Trig-precalc-H-2020

Trigonometry/Precalculus Summer Assignment The summer assignment for Trig/Precalculus will reinforce some necessary algebra and geometry skills. Complete the review exercises accompanying these Instructions as follows: • Exercises are to be done in a spiral or marble notebook. • Show the initial problem and all work necessary to obtain your answer. • Work is to be neat, well-organized and complete; circle or box your answers. • You are encouraged to refer to resource materials available to you such as your notebooks from previous math courses and the Internet for assistance in solving the problems; however, the work shown must be your own. • Your notebook will be collected on the first day of school. As you complete the review exercises, you are preparing for the first TEST of the first quarter. Trigonometry/Precalculus Summer Topics These are the topics which you will need to know in order to do the review exercises. • The number system: integers, rational, irrational, complex numbers • Properties of exponents: multiplying, dividing, raising to a power, 𝑥 0 , negative exponents • Absolute value • Distance formula (based on the Pythagorean Theorem) • Midpoint formula • Standard form of the equation of a circle • Inequalities • Lines: slope, point-slope form, slope-intercept form, vertical line, horizontal line, general form, parallel and perpendicular lines, graphing lines • How to find the point of intersection of two lines • Quadratic equation including the general form and graphing • Completing the square • Quadratic formula • Parabola: vertex, axis of symmetry, x and y intercepts • Definition of the imaginary number i • Powers of i • Complex numbers: standard form, add, subtract, multiply, divide, conjugate • Projectile motion: distance above the ground at any time t is given by 𝑑 = − 16 𝑡 2 + 𝑣 0 𝑡 + 𝑑 0 ➢ d is the distance the object is above the starting point ➢ t is the time the object is in the air ➢ 𝑣 0 is the initial velocity with which the object is thrown ➢ 𝑑 0 is the initial position (height) of the object

60 CHAPTER P Prerequisites CHAPTER P Review Exercises Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator . The collection of exercises marked in red could be used as a chapter test. In Exercises 1 and 2, find the endpoints and state whether the interval is bounded or unbounded. 1. 3 0, 5 4 2. 1 2 3. Distributive Property Use the distributive property to write the expanded form of . 4. Distributive Property Use the distributive property to write the factored form of . In Exercises 5 and 6, simplify the expression. Assume that denomina- tors are not zero. 5. 6. In Exercises 7 and 8, write the number in scientific notation. 7. The mean distance from Pluto to the Sun is about 3,680,000,000 miles. 8. The diameter of a red blood corpuscle is about 0.000007 me- ter. In Exercises 9 and 10, write the number in decimal form. 9. Our solar system is about years old. 10. The mass of an electron is about g (gram). 11. The data in Table P.9 give the Fiscal 2009 final budget for some Department of Education programs. Using scientific notation and no calculator, write the amount in dollars for the programs. 9.1094 * 10 - 28 5 * 10 9 1 3 x 2 y 3 2 - 2 1 uv 2 2 3 v 2 u 3 2 x 3 + 4 x 2 2 1 x 2 - x 2 2, q Table P.9 Fiscal 2009 Budget Program Amount Title 1 district grants $14.5 billion Title 1 school improvement grants $545.6 million IDEA (Individuals with Disabilities $11.5 billion Education Act) state grants Teacher Incentive Fund $97 million Head Start $7.1 billion Source: U.S. Departments of Education, Health and Human Services as reported in Education Week, May 13, 2009. (a) Title 1 district grants (b) Title 1 school improvement grants (c) IDEA state grants (d) Teacher Incentive Fund (e) Head Start 12. Decimal Form Find the decimal form for . State whether it repeats or terminates. - 5/11 In Exercises 13 and 14, find (a) the distance between the points and (b) the midpoint of the line segment determined by the points. 13. and 14 14. 1 and 2 In Exercises 15 and 16, show that the figure determined by the points is the indicated type. 15. Right triangle: , 1 3, 11 2 , 1 7, 9 2 16. Equilateral triangle: 1 0, 1 2 , 1 4, 1 2 , In Exercises 17 and 18, find the standard form equation for the circle. 17. Center 1 0, 0 2 , radius 2 18. Center radius 4 In Exercises 19 and 20, find the center and radius of the circle. 19. 20. 21. (a) Find the length of the sides of the triangle in the figure. (b) Writing to Learn Show that the triangle is a right trian- gle. 22. Distance and Absolute Value Use absolute value notation to write the statement that the distance between z and is less than or equal to 1. 23. Finding a Line Segment with Given Midpoint Let 1 3, 5 2 be the midpoint of the line segment with endpoints and 1 a , b 2 . Determine a and b . 24. Finding Slope Find the slope of the line through the points 25. Finding Point-Slope Form Equation Find an equation in point-slope form for the line through the point with slope 26. Find an equation of the line through the points and in the general form In Exercises 27-32, find an equation in slope-intercept form for the line. 27. The line through with slope 28. The line through the points and 1 3, 2) 29. The line through 1 , 4 2 with slope 30. The line 31. The line through and parallel to the line 32. The line through 1 2, 2 and perpendicular to the line 2 x + 5 y = 3 - 3 2 x + 5 y = 3 1 2, - 3 2 3 x - 4 y = 7 m = 0 - 2 1 - 1, - 4 2 m = 4/5 1 3, - 2 2 Ax + By + C = 0. 1 2, - 5 2 1 - 5, 4 2 m = - 2/3. 1 2, - 1 2 1 - 1, - 2 2 and 1 4, - 5 2 . 1 - 1, 1 2 - 3 x 2 + y 2 = 1 ( x + 5) 2 + ( y + 4) 2 = 9 1 5, - 3 2 , 1 2, 1 - 2 2 3 2 1 - 2, 1 2 1 5, - 1 - 4, 3 2 - 5 y x (5, 6) (-3, 2) (-1, -2)

CHAPTER P Review Exercises 61 (a) Let represent 2000, represent 2001, and so forth. Draw a scatter plot of the data. (b) Use the 2001 and 2006 data to write a linear equation for the average SAT math score y in terms of the year x . Su- perimpose the graph of the linear equation on the scatter plot in (a). (c) Use the equation in (b) to estimate the average SAT math score in 2007. Compare with the actual value of 515. (d) Use the equation in (b) to predict the average SAT math score in 2010. 34. Consider the point 1 and Line . Write an equation (a) for the line passing through this point and par- allel to L , and (b) for the line passing through this point and perpendicular to L . Support your work graphically. In Exercises 35 and 36, assume that each graph contains the origin and the upper right-hand corner of the viewing window. 35. Find the slope of the line in the figure. L : 4 x - 3 y = 5 - 6, 3 2 x = 1 x = 0 Table P.10 Average SAT Math Scores Year SAT Math Score 2000 514 2001 514 2002 516 2003 519 2004 518 2005 520 2006 518 2007 515 2008 515 Source: The World Almanac and Book of Facts, The New York Times, June, 2009. [-10, 10] by [-25, 25] 36. Writing to Learn Which line has the greater slope? Explain. (a) [-6, 6] by [-4, 4] (b) [-15, 15] by [-12, 12] 33. SAT Math Scores The SAT scores are measured on an 800-point scale. The data in Table P.10 show the average SAT math score for several years. In Exercises 37-52, solve the equation algebraically without using a calculator. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. Completing the Square Use completing the square to solve the equation . 54. Quadratic Formula Use the quadratic formula to solve the equation . In Exercises 55-58, solve the equation graphically. 55. 56. 57. 58. In Exercises 59 and 60, solve the inequality and draw a number line graph of the solution. 59. 60. In Exercises 61-72, solve the inequality. 61. 62. 63. 64. 65. 66. 67. 68. 4 x 3 - 9 x + 2 7 0 x 3 - 9 x ... 3 9 x 2 - 12 x - 1 ... 0 2 x 2 - 2 x - 1 7 0 4 x 2 + 3 x 7 10 ƒ 3 x + 4 ƒ Ú 2 ƒ 2 x - 5 ƒ 6 7 3 x - 5 4 ... - 1 5 x + 1 Ú 2 x - 4 - 2 6 x + 4 ... 7 ƒ 2 x - 1 ƒ = 4 - x 2 x 3 - 2 x 2 - 2 = 0 x 3 + 2 x 2 - 4 x - 8 = 0 3 x 3 - 19 x 2 - 14 x = 0 3 x 2 + 4 x - 1 = 0 2 x 2 - 3 x - 1 = 0 x 2 - 2 x + 4 = 0 x 2 - 6 x + 13 = 0 4 x 2 - 4 x + 2 = 0 x 2 = 3 x - 9 x 2 + 12 x - 4 = 0 4 x 2 - 20 x + 25 = 0 ƒ 4 x + 1 ƒ = 3 x 1 2 x + 5 2 = 4 1 x + 7 2 2 x 2 + 8 x = 0 6 x 2 + 7 x = 3 16 x 2 - 24 x + 7 = 0 x 2 - 4 x - 3 = 0 3 1 3 x - 1 2 2 = 21 2 1 5 - 2 y 2 - 3 1 1 - y 2 = y + 1 x - 2 3 + x + 5 2 = 1 3 3 x - 4 = 6 x + 5