Honors Algebra II Summer Assignment 017 These are the directions for your summer assignment for next year s course. This is an opportunity for you to review selected topics from Algebra One to make sure you are ready for the new material in Algebra Two. Your summer assignment: 1. Read through the vocabulary and the examples on the first couple of pages to review the concepts. You may need to look for help on an on-line tutorial if you have trouble remembering certain concepts.. Complete all the practice problems attached in this packet. These need to be completed before the first day of school. Do the problems right on the worksheet. You must use pencil. Use a ruler for drawing linear graphs. Show all work. Your summer assignment will count for 5 homework checks and will be collected the first day of class. The third day of school, you will have a test on the summer assignment material. Two class days is not enough time to re-teach the information in the packet. It is your responsibility to come to school on the first day with only the questions that you could not work out on your own. For the first day of class: Have your summer assignment stapled and ready to turn in. Solely for Algebra II, have a three ring binder ready with dividers, white lined paper and graph paper. It is recommended that you have at least a binder. Bring your graphing calculator. We recommend the TI -84 or TI-84 Plus. Bring your pencils (not pen!) and a ruler. You also need erasers!! This will help us get off to a great start and lead us to an enjoyable and rewarding school year! 1
Vocabulary and examples: All of the practice problems to follow should be familiar to you, but you may not have done them in a while. This introduction vocabulary and example section is here to help you remember the concepts required in the practice problems. If there is a concept in the practice problems that you do not remember, or a word you do not understand, please google the word to find a definition or google the concept to see if you can find an on-line tutorial that explains how to do the problem. There are many on-line resources to help you. One site that is very helpful in mathematics is Kahn Academy. Here is a link that may help you www.khanacademy.org There is a search bar at the top of the site where you can type in the math concept you are looking for help on. Section A. - Believe it or not you will be required to know basic arithmetic with fractions. We build on adding, subtracting, multiplying and dividing fractions and you need to remember how to do this. If you don t remember, look it up. Section B Linear equations You should be familiar with many concepts in linear equations such as: o An x-intercept is the x-coordinate of a point where a graph crosses the x-axis. The y- coordinate of this point is 0. So to find an x-intercept simply substitute 0 in for y and solve. o A y-intercept is the y-coordinate of a point where a graph crosses the y-axis. The x- coordinate of this point is 0. So to find an y-intercept simply substitute 0 in for x and solve. o The linear equation y = mx + b is written in slope-intercept form. The slope of the line is m. The y-intercept is b. You should be able to write this equation given information about the line and you should be able to take a linear equation in another form and get it into this form. o The formula to find slope is y y m x x 1 1 o How to graph Linear equations Section C. How to solve linear systems using the graphing method, substitution or elimination (also called linear combination) There are many on-line tutorials for this. This was studied extensively in Algebra 1. Section D. How to solve linear equations for an answer this should be easy. Section E How to solve literal equations - Solving literal equations: Solve the equation or formula for a specific variable (in other words get that variable alone on one side of the = by using algebra) Example below:
9 F C 5 9 F C 5 5 5 9 F C 9 9 5 5 F C 9 Solve this temperature equation for C. I now have a new equation solved for a different variable Section F Scientific Notation - A number is in scientific notation if it is the form : absolute value of c is a number between 1 and 9.999. For example 41,000 is written as c 10 n where the 6 4.1 10. Your calculator shows the same number as 4.1 E6. To write a number in scientific notation, follow these steps: Move the decimal to the right of the first integer. If the original number is greater than 1, multiply by 10 n, where n represents the number of places the decimal was moved to the left. If the original number is less than 1, multiply by 10 -n, where n represents the number of places the decimal was moved to the right. Section G Inequalities You should be able to solve inequalities and graph the solutions on a number line. Remember that if you multiply or divide by a negative number the direction of the inequality number switches! Section H Rules of exponents o To multiply exponential expressions with the same base, add the exponents: a m n mn * a a. 6 o To raise a power to a power, multiply the exponents. ( x ) x Every number and variable inside parenthesis is being raised to the power to the right of the parenthesis. ( ) ( 4x ) ( 4 x ) 16x 6 5 4 o To divide powers with the same base, subtract the exponents. Section H PSAT Practice problems Different types of math concepts in no special order. These problems are right off a practice test. 4 4
Name Date: A. Fraction Arithmetic DO NOT USE A CALCULATOR HERE Give all answers as reduced fractions. 4
B. All about Linear Equations Write an equation of the line in slope-intercept form. 1. Theslopeis - ; the y - intercept is 5.. The slopeis 0; the y - intercept is. Write an equation of the line that passes through the point and has the given slope (where m stands for slope). Write the equation in slope-intercept form: y mx b.. (1, 6), m 4. (, ), m 4 Calculate the slope through each set of points. 5. (19, -16) (-7, -15) 6. (-4, 7) (-6, -4) 7. (a, b) (c, d) Write an equation in slope-intercept form of the line that passes through the points. 8. (4, 9) and (1, 6) 9. (0, 7) and (1, 1) 10. (, ) and (0, ) 5
Find the x-intercept of the graph of the equation. 11. xy 6 1. x y 4 Find the y-intercept of the graph of the equation. 1. xy 6 14. x y 4 Find the x-intercept and the y-intercept of the line. Use the intercepts to sketch a quick graph of the equation the graphs provided. 15. y x 6 16. x5y 15 17. x4y4 x- intercept: x- intercept: x- intercept: y- intercept: y- intercept: y- intercept: 6
Write an equation in slope-intercept form. Find the slope and y-intercept. Equation Slope-Intercept form Slope y-intercept 18. x y 5 19. -x 7 y 0. x 4y 4 0 Graph the equation. If necessary, write the equation in slope-intercept form first. 1. y x 4 x 6. y. y 4 4. x = - 7
C. All about Systems of Linear equations. Write the equation in slope-intercept form and then solve each system of equations by graphing. Determine the number of solutions. Original system 5. x y 0 x-1 y 6. y + 4 = x xy 7. y - x = 6 x-1 y Slopeintercept form Graph Give Solution(s) Solve each system using substitution. Show all steps and check your solution. 8. -x y - y x 6 9. y 4 x -x y 8 8
Solve each system of equations using Linear combination (elimination). Show all work. 0. x y 17 x y 9 1. 5 f 4m6 f m 1 Write a system of equations and solve using linear combination, substitution, or graphing. Choose the most appropriate method. Show all work to solve.. Mary ordered lunch for herself and several co-workers on Monday and Tuesday. On Monday, she paid $7 for five sandwiches and four sodas. On Tuesday, she paid $6 for four of each. Find the price of a sandwich and the price of a soda.. A local landscape company had a one-week sale. On Monday, Mrs. Jones had $8 to spend. After purchasing 5 trees, she had just enough money left to purchase 1 shrub. Later in that same week, she purchased trees. She had $7 with her, so she again had enough money left to purchase 1 shrub. Find the cost of a tree. 9
D. Solving Linear Equations: Solve each equation to find the correct answer for x. Show all work. 4. 0 4x 6x 5. 8x 9 7x 6. (4x ) 8 4 x E. Solve each equation for the indicated variable (called literal equations) 7. u x k for x 8. k u for k 9. a k u for a a 40. m n m n for m 41) a y 4 a for y b F. Scientific Notation: Write each number in scientific notation. Do not use your calculator! 4. 40, 000 4. 6,100,000,000 44. 80 million 45. 0.00075 10
Write each number in standard notation. Do not use your calculator! 46. 8 6.45*10 47..*10 5 48..581*10 49. 5 7.65*10 If your calculator gives you the following answer on your main screen, give the answer in standard notation. 50. 9.6 E8 51. -.4 E-7 G. Inequalities: Solve each inequality and then graph the solution set on the number line. 5. 5. 54. 55. 11
H. Rules of Exponents: Simplify each expression using the rules of exponents: 59. xxxx 60. x x 61. 4 a a 6. x 4 6. a 64. x 65. x 66. x 67. xx x 68. x x 4 69. 5 9x x 70. 5a 10a I. SAT Practice Problems: 1. 1
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