The Distributive Property

Transcription

1 Dear Student, Please find attached your summer review packet for Honors Algebra 2. The problems in this packet are taken from Algebra 1 and Geometry and they should be familiar to you. However, if you need review, you can use the attached websites for additional information. Internet access is available at all public libraries. The packet is due the first day of class and will be graded. To receive full credit, you will need to show all work. This assignment will count toward your first quarter grade and your first quiz of the year will be on this material. Don't wait until the last minute!! A good overall resource for math help is: If you have any questions please do not hesitate to contact the High School at: or you can Mrs. Bastiaanse at: bastiaansem@granby.k12.ct.us will be checked every few days during the month of August. We are looking forward to seeing you on the first day of school! - The Math Team at GMHS Below is a list of topics covered in the packet with formulas and helpful websites: Order of Operations The Distributive Property Evaluating Algebraic Expressions orderop/ evalprac.htm Solving One-Step Equations and Two-Step Equations Absolute Value Solving Literal Equations y -y Slope of a Line: m = 2 I x 2 -XI

2 Writing Linear Equations: form.html 05/study guide/pdfs/alg1 pssg GO 41.pdf Parallel and Perpendicular lines Inequalities- Simple, Compound, Absolute Value d7 /Linegual.htm Ollpdf/0704.pdf Solving Systems of Linear Equations: Exponents: exp/lexp.htm Polynomials - Vocabulary, Add/Subtract/Multiply / Smul bin.htm / Strinom.htm Factoring: Graphing Linear Equations: linear eguations.html Xl + X, Yl + y, ) Midpoint of a line segment. 2 -, 2- ( int. htm Distance between two points: d = ~(X2 - XI)2 + (Y2 - YI)2

3 HONORS ALEGEBRA II 2009 SUMMER REVIEW PACKET If additionals space is needed, do work on a separate piece of paper! ALL WORK must be shown to receive full credit for this packet. DUE FIRST DAY OF SCHOOL. 1. The sentence 3 + (5 + 2) = (5 + 2) + 3 illustrates a) the commutative property of addition b) the associative property of addition c) the distributive property of multiplication over addition d) the additive identity element 2. Which sentence illustrates the distributive property? a) xy = yx b) x(yz) = (xy)z c) x(y + z) = xy + xz d) l(xy) = xy 3. Which number is rational? a) -IJ2 b) JI5 c) ~J3 d) JIG 4. The reciprocal of!,x =f- 0 is x 1 a) -- x b)x c) -x 1 d) 1 -- x 5. The greatest common factor of the numbers 12,40, and 60 is a) 480 b) 2 c) 5 d) 4 6. Which represents an irrational number? a) 0 b) ~ c) J3 7. Which sentence illustrates the associative property for multiplication? a) ab = bu b) a(bc) = (ab)c c) a. 1= a d) a(b + c) = ab + ac

4 Page 2 8. If two fair dice are tossed once, the probability of getting 12 is 3~. What is the probability of not getting 12? 9. A bag contains 2 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is red? 10. If Debbie has 3 blouses and 4 skirts, how many different outfits of a blouse and skirt can she wear? 11. In the accompanying graph, the color of the pants worn by the students in a class is shown I Blue Black Brown What is the probability that a student selected at random from the class is wearing black pants? 12. A set of data consists of 3, 3, 6, 4, and 9. The median for these data is a) 6 b) 5 c) 3 d)4 13. Pat's grades on Course I tests were 90, 75, 98, 82, 90, and 87. The mode of her grades is a) 90 b) 89 c) 87 d) A student's four test scores were 88, 91, 93, and 86. What score would be needed on a fifth test to obtain a mean of 90 for all five tests?

5 Page Based on the data in the table below, which interval contains the median? a) 0-5 b) 6-10 c) d) Interval Frequency The accompanying histogram shows the distribution of the number of children in the families of the students in a ninth-grade class. The mode of the set of data in the histogram is a) 5 b) 2 c) 3 d) 7 7» 6 g 5 ~ 4 g 3 r:: umber of Children in a Family 17. If Y = -1, find 7-4y. 18. Evaluate (3e)3, for e = Given 9 = 3, find 6(7-2g). 20. Evaluate 2t - (13 + 6t) for t = Solve: -~a = 8

6 Page Solve: 9 = x 23. Find the solution of -8 = -4r Solve: 5(6-3x) = -15(x - 2) 25. Solve: 15d - 81 = Solve for w in the equation V = Ewh. 27. (3,12) (9,10) 28. What is the slope of the line whose equation is y = -3x What is the slope of the line -6x + 15y = Of the following coordinates, which is a point on the graph of x + 3y = 137 a) (4, -3) b) (4,4) c) (-5,6) d) (-2,3) e) (3,2) 31. What is the y-intercept of the line whose equation is y - 2x = 47

7 Page Which graph represents the line containing the point (-2, 1) and having the slope of!? a) y b) y c) y ", a: d) e) y.r 33. Find the equation of the line which passes through point (0,0) and has a slope of -~. 34. In which graph does line have a negative slope? b) y x c) y a: d)~ 35. Find the equation of the line which passes through point (l l, -1) and with a y-intercept of 2.

8 Page In the given figure line segment PQ has endpoints P(2, 1) and Q(4, 7). What is the equation of the line parallel to PQ and passing through the origin? y I r ~ /r 1&,: Ip I x 37. The price of a new cruise line is determined by the formula p(d) = 125d + 200, where p is the price of the cruise in US dollars and d is the number of days the person is on board. If you graphed this function, what would be the meaning of the 200? a) It is the y-intercept. c) It is the x-intercept. b) It is the slope. d) It is the coefficient of growth. 38. Solve the following system of equations algebraically and check: x - 4y = 16 y=l-x

9 Page Solve the following system of equations graphically and check. 3x + y = 3 y = 2x Ace Construction built five less than twice the number of houses that Ben's Construction built. If the total number of houses built by both firms was US, how many did each build? [Only an algebraic solution will be accepted.]

10 Page 8 4l. Which graph represents the solution to 3x - 2 > I? a) b) c) d) e) Solve the inequality -4x > Solve: 2 + 3x > x Solve: 8x ~ 3(x - 5) 45. Solve: 4 > -3m - 7 ~ Solve: 3x - 7 > -10 or 5x + 2 ~ Solve the system: x - 4y = 13 -x+6y= -18

11 Page Solve the system: 3x - 5y = 10 6x - loy = If the graph of a system of linear equations are two parallel lines, which of the following is true of the solution? a) it has exactly one point c) it has exactly three points b) it has exactly two points d) it has an infinite number of solutions e) there is no solution 50. Which graph represents the inequality 3x + 2y ~ 6? a) b) _ y c)., y ~ ~3 a: a: a: d) Y -2-3 x X'

12 Page Which graph represents this system? 4x + 3y ~ 6 x - 2y ~ 4 a) y y b) c) a: d) - e) -2 a: 52. Simplify the expression m 6. m Simplify the expression -4p3. (ip4). 54. Simplify the expression 3m 2 n. 5mn Find the expression equivalent to (m 3 ) Simplify the expression (- 3x 2 y5)3.

13 Page Simplify the expression 3 Y :. 5y 58 W h f. 8 x.f y3.. I f. nte t e racnon --3 ill simp est arm. 2xy 59. Simplify: Simplify the expression (3p + 1)0. 2 6l. Write the expression Ls without a negative exponent. y- 62. What is the degree of the monomial -2X 3 y4z? 63. What type of polynomial is 4a 3 + 9a 2 b 2-15b 3? a) monomial d) four-term polynomial b) binomial e) not a polynomial c) trinomial 64. Simplify: (2x 2 + 3x - 4) + (x 2 - X + 3) 65. Simplify: (5x 3 + 2x2-3x + 9) - (7x 3-3x 2-2x + 2)

14 Page Simplify the expression 4y2(2y + 1). 67. Simplify the expression (-4ab 3 )(3a 2 + 2a 2 b 2 + 5ab). 68. Simplify: (r - 4)(r + 6) 69. Simplify: (5z 2 + 2z)(6z - 1) 70. Simplify the expression (2x - 1)(x 2 + 3x - 8). 71. Factor 6a - 9 completely. 72. Find the greatest monomial factor of the expression m 2 n 3 - rnnp + 3n 3 p. 73. Factor h 2-12h + 35 completely. 74. Factor w 2-13w - 30 completely.

15 Page 13 Graph. 75. y=-jx x + 5y = x = 5

16 Page Y = Y = -4x Find the length of the segment with endpoints (-8, -3) and (-3, -8).

17 Page 15 Simplify, if possible. 81. J J4Q 83. J35 M 84. (5j2)(-4Ji3) 85. ls -- Jf7 86. M-- J3 87. /IT +4/IT lS + 10lS 89. J50 + J98 + JIB 90. An airplane travels 4110km in 5 hours. What is the airplane's speed? 91. Jean left on a bicycle trip at 1:00pm and returned at 3:45 pm. Her average speed on the trip was 16 mph. What was her total distance? 92. What is the average speed of a bicyclist who goes 54 miles in 3 hours? 93. How long (in minutes) does it take someone to run a 10km race whose average speed is 15km/hr?