June Dear Future Algebra 2 Trig Student,
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- Derrick Horton
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1 June 016 Dear Future Algebra Trig Student, Welcome to Algebra /Trig! Since we have so very many topics to cover during our school year, it is important that each one of you is able to complete these Algebra I problems. I will assume that you know how to use the algebraic and graphing skills necessary to complete these problems as we build on these topics throughout the year. Remember these simple policies (that will also apply to each and every homework, quiz, test, and classwork assignment) in Algebra /Trig: Show all work IN THE PACKET When I say show your work, I mean every step of your algebraic work or sketch of a graph necessary. Simplify all answers completely. Reduce all fractions, rationalize denominators, do not leave negative exponents (unless otherwise stated), etc. Ask/search for help! Ask your friends, parents, teachers, tutors and use books and the internet to find help if you can t remember a skill. Just make sure that in the end, you can complete the work independently, without the help, for next time. Complete all work yourself, even if you are seeking the help of others. Feel free to Ms. Groves during the summer at grovesea@pwcs.edu if you have any questions. I will be checking my periodically, so be patient I will get back to you! Do not wait until the last week (or night) of the summer to complete these. By then, it will be too late to get help. Here are a few internet sites that may be of some help: This assignment is optional. However, I strongly suggest that you complete this assignment. If completed and turned in by Tuesday, Sept. 6 th, you can receive up to extra credit points on your quarter grade. Your life this year in Algebra /Trig will be much better if you have mastered these skills prior to September. We look forward to working with you! Algebra /Trig Team!!
2 SUMMER ASSIGNMENT FOR ALGEBRA II/TRIGONOMETRY This summer assignment is designed to ensure that you are prepared for Algebra II/ Trigonometry. Nothing on the summer assignment is new. Everything is a review of topics students learned in Algebra I and Geometry. If you want to be successful during Algebra II/Trig, you must be able to understand and apply this information throughout next year. The assignment may be completed with another student but be certain that YOU understand how to complete every problem. Be sure to check every problem. Neatly show all work for each problem, using a pencil. Graphing calculators should not be used. There will be a quiz on the summer assignment during the second week of school. If you need to review these topics or see examples of problems, we recommend the websites or which lists many Algebra review topics. If, after reviewing, you need further assistance, please Ms. Groves at grovesea@pwcs.edu with questions. She will try her best to answer your questions as soon as possible. The assignment should be completed and brought to school on the first day of class and will count for extra credit on your marking period grade if completed correctly and on time. Simplify expressions, using order of operations: 1. [(8 4) 1] -. (x 8) (x + 5) Evaluate the expression. 4. x 4x when x = - 5. ( y 1) when y = 4 6. b 4ab when a =,b = y Simplify each expression
3 1. 6 [x (x + 4) + (x )] 14. x² + y² [x(x + y) y(y x)] 15 7[ (x 4) + 4(x 6)] Solving equations and inequalities. Be sure to show your work. 16 (4x 7) = (x 10) 17 7 = 7(b + 5) 6(b + 8) 18 4x 4 = ( x) 19 a 6 (a + 4) = 10 4a x b (x + 5) (x 1) = a1 a [1 ( y) y] = (1 y) 5. ( b 5) ( b 9) 6 4 4
4 For #1 4 - Solve. Graph the solution to the inequality on a number line. 6. x x + 1 or x x 5x y Factoring: Always look for a greatest common factor first: a b ab ab( a 1) Perfect Square Trinomials: or a a ab b ( a b ) ab b ( a b Difference of Squares: a b ( a b)( a b) Sum of Cubes: a b ( a b)( a ab b ) Difference of Cubes: a b ( a b)( a ab b ) ) PurpleMath Topics: Beginning Algebra Topics: Simple Factoring Intermediate Algebra Topics: Factoring Quadratics Special Factoring Formulas Factor the following expressions. 0. 6xy 4x y. a a ax ay + bx by 4. x 8x 15. ax + 6ay + bx + by 5. x 5x
5 9. 18m 8mn 6. 4y y m n 7. 8x 10x 41. 8x x x Solve Quadratics: By Factoring: If (jx + k) is a factor of f(x), then k x is a solution to f(x) = 0. j b b 4ac Quadratic Formula: x a PurpleMath Topic: Intermediate Algebra Topics: Solving Quadratic Equations Quadratic Formula Solve the following quadratic equations showing the requested method. Simplify when possible. 4. Solve by factoring: x x Solve by factoring: x 11x 4. Solve by factoring: y y Solve by quadratic formula: x 5x Solve by factoring: x Solve by quadratic formula: y y 5 0
6 Systems of Equations: f ( x) The solution to a system of equations,, g( x) is the point of intersection, (x, y), of the functions. 48. Solve the system using substitution: x + y = 5 x + y = 5 PurpleMath Topics: Advanced Algebra Topics: Solving Systems of Linear Equations Sections: Substitution (p. 4) Elimination/addition (p. 5) System-of-equation Word Problems 51. Solve the system using elimination: x y = -5 y + x + 4 = Solve the system using substitution: x = y 6½ 4x + y = 6 5. Write a system of equations and solve: The line with equation y + ax = c, passes through the points (1, 5) and (, 1). Find a and c. 50. Solve the system using elimination: x + 5y = 4 4x + y = 0 5. Write a system of equations and solve: The curve y = ax + bx passes through (, 0) and (4, 8). Find a and b.
7 PurpleMath Topics: Beginning Algebra Topics: Slope of a Straight Line Straight-line Equations Graphing Straight-line Equations Lines: y y slope: m x x equation of a line: 1 1 y mx b 54. Find the slope and y-intercept and hence 55. Find the slope and y-intercept and hence graph 1 graph y x 9 0. y x Find the equation of the line that passes through (, ) with a slope of. 57. Find the equation of the line that passes through (, -) and (9, -1). Literal Equations: Use the properties of equations to isolate the indicated variable in a formula. PurpleMath Topic: Beginning Algebra Topics: Solving Literal Equations Solve the literal equation for the letter in square brackets. 58. cb ay + c = 5 [c] a 60. w w a [a] 59. abx + cd = ex [x]
8 Properties of Exponents: n a m n ax n ( x ) x x m n mn ( x )( x ) x x 0 1 mn PurpleMath Topics: Beginning Algebra Topics: Exponents: Basic Rules Negative Exponents Simplifying with Exponents Simplify the following expressions using the properties above. Leave no negative exponents. 61. x 10 x 64. 5y 10 5 y 6. 4w w 4h 16 h d 66. p p Rational Exponents: n m x x m n PurpleMath Topics: Beginning Algebra Topic: Exponents: Fractional Exponents Simplify the following expressions using the property above. Express radicals as fractional exponents. 67. m t n b 6
9 Rational Expressions: You must have a common denominator to add or subtract fractions. The denominator of a fraction cannot equal zero. PurpleMath Topics: Advanced Algebra Topics: Rational Expressions: Simplifying Rational Expressions: Adding Simplify completely. State any restrictions. 71. x 1 6x 76. x x 4 7. xy 9xy 6x x 7. x x x x 78. x x x x x 4x x x 75. x x x 7
10 80. George s apartment costs $400 per month plus a $00 deposit. Write a function rule that relates the total cost to the number of months they rent. How much will it cost to rent the apartment for years? Label your answer. a. Write a function rule to calculate the total cost. b. How much will it cost to rent the apartment for years? (HINT: x is the number of MONTHS) 81. The length of a rectangle is more than three times the width. If the perimeter is 8in, find the width and the length. Length: Width: 8. Jackie went shopping for a pair of shoes, socks and a belt. The shoes cost $7 more than ten times the cost of the belt. The socks cost $1 less than the cost of the belt. Jackie spent $1. How much did she spend on each item? 8. Suppose a camper took hrs. to ride around a reservoir at 10mi./hr. at the beginning of the summer. 1 By the end of the summer, she could ride around the reservoir in 1 hrs. What was her rate at the end of the summer? (Hint: think direct or inverse variation).
11 84. A tree that is 5 feet tall casts a shadow feet long. A nearby building casts a shadow that is 0 feet long. How tall is the building? (Hint: think direct or inverse variation). 85. Nora and Addison went shopping for new summer clothes. Nora bought 4 pairs of shorts and 7 tank tops for $ Addison bought pairs of shorts and 6 tank tops for $ Find the cost of the shorts and tank top. Equations: Shorts Tank Top 86. Kris is trying to decide which cell phone plan is best for her. She has two choices. Choice A: $40.00 monthly charge plus $.5 per minute. Choice B: $60.00 monthly charge plus $.05 per minute. Write an equation that represents the cost per month for each plan. Solve the system of equations. How many minutes is the break-even point? What advice would you give Kris? Be specific. Equations: Break-even point:
12 Graph each system. 87. x4y y x5 y x Circle the points that are solutions. to the system graphed below? A. (-, 0) B. (-5, 8) C. (1, ) D. (, 4) E. (, -4) F. (0, 0)
13 90. Simplify: 4x x If x, find the quotient of x 4. 9x 9x 4 and 97. Identify each expression that is in simplest radical form. A. 4 x B. C. y x 8xy 9. Simplify, if n 0: 16n 4 4n n D. y 75 E. 16x y x 9. Which polynomial is equivalent to this 8 nn expression if n? n 94. Identify one of the factors of x 7x0 when it is completely factored. A. (x + 5) B. (x + 6) C. (x 5) D. (x ) 95. Identify one of the factors of x 6x7when it is completely factored. A. (x + 1) B. (x + 1) C. (x + 6) D. (x 7) 96. A polynomial function has zeros at x = and x = 6. Which function could be this polynomial function? A. f x x x 6 B. f x x x 6 C. f x x x 6 D. f x x x What property justifies the work between step 1 and step? Step 1: -x 6 = x + 4 Step : x + -x 6 = x + x +4 A. Commutative property of addition B. Inverse property of addition C. Addition property of equality D. Associative property of addition 99. Identify the solutions to the equation: 9x 6x 8 A. B. C. D., 4, 4 4, 4, 100. What is the solution to 5 x 4 16 x x 1?
14 101. What describes the solution to 5 x 6 x x 0 A. There is an infinite number of real solutions B. There are no real solutions C. The only solution is 0 D. The only solution is James bought a total of 15 bottles of drinks for his team. Each drink was either a bottle of water or a bottle of juice He spent $1.50 on each bottle of water. He spent $.00 on each bottle of juice. James spent a total of $8.50 How many bottles of juice did James buy? 10. Find the solution to the equation shown: 9x 4 x 6 A. x = 0.5 B. x =.5 C. x = -5 D. x = Find the solution: x.6.8 x 104. What is the x-value of the solution to this system of equations? 5x 5y10 x y Which ordered pairs are solutions to this system if inequalities? x y 5 x y4 A. (-1, -6) D. (0.5, -) B. (0, -5) E. (0.75, ) C. (0, 4) 108. Which ordered pair is a solution to this system of inequalities? x 5 y x A. (5, 1) B. (4, 11) C. (, 6) D. (, 5) 109. Find the slope of the line passing through the points (8, 1) and (6, 9) What appears to be the closest x-value of the solution to this system of equations? 110. Line p has an x-intercept = 5 and a y- intercept =. a. Find the slope of line p. b. Find the equation of line p.
15 111. Which function appears to have two distinct zeros? A. f x x 6x 9 B. f x 0.5x Point A lies on the graph of direct variation. Identify two other points with integral coordinates that lie on the graph of the direct variation. C. f x x D. f x 9 4x What are all the zeros of the function f x 1x 5x? 117. Identify the graph that represents a direct variation. A. B. 11. Find the values of f x x domain values of {-, 6}. 9 1for the C. D The number of calories, c, burned while walking is directly proportional to the distance, d, a person walks. Tom burned 180 calories walking a distance of miles. Which equation represents this relationship? A. c = d B. c = 90d C. d = 90 + c D. d = 180c 115. Create a direct variation using two of the ordered pairs from those shown. {(-5, -), } A. (-10, -4) B. (-, -5) C. (4, 10) D. (5, ) 118. The number of days, d, it takes workers to set-up for the Summer Music Festival varies inversely as the number of workers, w. The Summer Music Festival was set-up in days by 50 workers. Which equation represents this situation? A. 100 = d + w B. 100 = dw C. d = 50 + w D. d = 50w 119. A data set is shown. {,,, 4, 4, 4, 5, 5, 6, 6} If the standard deviation of the data set is approximately 1.5, how many of these elements are within one standard deviation of the mean?
16 10. A data set has a mean of 45. An element of this data set has a value of 50 and a z-score of What is the standard deviation of this data set, rounded to the nearest hundredth? 11. Use two of the three numbers shown in the list to complete this sentence. A data set could have a variance of and a standard deviation of. 15. This set of ordered pairs shows a relationship between x and y. {(-, 0), (-1, -), (0, -6), (, 6), (4, 40), (6, 10)} Which equation best represents this relationship? A. y9.1x B. y 11.5x 6 C. D. y x x 6 y x x #1 14 Use the following box and whisker plots 16. This set of ordered pairs shows a relationship between x and y. {(0, -), (, 7), (6, 16), (6, 15), (8, 1), (10, 8), (11, 1)} Using the line of best fit, which is closest to the output when the input is 5? A..7 B C. 1.7 D Which two plots appear to have the same value of the range? 1. Which two plots appear to have the same value for the interquartile range? 17. Which equation best models the relationship shown on the grid? A. yx 8 B. y x 8 C. y x x 6 4 D. y x x Which two plots appear to have the same value for the median?
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