Name: Date: SUMMER ALGEBRA II ASSIGNMENT ONLY REQUIRED FOR ADVANCED ALGEBRA II & HONORS ALGEBRA II The following review assignment is required to be completed by ALL students who plan on taking Advanced Algebra II or Honors Algebra II next school year. The goal of this assignment is to review the key components of Algebra I necessary for success in Algebra II. In addition, Section 2 is designed to prepare students for questions they will encounter on the PSAT (October 10 th, 2018) and SAT examinations. Due Date: Tuesday, September 11 th The packet will be collected and graded by your teacher. Record your answers on the answer sheet provided (pages 10-12) and show all work in the boxes provided for each question. ALL WORK is required for full credit. If you need additional resources to assist in completing this assignment, it is STRONGLY RECOMMENDED you utilize all the resources found at https://www.khanacademy.org/. The Math Lab will be open after school starting on September 7 th in the 9/10 Library after school from 2:15-3:00pm on Mondays, Tuesdays and Thursdays. Please contact Mr. Michael Concilio mconcilio@srsd.net if you have questions or concerns over the summer. 1
Section 1 Solve the following equations and inequalities. 1. 9 141 x = 6x + 9 7 28 4 2. 6 4x < 18 3. 35 15 + 10p < 25 Determine the equation of the line for each of the following. 4. Write the equation of the line passing through points (2, -2) and (1,0) in slope intercept form. 5. Write the equation of the line that passing through point (0, 5) and perpendicular to the line y 3 = 2(x + 4). Completely simplify the following exponential expressions. 6. 36x5 y 3 z 9x 8 y 2 z 4 7. (9a 5 b 2 c) 3 (2abc) 2 2
Factor the following polynomials completely. 8. 32x 6 z 4 8x 2 z 2 y 2 28xz 3 9. p 2 15p + 26 10. x 2 + x 600 11. x 2 + 24x + 95 12. 25x 2 121 13. 10p 3 + 75p 2 + 4p + 30 Solve each of the following quadratic equations using an appropriate method. Express any irrational solutions as decimals rounded to the nearest hundredth. 14. 7x 2 + 21x = 0 15. 3x 2 + 1 = 12x 3
Solve each of the following word problems. 16. The height of a plant in inches, h(t), is modeled by the equation h(t) = 3.2t + 1.8 where t is the time in weeks. In terms of this problem, what is the meaning of 3.2? In terms of this problem, what is the meaning of 1.8? 17. Penny purchases 100 tickets for her youth services group to attend a waterpark. Child admissions are $14.00 each while adult admissions are $19.00 each. If the total cost for the tickets was $1470, how many of each type of ticket did she purchase? 18. The formula C = 5 (F 32) is 9 used to convert from Fahrenheit to Celsius temperature. Determine what the equivalent Fahrenheit temperature is for 42 Celsius (Exact) On the ANSWER SHEET found on the last pages of the packet, answer the following questions pertaining to graphing. SHADE when appropriate. All graphs should be neat using a ruler for lines. 19. Graph: f(x) = 5 4 x + 8 20. Graph: y + 10 = 1 (x + 4) 2 21. Graph: 9x 2y = 18 22. Graph: 4x 5y -20 23. Graph: f(x) > 2 3 x 24. Graph: y = x 5 + 2 25. Solve the following system by graphing: { y = 1 6 x 2 y = 2x + 9 4
Section 2: Multiple Choice Questions. Enter the letter of the correct answer choice on the answer sheet. 26. If 7x + 12y = 10 and 3x 2y = 5, what is the value of 5x + 5y? (A) 5 (B) 7.5 (C) 10.5 (D) 15 R F N F 27. A website uses the formula above to calculate a seller s rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. Which of the following expresses the number of favorable reviews in terms of the other variables? (A) F = RN R 1 (B) F = RN 1 R (C) F = N 1 R (D) F = N R 1 28. A quality control manager at a factory selects 7 lightbulbs at random for inspection out of every 400 lightbulbs produced. At this rate, how many lightbulbs will be inspected if the factory produces 20,000 lightbulbs? (A) 300 (B) 350 (C) 400 (D) 450 29. Xerxes is x years old and 4 years older than Zara. How old was Zara 7 years ago? (A) x 3 (B) x 4 (C) x 7 (D) x - 11 30. If x 1 = k and k = 3, what is the value of x? (NC) 3 (A) 2 (B) 4 (C) 9 (D) 10 x + 3 = 6 y 2 = 7 31. For the equations shown above, which of the following is a possible value of x y? (A) -14 (B) -4 (C) -2 (D) 14 5
Students Sibling Rivalry Number of siblings Lincoln School Washington School 0 120 140 1 80 110 2 60 30 3 30 10 4 10 10 There are a total of 2,400 students at Lincoln School and 3,300 students at Washington School. 32. What is the median number of siblings for all the students surveyed? (A) 0 (B) 1 (C) 2 (D) 3 Results on the Bar Exam of Law School Graduates Passed Bar Exam Did Not Pass Bar Exam Took Review Course 18 82 Did Not Take Review Course 7 93 33. The table above summarizes the results of 200 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course? (A) 18 25 (B) 7 25 (C) 25 200 (D) 7 200 34. In the system of inequalities y > 2x + 1 and y > ½ x 1 is graphed on the xy-plane below, which quadrant contains no solutions to the system? (A) Quadrant II (B) Quadrant III (C) Quadrant IV (B) There are solutions in all four quadrants. II I 35. 22 x If 2, what isthevalue of x? x 1 x 2 III IV (A) ¼ (B) ½ (C) 0 (D) 2 6
36. According to the line of best fit in the scatterplot at right, which of the following best approximates the year in which the number of miles traveled by air passengers in County X was estimated to be 550 billion? (A) 1997 (B) 2000 (C) 2003 (D) 2008 Number of miles traveled (billions) 600 500 400 300 200 100 Miles Traveled by Air Passengers in County X, 1960 to 2005 1960 1970 1980 1990 2000 2010 37. If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5? (A) 6 (B) 15 (C) 20 (D) 23 38. The equation x 2 + kx + 12 = 0, where k is a negative integer, has two integer roots. Which of the following is a possible value of k? (A) -13 (B) -12 (C) -6 (D) -1 39. In the xy-plane at right, line l is parallel to line k. What is the value of p? (NC) (A) 4 (B) 5 (C) 8 (D) 10 l (0,2) (-5,0) O (0, -4) k (p,0) Lengths of Fish (in inches) 8 9 9 9 10 10 11 11 12 12 12 12 13 13 13 14 14 15 15 16 24 40. The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data? (A) Mean (B) Median (C) Range (D) They will change by the same amount. 7
Use the following data displays for questions 40 and 41 Week Weight (0z) 0 0 3 0.02 140 Fetus Weight Over Time 6 0.04 9 0.07 12 0.49 15 2.47 18 6.7 21 12.7 24 21.12 27 30.88 30 46.56 33 67.68 36 92.48 Weight (ounces) 120 100 80 60 40 20 0 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 39 116 Time (Weeks) A team of research obstetricians conducted a study to determine the growth rate of a fetus. The graph and table above model the weight, w, in ounces of a fetus t weeks after conception. 41. Over which time period is the average growth of the fetus the greatest? (A) Week 0 to Week 12 (B) Week 12 to Week 24 (C) Week 30 to Week 39 (D) Week 39 to Week 42 42. The growth rate of a fetus from Week 33 to Week 39 is nearly constant. On this interval, which of the following best models the weight, w, in ounces of a fetus t weeks after conception? (A) w = 2.5t 220 (B) w = 5.8t 180 (C) w = 8.1t 200 (D) w = 12.4t 150 8
Factor the following: 43. 7h 2 24h + 9 44. 8x 2 + 2x 15 Simplify each of the following. Assume all variables are positive. 45. 128p 5 q 6 r 8 46. 98m3 25p 10 47. 4 7 Solve the following word problem 48. Huey purchases a helicopter for $576,001. The helicopter decreases in value at an 11% rate each year. What will be the value of the helicopter after 12 years? Round to the nearest dollar. 49. Graph f(x) = 2 ( 1 3 )x on your answer sheet. 9
Name 1. X = 16. 3.2 means 2. 1.8 means 3. 17. Children Tickets 4. Y = Adult Tickets 5. Y = 18. 42 C = F 6. 7. 8. ( )( ) 9. ( )( ) 10. ( )( ) 11. ( )( ) 12. ( )( ) 13. ( )( ) 14. X =, 15. X, 19. f(x) = 5 4 x + 8 20. y + 10 = 1 (x + 4) 2 21. 9x 2y = 18 10
22. 4x 5y 20 24. y = x 5 + 2 23. f(x) > 2 3 x 25. y = 1 6 x 2 y = 2x + 9 Section 2: Multiple Choice 26. 35. 27. 36. 28. 37. 29. 38. 30. 39. 31. 40. 32. 41. 33. 42. 34. 43. ( )( ) 44. ( )( ) 45. 46. 47. 48. $ 11
49. 49 f(x) = 2 ( 1 3 )x 12