June Mr. Brown

Transcription

1 June 06 Hello, future Algebra II students: The packet attached to this letter contains a series of problems that will overview the Algebra I skills you must have mastered in order to have a good start in Algebra II. Completing this packet over the summer will help you practice and maintain these skills. I epect that you will work through these as best you can, and that your work will be neat and accurate. This assignment will be collected on the first day of classes, and after spending our first two days reviewing it, you will be tested on the material and that grade will count as your first test grade of quarter one. Therefore, I strongly suggest that you make a photocopy of your packet once it is completed so that you will have a copy of your own from which to study. Bring both copies to class with you on the first day. You must present your work in an organized and systematic way. In this course, the way you arrive at an answer is often more important than the answer that you get. Please be mindful of this when you are working through this packet. If you turn in a paper without sufficient work on problems for which work must be shown, no credit will be given on those problems. Lastly, it is essential that you purchase the appropriate materials for this course: A -ring binder with dividers: Homework, Class Notes, Assessments. A pack of filler paper for the Homework portion of your binder A graphing calculator: a Teas Instruments TI-8, TI-8 Plus, TI-8, or TI-8 Silver Edition. This can be purchased at Staples, Wal-Mart, Amazon, ebay etc. You will need it for this packet as well as for the course. It will be used frequently throughout the year as well as in subsequent math courses. I look forward to meeting you all in the fall, and I hope you look forward to an eciting and interesting learning eperience. Mr. Brown brownr@mersd.org

2 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!

3 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 of 6. % of Provide the reciprocal of each as a fraction in simplest form. No decimal answers are allowed here 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.

4 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 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 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 8 a. for = 0 b. for = c. for = - d. for = e. for = - SHOW ALL WORK.. Given the epression [ 9], a. evaluate it for = 6 b. simplify it without substituting a value for. SHOW ALL WORK. c. evaluate your epression in part (b) for = 6 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?

6 . 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. h. i. j. k. 0. m... Refer to #. Using the value = 0, we epect that each statement that is equivalent to the statement half of a number should equal. Are your answers correct? If not, make appropriate changes, and review your errors. V. Simplifying Algebraic Epressions. Simplify each: y y VI. Properties of Real Numbers. Carefully review the following properties. 6. Is subtraction a commutative operation? Use a numerical eample to defend your answer. 7. Is division an associative operation? Use a numerical eample to defend your answer. 8. State the inverse for multiplication for each value of a. a. a 7 b. a c. a 7 d. 9. Refer to #8. 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.

7 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 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.

8 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 For each of the problems in #7-79, 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 #80 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. y 8. y 86. y 87. Write an equation of the line whose slope is and y-intercept is. 88. Write an equation of the line whose -intercept is and y-intercept is. 89. Write an equation of the line that contains the points (6, -) and (, ). 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 Answer: Eample: Multiply Multiply. SHOW ALL WORK. F (first two terms) = = O (outer two terms) = 9= 9 I (inner two terms) = 0 = = 90 L (last two terms) = Add them up to get your answer: Factor. Eample : Factor 7 8. Answer: 9 Check by using FOIL: 9 8 =

9 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: 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 - to eliminate instead.) y = 0 ( + y = 6) y = y = 7 = 7 7_ = 6 Then, replacing with 6 in the top equation (either works), we get (6) y = 0 0 y = y = 0 - -_ y = 0 Solve each system using either method: substitution or elimination. SHOW ALL WORK. 0. y 6 y 0. y y 0. y y 0. y y 0. y 0 y y y 07. 8y y 08. y 80 y 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.

10 XII. Proportions. Solve each for. (hint: set the cross-products equal) SHOW ALL WORK 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 0 Answer: Factor to get 9 0 Solve each for by using factoring. SHOW ALL WORK Then, + 9 = 0 or = 0 So = -9 or = For each of the problems in #-, 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 $0 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?. 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