ALGEBRA HONORS SUMMER WORK June 0 Dear Algebra Students, Attached you will find the Summer Math Packet for Algebra. The purpose of this packet is to review and sharpen your Algebra skills so that when we return to school in August you will be ready to go. Algebra is a challenging course which will stretch you in new ways and allow you to delve deeper into the study of advanced mathematics. With this in mind, please take the time to do your best work on this packet. In order to receive full credit on this packet you must show all necessary work. You will be tested on the material in this packet within the first week of the start of school. Please also remember that it is essential that you have a TI-8 Plus or TI-8 Silver Edition calculator. We will learn how to use this calculator to a greater etent than you have in the past and eplore its many functions and uses. If you are unable to purchase one, please come see me at the start of the school year. Check craigslist for deals!!! Have a great summer! I look forward to working with you this fall.
Calculator Reference Page Use this as a guide as you work through problems on which you may use a calculator. To get back to the home screen (where calculations are performed), press nd MODE. MATH key allows us to access features such as absolute value and converting decimal answers to fractions DELetes one character CLEARs an entire line of tet Eponent key STORE key allows us to evaluate variable epressions for a specified value ENTER at the end of a sentence. Works as the = key does on a regular calculator Negative key NOT the same as the subtraction key!
Prerequisite Algebra skills for Algebra II Honors Directions: All work must be done NEATLY, on separate paper. You are epected to recopy and number each problem, show work clearly, and circle your final answer. Papers will not be accepted unless all of these conditions are met. All graphs must be done on graph paper. (print some from my website if necessary) Questions with the icon indicate that a calculator may not be used. Eplanations, if required, must be written in complete sentences. I. Operations with fractions. Write each as a single fraction in simplest form. SHOW ALL WORK.. 5 7.. 8. 5. 5 7 9 6 7 6 6. 5 8 7. 6 5 5 8. 6 5 5 9. 6 5 5 0. 5 6. of 6. 5% of 0. 0.5.. 5. 0.5 Provide the reciprocal of each as a fraction in simplest form. No decimal answers are allowed here. 5 6. 7. - 8. 9. 0. 0. 0.5 9 To check your answers using your graphing calculator, review and apply the keystrokes below. Eample: Let s evaluate 9 a. Type the epression into the b. Press (the key below c. Press. This will homescreen. Use parentheses the green key), followed epress the computation in to group each fraction. by. fractional form. Answer: 9/9.
Eample : Let s find the reciprocal of. a. Remember: Always place b. Type. parentheses around a fraction. Answer: the reciprocal of is. Now, use your graphing calculator to check #-0. If your answers do not match, check your work, and check how you typed the epression into the calculator. Can you find your mistake(s)? II. Use of zero and one, Eponents. Evaluate, if possible. If not possible, write undefined.. 0 5. 5 0. 0 5. 555 55 5 0 5555 5. 5 6. 0 7. 8. 9. 0. To check your answers using your graphing calculator, review and apply the keystrokes below. Eample: Let s evaluate. Process: Type. Answer: Now, use your graphing calculator to check #-0. If your answers do not match, check your work, and check how you typed the epression into the calculator. Can you find your mistake(s)? Do you think that the calculator is wrong on any of them?
III. Order of Operations, Absolute Value. Evaluate:... 5. 5 8 9 5. 5 6. 5 7. 5 8. 8 9. 00 57 0. 57 00 To check your answers using your graphing calculator, review and apply the keystrokes below. Eample: Let s evaluate 7 9. a. Type the first part of the b. Locate absolute value in the NUM menu. epression we wish to evaluate. Press. c. Finish typing the epression. e. Press. Be sure to end your parentheses. Answer: -. Now, use your graphing calculator to check #-0. If your answers do not match, check your work, and check how you typed the epression into the calculator. Can you find your mistake(s)? IV. Evaluating Epressions, Equations, and Inequalities. Find two values of one positive and one negative that satisfy each statement below. a. b. c. d. e. f. g. h.. Evaluate 5 8 a. for = 0 b. for = c. for = - d. for = e. for = - SHOW ALL WORK.
. Given the epression [ 5 9 ], a. evaluate it for = 7 b. simplify it without substituting a value for. SHOW ALL WORK. c. evaluate your epression in part (b) for = 7 and show that you get the same answer as in part (a). (Of course, if you don t get the same answer as in part (a), then you should check over your work.) Now, use your graphing calculator to check #-. If your answers do not match, check your work, and check how you typed the epression into the calculator. Can you find your mistake(s)? Is the calculator wrong?. Circle all epressions that are equivalent to the statement half of a number in the list below. a. b. c. d. e. f. g. 0. 5 h. i. j. k. 0.5 m.. 5 5. Refer to #. Using the value = 0, we epect that each statement that is equivalent to the statement half of a number should equal 5. Are your answers correct? If not, make appropriate changes, and review your errors. V. Simplifying Algebraic Epressions. Simplify each: 6. 5 7. 5 8. 5 9. 5 50. 5. 5. 5. 5. 5 7 55. 5y y VI. Properties of Real Numbers. Carefully review the following properties. 56. Is subtraction a commutative operation? Use a numerical eample to defend your answer. 57. Is division an associative operation? Use a numerical eample to defend your answer. 58. State the inverse for multiplication for each value of a.
a. a 7 b. a c. a 7 d. 59. Refer to #58. State the inverse for addition for each of the given values in parts a d. a 60. Are there any numbers that do not have an identity for addition? If so, provide one. If not, write an eplanation in defense of your position. 6. Are there any numbers that do not have an identity for multiplication? If so, provide one. If not, write an eplanation in defense of your position.
VII. Number Types. Carefully review the following definitions: Eample: To which number set(s) does -7 belong? Answer: -7 is an integer, and it is a rational number (since it can be written as 7, a ratio of two integers). #6-69. State the number set(s) to which each number belongs. 6. 6. 6 6. 0. 65. 0 66. - 67. 68. 70. State a number that satisfies each statement. If it is not possible, eplain why. a. A number that is a whole number but is not a natural number. b. A whole number whose reciprocal is a whole number. c. A number that is an integer but is not a whole number. d. A number that is a rational number but is not an integer. e. A number that is a real number but is not a rational number. f. A number that is a natural number but is not an integer. g. A whole number whose opposite is a whole number. 69.
VIII. Linear Equations. Solve each equation for : Provide answers as fractions in simplest form. If an equation has no solution, eplain why. SHOW ALL WORK. 7 7. 8 7. 7 8 7 76.. 77. 7. 7. 8 0 75. 0 8 78. 6 0 79. 80. 6 8 8. For each of the problems in #7-80, prove to me that your answers are correct by substituting each into the original equation and verifying that it makes a true statement. I have worked #78 out for you to model the skill and to show you what I epect. 8 6 Check answer = /: 6 0 IX. Equation of a Line. For #8-86, solve for y in terms of. In other words, write each in y = m + b form by isolating the variable y. SHOW ALL WORK. 8. y 8. y 6 8. 87. Write an equation of the line whose slope is 5 and y-intercept is. 88. Write an equation of the line whose -intercept is 5 and y-intercept is. 89. Write an equation of the line that contains the points (6, -) and (, ). y 85. y 86. y 90. On graph paper, graph each line in problems #8-89 on the y-plane. Label two points on each line. X. Operations with Quadratic Epressions. 0 9. Answer: Eample: Multiply Multiply. SHOW ALL WORK. F (first two terms) = = O (outer two terms) = 9 = 9 I (inner two terms) = 0 = 0 0 9 = 90 L (last two terms) = Add them up to get your answer: + 90 9. 9. 9. 9. 95. Factor. Eample : Factor 7 8. Answer: 9 Check by using FOIL: 9 8 = 7 8 96. 0 97. 0 98. 5 6 99. 0 00. 0
XI. Operations with Linear Systems For #0-08, solve the system of equations by any method. I have provided eamples of each method substitution and elimination to refresh your memory on this skill. Sample : Solve: y 9y I ll use substitution. Replace with y in the second equation: ( y) + 9y = - 6y + 9y = - + y = - - -_ y = -6 y = - Then, replacing y with - in the top equation, we get = (-) = + 6 = 7 Sample : Solve: 5 y 0 y 6 I ll use elimination. Multiply the bottom equation by so that the y s will cancel when the equations are added together. (Note: you could have multiplied the bottom equation through by -5 to eliminate instead.) 5 y = 0 ( + y = 6) 5 y = 0 + + y = 7 = 7 7_ = 6 Then, replacing with 6 in the top equation (either works), we get 5(6) y = 0 0 y = 0-0 -0 y = 0 - -_ y = 0 Solve each system using either method: substitution or elimination. SHOW ALL WORK. 0. y 6 y 0. y 5 5y 0. y y 5 0. y 5y 05. y 0 y 5 06. 8 7y 5 y 07. 8y 5y 08. y 80 y 8 09. For each of the problems in #0-08, prove to me that your answers are correct by substituting each into the original equations and verifying that both equations are satisfied.
XII. Proportions. Solve each for. (hint: set the cross-products equal) SHOW ALL WORK. 0. 9 5. 5 6. 5 6. 8. For each of the problems in #0-, prove to me that your answers are correct by substituting each into the original equation and verifying that it makes a true statement. XIII. Quadratic Equations. Eample: Solve 5 0 Answer: Factor to get 9 5 0 Solve each for by using factoring. SHOW ALL WORK. 5. 7 6 0 Then, + 9 = 0 or 5 = 0 So = -9 or = 5. 6. 6 0 7. 5 6 0 8. 6 6 9. 5 0 0.. 6. 5 5. For each of the problems in #5-, prove to me that your answers are correct by substituting each into the original equation and verifying that it makes a true statement. XIV. Number Sense, Open Response, Applications.. A sweater that originally costs $50 is marked 0% off. In addition, you have a coupon that entitles you to take 0% off of the sales price. Assuming that clothing purchases are ta eempt, a. determine the sale price of the sweater; b. determine the price that you will wind up paying with your coupon; c. what fraction of the original price do you wind up paying? 5. a. Provide a simplified epression, in terms of c and d, that represents the perimeter of the figure. b. Using c = 0 and d = 8, determine the area of the figure. Assume that all angles are right angles. c. If the values of c and d are both doubled, determine the effect that would have on the i. perimeter ii. area