = 29

  3. 2) A bag of lollipops contains 20 lollipops. Each lollipop costs $ .10. How much will a club have to sell each lollipop to make a profit of $ 5 per box? 20 x – 2 = 5 20 x = 7 x = $ .35

  4. 3) Cell Phone company A charges $ 20 per month plus $ 0.10 per text. Cell Phone B charges $ 25 per month with no charge per text. Write the function that represents: A: f(x) = .1 x + 20 a) Each plan B: g(x) = 25 b) The combined costs of the two plans. f(x) + g(x) = .1 x + 45 c) The difference in cost between A and B. f(x) – g(x) = .1 x – 5

  5. 4) Find the slope, y-intercept, and x-intercept of the following. Then circle the highest slope, highest y-intercept, and the largest x-intercept. a) The line going between (2, 3) and (4, 5). - 1 y-intercept 1 x-intercept Slope: 1 b) x-intercept of 3; y-intercept of - 4 y-intercept x-intercept Slope: - 4 4/3 3 c) -2 Slope: 6 y-intercept 3 x-intercept

  6. 5) The exchange rate (including a transfer fee) from Japanese Yen to US Dollar is D = .0097 Y + 4 where D is dollar and Y is Yen. (multiple choice) a) The amount of dollars increases by 4 per yen. b) The amount of dollars increases by .0097 per 100 yen. c) The amount of dollars increases by 40 per 100 Yen. d) The amount of dollars increases by .97 per 100 yen.

  7. 6) The equation for Jack’s savings is f(x) = 8 x + 20 and for Paul’s savings is g(x) = 14 x + 3 where x is the number of weeks. a) How much is Jack’s savings per week? $ 8 b) How much did Paul have in his account initially? $ 3 c) What is the meaning of f(x) = g(x)? Find it algebraically and by graphing both equations. When their savings will be the same. 8 x + 20 = 14 x + 3 -6x = - 17 x = 2.833 weeks

  8. 7) There were originally 4000 trees in the forest. Each year, a certain number of trees were cut down. After 15 years, there were 1900 trees. Find the equation that determines how many trees there are per year. (15, 1900) (0, 4000) y = - 140 x + 4000

  9. 8) The surface area of a sphere is 500 cm2. What is the approximate diameter of the sphere? (SA = 4 п r2) 4 п r2 = 500 r = 6.31 d = 2 r = 2(6.31) = 12.62

  10. 9) F(x) = 3 x + 2. g(x) is defined by the line that goes through (5, 6) and (7, 8). 6 = 1(5) + b g(x) = x + 1 6 = 5 + b 1 = b a) Find the difference of their slopes. 3 – 1 = 2 b) Find the difference of their y-intercepts. 2 – 1 = 1

  11. 10) Solve for x: 2x – 3 – 7x = 10 – 4x + 6 -5x – 3 = -4x + 16 -x – 3 = 16 -x = 19 x = -19

  12. 11) Solve for c: 5ab – 3bc = 10 for c. -3bc = -5ab + 10 c = -5ab+10 -3b ---- ------------ - 3b -3b

  13. 12) Find the x and y-intercepts of the following f(x) = 5x – 4 b. f(x) = x2 + 4x – 5 c.f(x) = 3(2)x + 1 Yint: -4 X int: 0=5x – 4 4 = 5x 4/5 = x Yint: -5 X int: 0=(x+5)(x-1) =-5, 1 Yint: 3 + 1 = 4 X int: none

  14. 13) Jack has no more than $80 to buy tickets for a football game for family. Student tickets cost $3 and Adult tickets cost $5 each. Jack graphed 3x + 5y < 80 to determine how many of each ticket she can buy. Which describes the point (5,13) A. He has $5 after buying 13 adult tickets. B. He has $13 after buying 5 student tickets C. He can buy 5 adult and 13 student tickets. D. He can buy 13 adult tickets and 5 student tickets. Adult = y = 13; Student = x = 5

  15. 14) Which describes the domain and range of the function y = 5x – 3? • Domain: all real numbers. Range all real numbers • B. Domain: positive real numbers. • Range: real numbers greater than -3 • C. Domain: nonnegative real numbers • Range: positive real numbers • D. Domain: all real numbers Range: real numbers great than 3/5

  16. 15) John has budgeted $60 to buy pork ribs and chicken legs for a barbecue. Ribs are $3.75 per pound and chicken legs are $3.00 per pound. If Carl buys x pounds of chicken, which represents the number of pounds y of ribs he can buy and not exceed his budget? • y< -3x + 60 • y < -0.8x + 16 • 3.75y – 60 < 3x • 3x + 3.75y > 60 3x + 3.75y < 60 3.75y < -3x + 60 y < -.8x + 16

  17. 16) A company has monthly expenses represented by a function C(x) = 16x + 4200 where x represents the number of items produced. For how many items produced is the monthly cost $81,000? • 1,300,200 B. 5,325 • c. 5,063 D. 4,800 81000=16x + 4200 76800= 16x 4800=x

  18. 17) An Internet wholesaler charges vendors $5.10 for each bottle of herbal hand lotion plus $27.50 per order for shipping. What is the total cost to a vendor ordering 72 bottles of hand lotion? • $367.20 B. $387.50 • C. $394.70 D. $2,347.20 C = 5.10x + 27.50 C = 5.10(72) + 27.50

  19. 18)A company manufactures and sells surfboards uses the function P=40s – 200,000 to estimate its profit P on the sale of s surfboards. How many boards must the company sell to make $1,200,000 in profit? 1,200,000= 40s – 200,000 1,000,000 = 40s 25,000 = s

  20. 19) Which of the following is a solution of y = - 2 • (1/2)x? (Circle all that apply.) a) (- 2, 0) d) (- 1, 4) b) (1, - 1) c) (- 3, - 16) a) 0 = - 2 • (1/2)-2 b) - 1 = - 2 • (1/2)1 c) - 16 = - 2 • (1/2)-3 d) 4 = - 2 • (1/2)-1

  21. 20) Which of the following is a solution of x = 10 – 4 y? (Circle all that apply.) a) (2, 2) d) (- 6, 4) b) (- 8, 42) c) (2, 3) a) 2 = 10 – 4(2) 2 = 10 – 8 b) - 8 = 10 – 4(42) - 8 = 10 – 168 c) 2 = 10 – 4(3) 2 = 10 – 4(3) d) - 6 = 10 – 4(4) d) - 6 = 10 – 16

  22. 21) Find the radius if the volume of a cone is 226.98 cm3 with a height of 3 cm. V = 1/3пr2 h. (Round to the nearest tenth.) r2 = 72.249 r = 8.5

  23. 22) Find the radius of a sphere if the volume is 523.6 cm2. V = 4/3пr3. (Round to the nearest tenth.) r3 = 125 r = 5

  24. 23) Jack has $ 4000 in her savings account and she deposits $ 300 every month. Create an equation in two variables to represent this situation. Graph this equation and find how much money will Tatiana have in her savings account after 3 years. y = 300 x + 4000 y = 300(36) + 4000 = 14800

  25. 24) John has $48 to buy songs and games. A song is $0.50 and a game is $4. a. 0.50x + 4y = 48 b. 0.50x + 4(0) = 48 .5x = 48  x = 96 games c. 0.50(0) + 4(y) = 48 4x = 48  x = 12 songs 0.50x + 4(10) = 48 .50X + 40 = 48 .5X = 8 X = 16

  26. 25) The length of a rectangle is (5 x + 8) and the width is (2 x + 1). What are the possible values for x, if the perimeter of the rectangle is less than 64 yards? 2(5 x + 8) + 2(2 x + 1) < 64 10 x + 16 + 4 x + 2 < 64 14 x + 18 < 64 14 x < 46 x < 3.29

  27. 26) Which inequality describes the graph? m = 3/2 b = 3/2 y = -3/2 x + 3/2 A) - 2 y + 3 > 3 x B) 2 y + 3 > 3 x C) - 2 y + 3 > - 3 x D) y ≥ - 3/2 x + 3/2

  28. 27) 2x + y >3 y > -2x + 3 m = -2, y-intercept is 3, shade above so the answer is A

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