Summer Algebra Review

Transcription

1 Summer Algebra Review Students entering Geometry should complete this Algebra Review packet. Directions: Students entering Geometry at Friends Academy Upper School should complete this packet prior to the start of school as a review of concepts needed for further study of mathematics at FA. Name: Date: School where Algebra I was taken:

2 Helpful Formulas

3 Directions: For questions 1 41, DO NOT USE A CALCULATOR. Please show all work. Simplify. 1. (-16) + (-42) + (-25) + (-19) (-4)(6) + (-44) + (-11) 2. Evaluate if a = 18, b = 3, c = 4, d = 5 3. a - bc + d a (bc + d) a b(c + d) (a b)c + d 6. Simplify. 7. 6x 7y + 8x 2y m(n-2m) 2m(2m-3n) (2a 5) (4a + 6) + (7 2a) ( ) 12. Solve a + 2a 6 = 4a x = = 1 15.

4 16. A year-end clearance sale is advertised as 30% off all prices as marked. What is the sale price of a sofa that is marked as $925? If a calculator costs $12.90 after a 25% discount, what is the original price of the calculator? Evaluate Evaluate Evaluate 20. Write an expression or equation for each of the following. 21. The product of six less than a number and five more than the same number. 22. The number c equals the cube of the sum of 2 and three times m Twelve decreased by the square of a is equal to b. 23. Simplify Find p if 30.

5 Find each product. 31. (x 5)(x 4) (4n + 3)(3n 4) (a 4)(a 2 + 5a 7) (2x + 9y)(3x y) 34. Factor x 2 7x b 2 + 5b r 2 3r x 2 5x y The length of a rectangle is 3 feet less than twice the width. If the area of the rectangle is 54 ft 2 find the dimensions of the rectangle. 41. Solve these quadratics. 42. (x 8)(x 4) = x 2 8x 20 = k 2 12k 1 = Find the slope of a line that passes through the points (-6, 4) and (3, 5) X and Y are points with coordinates X(-12,6) and Y(14,-6) respectively. Find the coordinates of the midpoint of segment. 46.

6 47. Point M(5, 2) is the midpoint of segment. Point X has coordinates (-4, 6). Find the coordinates of point Y. 47. Graph the linear equations. 48. y = -3x x 2y = y = 2 Simplify. Rationalize the denominator when necessary The points (4,2) and (-1, y) are units apart. What is the value of y? 57. Solve these systems of equations. 58. { 58.

7 59. { x 1 = y and 4y = 3 2x Glen Cove has a population of 7,200, which is decreasing at a rate of 80 people per year. Locust Valley has a population of 5,000 and is gaining 120 people per year. In how many years will the populations of Glen Cove and Locust Valley be the same? 62. One evening, the candy counter at the Cineplex sold 532 buckets of popcorn for $1, A large bucket sells for $2.25 and a jumbo bucket sells for $3.75. How many jumbo buckets of popcorn were sold? In the graph below, name the coordinates of point P, Q and R. 62. P R 63. Q Solve

8 67. On the blue prints for a house, 2 inches represents 3 feet. If the width of a room on the plan is 6 ½ inches, what is the actual width of the room? Find three consecutive integers whose sum is Lynn has scores of 95, 91, and 88 on three tests. Write and solve an equation to find a fourth score that will produce an average of 90 for the four tests. 69. Find the missing side lengths. Leave your answers in simplest radical form x y x 45 y x 8 y 18 y Simplify the radical expressions x

9 Solve the following by writing a line in slope-intercept form 76. Write the equation of a line parallel to y = ½ x +5 and going through 76. the point (-7, -2). 77. Write the equation of a line perpendicular to 3y 6x 12 and going through the point 4, 1. (Use slope-intercept method) 77. Answer the following questions regarding probability and statistics. A box contains 2 red marbles, 3 white marbles, 4 green marbles and 1 blue marble. Two marbles are drawn at random without replacement. Find the probability of: 78. Selecting a green marble on the second draw if the first marble is blue Selecting a red or white on the first draw and green or blue on the 79. second draw. A card is drawn from a deck of 52 cards. 80. Find the probability of drawing a heart Find the probability of drawing either a spade or diamond. 81. Calculate the Mean, Median, Mode and Range. 120, 320, 330, 220, 202, 210, 230, 320, 210, 201, 310, 330, 240, 210, 330, Mean: Median: Mode: Range: 83. Determine whether the following situations would require calculating a permutation or combination. Then calculate the number of possible arrangements or listings. a.) Selecting three out of ten students to attend a conference in Washington, D.C. b.) Selecting a lead and an understudy for a school play from 32 auditions. c.) Assigning a class of 12 students to their seats on the first day of school. 84. In how many ways can you arrange the letters of the word APPLE?

10 85 86, Graph the following quadratic functions. Label the Vertex, describe it as a maximum or a minimum point, write the equation for the Axis of Symmetry and label the roots and y intercept

11 Solutions x-9y 8.-10m 2 +9mn 9. -4a (-3a 2 +20ab) / /63 OR -1 62/ a a = 1/3 14. x = -3 1/3 or x = -10/3 15. r = -16/5 or r = -3 1/5 16. $ $ (x-6)(x+5) 22. c = (2+3m) a 2 = b x 3 +x 2-5x x 2 + x y a 5 x bx 3 / 3ay x 9 y p = x 2-9x n 2 7n a 3 + a 2-27a x xy 9y abc(ab-3c) 36. (x-6)(x-1) 37. (b+6)(b-1) 38. (2r+5)(r-4) 39. (3x+2)(2x-3) 40. (y-5)(y+5) 41. width = 6 feet, length = 9 feet 42. x = {4,8} 43. x = {-2, 10} 44. x = { 45. m = 1/9 }

12 46. Midpoint = (1,0) 47. (14, -2) y = {9} 58. m = 3, n = (0, 2) 60. (1/2, ½) years 62. x = 337 large buckets, y = 195 jumbo buckets 63. P (-3,3 ) Q(4,-3 ) R(5,0 ) 64. a = 5 1/3, or 16/3 65. y = x = {-2, 6} 67. width = 9.75 feet , 47, % 70. x = 71. x = 7, y = x = 4, y = x =, y = y = 1/2x + 3/2 77. y = 1/2x / / /4

13 81. 1/2 82. mean = 250.8; median = 230; mode = 210 & 330; range = C(10, 3) = 120 P(32,2) = 992 P (12,12) = 479,001, Vertex (1, 1); Minimum; Axis of Symmetry x = 1; no roots; Vertex (2, 2); Maximum; Axis of Symmetry x = 2; {.5, 3.5}; -2