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ALGEBRA 1 EOC REVIEW 4 EXPONENTS, FOIL, FACTORING, SYSTEMS

ALGEBRA 1 EOC REVIEW 4 EXPONENTS, FOIL, FACTORING, SYSTEMS. SIMPLIFY:. 7 x 2 – 5 x – 3 + 2 x. 1). A) 7 x 2 + 3 x – 3. B) x 4. C) – 3. D) 7 x 2 – 3 x – 3. SIMPLIFY:. (- 3 c 3 d 4 )(5 c 5 d 2 ). 2). A) - 15 c 15 d 8. B) - 15 c 8 d. C) - 15 c 8 d 6. D) - 8 c 8 d 8.

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ALGEBRA 1 EOC REVIEW 4 EXPONENTS, FOIL, FACTORING, SYSTEMS

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  1. ALGEBRA 1 EOC REVIEW 4 EXPONENTS, FOIL, FACTORING, SYSTEMS

  2. SIMPLIFY: 7 x2 – 5 x – 3 + 2 x 1) A) 7 x2 + 3 x – 3 B) x4 C) – 3 D) 7 x2 – 3 x – 3

  3. SIMPLIFY: (- 3 c3 d4)(5 c5 d2) 2) A) - 15 c15 d8 B) - 15 c8 d C) - 15 c8 d6 D) - 8 c8 d8

  4. SIMPLIFY: 3) B) A) - 15 x2 y3 z3 D) C)

  5. SIMPLIFY: (6 b2 c3)2 4) A) 12 b4 c6 B) 36 b4 c6 C) 12 b4 c5 D) 36 b4 c5

  6. SIMPLIFY: 5) B) A) D) C)

  7. SIMPLIFY: 6) B) A) D) C)

  8. SIMPLIFY: 7) B) A) D) C)

  9. 8) Find the perimeter of a triangle whose sides are (3 x2 + 5); (5 x – 2); and (6 x2 + 5 x). A) 9 x2 + 10 x + 3 B) 19 x2 + 3 C) 9 x4 + 10 x2 – 3 D) 7 x4 + 10 x – 3

  10. 9) Simplify: (2 x + 5) (2 x – 3) A) 4 x2 – 15 B) 4 x2 – 4 x – 15 C) 4 x2 + 4 x – 15 D) 8 x – 15

  11. 10) Simplify: (3 x2 + 5 x + 1) – (7 x2 – 2) A) - 4 x2 + 5 x + 3 B) - 4 x2 + 5 x – 1 C) x2 – 1 D) x2 + 3

  12. 11) Simplify: (x – 2) (3 x2 – x + 4) A) 3 x3 – 7 x2 + 6 x – 8 B) 3 x3 – 6 x2 + 6 x + 4 C) 3 x3 + 7 x2 – 6 x – 8 D) 2 x3 – 8

  13. 12) Find the perimeter of a rectangle if the width is (2 x – 4) and the length is (5 x + 1). A) 7 x – 3 B) 7 x + 3 C) 14 x – 6 D) 14 x + 6

  14. 13) Find the area of a triangle if the base is (2 x – 4) and the height is (x + 6). A) x2 + 4 x – 12 B) 2 x2 + 8 x – 24 C) 2 x2 – 8 x – 24 D) 3 x + 2

  15. SIMPLIFY: 14) A) 2 x y – 3 + 4 x B) 2 y – 3 + 4 x C) 2 y – 3 + 4 y D) 2 x y – 3 + 4 x2

  16. SIMPLIFY: 15) A) B) C) D)

  17. SIMPLIFY: 16) A) B) C) D)

  18. 17) The area of a rectangle is given by the expression: x2 – 5 x – 6. The length and width have only integral coefficients. Which of the following could represent the length of the rectangle? A) x – 6 B) x – 2 D) x – 1 C) x – 3

  19. Given: 2 x – 3 y = 12 6 x + 2 y = 42 18) What is x + y? 2(2 x – 3 y = 12) 4 x – 6 y = 24 3(6 x + 2 y = 42) 18 x + 6 y = 126 22 x = 150 x = 150/22 = 75/11 2(75/11) – 3 y = 12 x + y = 75/11 + 6/11 y = 6/11 150/11 – 3 y = 12 – 3 y = - 18/11 x + y = 81/11 = 7.4

  20. 19) A restaurant received 270 hamburger patties and 350 hotdogs on Monday for $ 450. On Friday the restaurant received 550 hamburger patties and 425 hotdogs for $ 630. a) How much did each hamburger cost? x = cost of a hamburger cost of a hamburger = $ .38 y = cost of a hotdog cost of a hotdog = $ .995 270 x + 350 y = 450 550 x + 425 y = 630 b) How much will 25 hamburgers and 50 hotdogs be? 25($.38) + 50($.995) = $ 59.25

  21. 20) A local pet store has triple the amount of fish as birds and has a total of 250 fish and birds. Write a system of equations represents the number of fish and birds using the variables F and B. F = number of fish B = number of birds F = 3(62.5) = 187.5 F = 3 B F + B = 250 No solution since you cannot have a fraction of a bird or of a fish. 3 B + B = 250 4 B = 250 B = 62.5

  22. Given: 4 x + 3 y = 60 x – y = 10 21) x = y + 10 What is the value of x ? 4(y + 10) + 3 y = 60 4 y + 40 + 3 y = 60 7 y + 40 = 60 7 y = 20 y = 20/7 = 2 6/7 = 2.86 x = 2 6/7 + 10 = 12 6/7 = 12.86

  23. Given: 2 x + y = 15 5 x – 6 y = - 22 22) y = - 2 x + 15 What is the value of x – y ? 5 x – 6(- 2 x + 15) = - 22 5 x + 12 x – 90 = - 22 17 x – 90 = - 22 y = - 2(4) + 15 y = 7 17 x = 68 y = - 8 + 15 x = 4 x – y = 4 – 7 = - 3 A) 11 B) 2 D) - 3 C) 3

  24. Given: w = 1 – v 2 v + w = 4 23) What is the value of w ? 2 v + 1 – v = 4 w = 1 – v = 1 – 3 = - 2 v + 1 = 4 v = 3 A) 3 B) 2 D) - 2 C) 1

  25. A limosine company charges a flat-fee of $ 80 plus $.05 per mile. A shuttle van company charges a flat-fee of $ 60 plus $.50 per mile. Approximately what mileage will yield the same fare for both? 24) limo: y = .05 x + 80 shuttle: y = .5 x + 60 .05 x + 80 = .5 x + 60 2000 = 45 x 5 x + 8000 = 50 x + 6000 44.4 = x A) 24 miles B) 34 miles D) 54 miles C) 44 miles

  26. The price of six sodas and four candy bars is $ 18.50. The price of two candy bars and eight sodas is $ 20.50. What is the price of a candy bar? 25) x = number of sodas y = number of candy bars 6 x + 4 y = 18.50 x = $ 2.25 y = $ 1.25 8 x + 2 y = 20.50 A) $ 1.25 B) $ 2.25 D) $ 2.15 C) $ 1.65

  27. The area of a rectangle is given by the expression: x2 – 5 x – 6. The length and width only have integral coefficients. Which of the following could represent the length of the rectangle? 26) (x – 6)(x + 1) A) x – 6 B) x – 3 D) x – 1 C) x – 2

  28. 27) Factor: x2 + 9 x + 18 (x + 6) (x + 3) 28) Factor: x2 – 13 x y – 30 y2 (x – 3 y)(x – 10 y)

  29. 29) Factor: w2 + 2 w – 15 (w + 5) (w – 3) 30) Factor: x3 + 5 x2 + 6 x x(x2 + 5 x + 6) x(x + 2)(x + 3)

  30. A restaurant makes at least 50 pizzas a night, but no more than 250 pizzas. The restaurant makes at least 20 salads but no more than 90 salads. A total of no less than 325 pizzas and salads are made each night. Each pizza makes a profit of $ 3.00. Each salad makes a profit of $ 2.25. What is the maximum profit the restaurant can make in a night? 31) Constraints: P(x, y) = 3 p + 2.25 s 50 ≤ p ≤ 250 20 ≤ s ≤ 90 p + s ≥ 325 A) $ 998.25 B) $ 881.25 D) $ 952.50 C) $ 907.50

  31. 31) x + y ≥ 325 P3(250, 90) Corner points: P1(235, 90) y ≤ 90 P2(250, 75) x > 50 y ≥ 50 x ≤ 250 P(235, 90) = 3(235) + 2.25(90) = $ 672.50 P(250, 75) = 3(250) + 2.25(75) = $ 918.75 HIGHEST PROFIT P(250, 90) = 3(250) + 2.25(90) = $ 952.50

  32. SIMPLIFY: 32) A) B) C) D)

  33. SIMPLIFY: 33)

  34. 34) Solve the following system of inequalities: 2 x + y < 3 x – 2 y ≤ 8 y < - 2 x + 3 y ≥ ½ x – 4 y = - 2 x + 3 y = ½ x – 4

  35. 34) Solve the following system of inequalities: 3 y ≥ 6 x – 9 3 x + 4 y < 12 y ≥ 2 x – 3 y < - ¾ x + 3 y = - ¾ x + 3 y = 2 x – 3

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