are topics that you have not covered yet. Just do the best you can.

Transcription

1 Summer assignment for Honors Algebra II 1 Honors Algebra II 010 Summer Assignment Dear student, Welcome to Honors Algebra II! You have signed up for a rigorous course that will challenge your minds, get you to think a little harder and dig a little deeper. In preparation for the fall, please complete this summer assignment. The concepts presented in this packet need to be understood when you come in the first day of class. Below are some directions explaining how to complete the assignment, the due date of the assignment, and how the assignment will be graded. We are not trying to scare you, just prepare you for the course you chose to take. If you have any questions over the summer please feel free to either of us. We will be checking our often throughout the summer. Please don t worry if there are topics that you have not covered yet. Just do the best you can. Good luck with the assignment and enjoy your summer. We look forward to meeting you in the fall. Sincerely, Mrs. Stabile (jstabile@nburlington.com) Mr. Malcolm (smalcolm@nburlington.com) Directions: Be sure to pay attention to the directions at the start of each section. DO NOT just begin solving. Where it is noted to SHOW ALL WORK we mean it. NO WORK = ABSOLUTELY NO CREDIT Packet is due the first day of class, i.e. the first time you see your teacher!!! LATE PAPERS WILL NOT BE ACCEPTED!!!!!!!! This will count as a 50 point homework grade, based on completion, not accuracy. The answers will be made available on the first day of school so that you can check your work. Upon review of the packet, there will be a test on the included material during the first week of school (the week of Labor Day).

2 Summer assignment for Honors Algebra II I. Solving Equations. Solve for x. SHOW ALL WORK!!!!!! 1. 3x + = 3. 5x 3 = x 4. 6x x x n 3n x = 7x x 1 = x x x x + 3 = 5x (x 4) = x 1 x (x + ) = 3(x ) 15. (x + 6) = -(x 4) (x + ) 1.5x = 5.(x 4)

3 Summer assignment for Honors Algebra II 3 II. Equations of a line. SHOW ALL WORK!!!!! Write the equation of a line in the slope-intercept form given the following information: 17. m (slope) = 1 and b (y-intercept) = m = - and b = m = 5 and b = 7 0. (0, 3) and (, -1) 1. (4, ) and (-, -4). (-3, -1) and (6, -4) 3. m = 3 and (5, -) 4. m = - and (3, 0) 5. Write the equation of a horizontal line that passes through the point (6, ). 6.Write the equation of a vertical line that passes through the point (-, -). Write the equation of the line that passes through the points: 7 X y

4 Summer assignment for Honors Algebra II 4 8. X y X y X -3 - y Write the equation of a line that passes through the point (-1, -) and is parallel to the graph of y = -3x. 3. Write the equation of a line that passes through the point (4, -1) and is perpendicular to the graph of 7x y = Given: 5x + y = a. Write an equation of a line parallel to the given equation. b. Write an equation of a line perpendicular to the given equation. c. Write an equation of a line intersecting to the given equation. Rewrite the equation in the standard form (ax +by = c) 34.y 5 = 4(x +) 35. y 3 =.5(x + 1)

5 Summer assignment for Honors Algebra II y + 3 = 3 III. Graph the following lines using m (slope) and b (y-intercept). SHOW ALL WORK!!! (i.e. m =, b = ) y x y x 3 3 Graph the following lines using the x-intercept and the y-intercept. SHOW ALL WORK!!!!!! 39. x + 3y = x - 4y = 8

6 Summer assignment for Honors Algebra II 6 IV. Linear Regression. Find a linear regression model using the calculator. 43. Space - Use the table that shows the amount that the United States government has spent on space and other technologies in the selected years. Use x = 0 as Year Spending (Billions of $) a. Write an equation of the line of best fit (round parts to hundredths). b. Using x = 0 as 1980, predict the spending for 006. c. Explain the meaning of the slope for this situation. d. Give the correlation coefficient and determine how well the model fits the data. 44. Use the table that shows the length and width of several humpback whales. Length ( ft.) Weight (long tons) a. Write an equation of the line of best fit (round parts to hundredths). b. Predict the length of a whale whose weight is 40 long tons. c. Predict the weight of a whale whose length is 60 feet. d. Give the correlation coefficient and determine how well the model fits the data.

7 Summer assignment for Honors Algebra II 7 V. Systems. Solve each system of equations algebraically. (Use substitution or elimination) SHOW ALL WORK!!!!!! 45. x + y = y = x + 5x + 3y = -6 y = x y = 7 x 48. x + y = 11 x - y = -3 x + y = x - 3y = x + y = 5 x + 3y = -3 6x + y = 10

8 Summer assignment for Honors Algebra II 8 Graph each system to solve. (Use calculator) Provide an explanation of how you determine the solution to a system graphically in the box provided. 51. y = x y 3x = 8 y = 4x x + = 3y 53. 3x + y = x + 3y = 1 8 6x y 4x - 5y = 13

9 Summer assignment for Honors Algebra II 9 VI. Polynomials. SHOW ALL WORK!!!!!! Simplify: 55 (4x x+10)+(5x-31) 56. 3x x 11 4x x x 57. 5x 3x x x x 8x x 1 x x 1 x x 6. x 3y x y 61. x x 3

10 Summer assignment for Honors Algebra II x 1 x 1 Simplify: x 65. x x x 3 Factor: Problem Answer x 1x 69. 6x 4 18x 3 15x x x 4x x 3x 10x x 5x 73. x 9x x 11x x 35x 60

11 Summer assignment for Honors Algebra II x 16 VII. Simplify (leave a in the answer for irrational numbers if necessary-don t estimate). SHOW ALL WORK!!!!!

12 Summer assignment for Honors Algebra II VIII. Absolute Value Inequalities Graph on a number line x x 8 or x 98. x 7 or x x 4 or x x x 1 Solve. 10. x x x x x