City of Brockton BROCKTON PUBLIC SCHOOLS Matthew H. Malone, Ph,D. + Superintendent of Schools

Transcription

1 City of Brockton BROCKTON PUBLIC SCHOOLS Matthew H. Malone, Ph,D. + Superintendent of Schools Robert Perkins Mathematics Department Head Brockton High School Phone (508) robertoperkins@bpsma.org June 6,2012 Dear StudentlParent, The attached Math Packet is intended for students taking a Pre-Calculus or Trigonometry Class in the fall. The packet contains problems emphasizing necessary skills for the student beginning this course. While completion ofthese problems is optional, it is important to note that ifyou complete this packet successfully you will be eligible for up to 5 points extra credit on your Term I average. You may seek help on the problems. It is hoped that you will do whatever is necessary to complete all ofthe problems successfully. You must submit the answer sheet (which details the problems that must be done) and your work on separate sheets ofpaper. The answer sheet and work should be stapled together and submitted to your teacher on or before Monday, September 10, Ifyou are in a second semester math class please return the completed packet to the Green Math Office by September 10,2012. Late packets will not be accepted. Once again, it is worth your effort to complete all ofthe problems in the packet successfully. You may seek help from family and friends, from Internet sites, books or any other available source. You must however show the work for each problem on paper separate from the answer sheet. It is important that you follow the directions in order to obtain the maximum 5 points. Good luck in completing this work. Remember while it is optional, it is an opportunity for all students to take a step in improving their term I grade and to review some important math skills at the same time. Ifyou have any problems with the math packets you may me at robertoperkins@bpsma.org. I check my frequently during the summer and I will get back to you as soon as possible. Thanks, Bob Perkins Brockton High School. 470 Forest Avenue +BI ockton. Massachusetts Brockton. Education. Industry. Progress.

2 Refer to the indicated lesson in the Algebra 1 textbook for help Multiplying Rational Expressions Find each product.' Dividing Rational Expressions Find each quotient. s.4(n + 2).!!:...::..! n(n - 2) n (,% - 2)('% + 2) 2(ax + 3) x(ax + 3) x - 2 Rational Expressions with Unlike Denominators Find the LCM for each pair of ' expressions. 3. 2r - 1, r + 4, 5.,x2-2x - 3, (x - 3)2 Find each sum. 7 1 y +.!. y2 Find each difference ~ - r2 x-5 6. X'+"3 + (x - 5) Mixed Expressions and Complex Fractions Write each mixed expression as a rational expression Ii 9 ~+~ 2m m b b::-f + b=4 ax x 13. %2 _ 25 X+5 x 4 17,X+2 - x::1 a 2 1 2a a b 21. b2-1 - b+1 3.4b+E. c Simplify each expression. 4 a! s 5! 44' 5

3 . Refer to the indicated lesson in the Geometry textbook for help Skills ~actice Distance and Midpoints Use the Pythagorean Theorem to find the distance between each pair of points. 5. y./ F V" (CI G x 7. K(2, 3), F(4, 4) Use the Distance Formula to find the distance between each pair of points. Y(2, 0), P(2, 6) 1l.A(-7, -3},B(5. 2) Find the coordinates ofthe midpoint of a segment having the given endpoints '(3, I), U(5, 3) 18. J( -4, 2), F(5, -2) Find the coordinates of the missing endpoint given that P is the midpoint ofnq. 1 N(2, 0), P(5, 2) 21. Q(3, 9}, P(-1, 5) Find x andy. Sldlls Practice Special Right Triangles 1. ~24 2. x/1 3. x~12 x~ ~32 ~ y y y 4'~R ~ 5 ID 16 Y 60" x

4 Refer to the indicated lesson in the Geometry textbook for help Sldlls Practice Special Right Triangles For Exercises 7-9, use the figure at the right. 7. Ifa = 11, find b and c. 8. If b == 15, find a and c. B 60" ~ A 30" c ~ b Ifc = 9, find a and b. For Exercises 10 and 11, use the figure at the right. 10. The perimeter ofthe square is 30 inches. Find the length ofbc. 11. Find the length of the diagonal BD. Al/1B D~C 12. The perimeter ofthe equilateral triangle is 60 meters. Find the length of an altitude. Trigonometry Use MST to find sin RJ cos R, tan R, sin SJ cos Sf and tan S. Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. r = 16, s = 30, t = r = 10, s = 24, t = 26 Use the figure to find each trigonometric ratio. Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth. tan C 10. sin A 11. cos C Find x. Round to the nearest tenth /'1~ 1:~ AL-----.dB A 27 B

5 Refer to the indicated lesson in the Geometry textbook for help Sldlls Practice The Law of Sines 2. Find x to the nearest tenth. ~ The Law of Cosines For Questions 1 and 2, find x to the nearest tenth 1...,~ 2.~ Solve MBT. Round your answers to S. Solve MBC. Round your answers to the nearest degree. R the nearest tenth. A~ 4!r C TU76 S Refer to the indicated lesson in the Algebra 2 textbook for help Pr ac t Ice e RelatIons and Functions Determine whether each relation is a function. Write yes or no R 4. y Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. 5. {(-4, -1), (4, 0), (0,3), (2, on 6.y = 2x - 1 y J J J I c x Find each value iff(x) - Z! 2 and g~) - -k f(3) 8. {(-4) 10. {(-2) 11.g(-6) 12.{(m - 2)

6 Refer to the indicated lesson in the Algebra 2 textbook for help Skills' Practice Writing Linear Equations State the slope and y-intercept of the graph of each equation. 3 2.y = -sx x+4y=4 8. 2)' = 6-5x 6.3x-2y+6=0 Write an equation in slope-intercept form for each graph 'II n1 2) II ICl II 1(-1-4) 1 j I I' x,++++(4,-1) 11...~y I 03), 1\!(J i\., (3-3)~.Ll L~ x Write an equation in slope-intercept form for the line that satisfies each set of conditions. 12. slope 3, passes through (1, -3) 14. slope -2, passes through (0, -5) 16. passes through (-1, -2) and (-a, 1) Simplify. 1. Y24 Radical Expressions 7. 4-id2f5 13. (4v'i2)(aV20) 1 (1 - V5)(1 + V5) 3.ru -f.; 10. v'i2-2v3 + Vi08 O. 4V50x 5 liz. 11. \j""5z 17. 2WB - \I'7s - v'i2

7 '"'''''--''' "",,-'"'''''''''',,,,,,,,,,,,--,,,,,,- Refer to the indicated lesson in the Algebra 2 textbook for help Solving Quadratic Equations by Factoring Solve each equation by factoring. 2.x 2-100::::: x x = x2-4x+3= x 2 + 5x - 3 == 0 6.x 2 - ax - 10 = x 2 - l3x - 10 == 0 Study Guide and Intervention Completing the Square Complete the Square To complete the square for a quadratic expression of the form x 2 + bx, follow these steps. 1. Find % Square %. -+ S. Add ( %Yto x 2 + bx. xample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial. Then write the trinomial as the square ofa binomial. Step 1 b == 22; %= 11 Step = 121 Step 3 c = 121 The trinomial is x x + 121, which can be written as (x + 11)2. example 2 Solve 2,x2 - ax - 24 = 0 by completing the square. 2x 2 - ax - 24 ::::: 0 Original equation 2x 2 - ax = 2" DIvide each side by 2. x2-4x - 12 ::::: 0 x 2-4x = 12 Add 12 to each side. il- 4x - 12 is not a perfect square. 2 x - 4x + 4 = Since (-tt =4.add4Ioeachslde. (x - 2)2 ::::: 16 Factor the square. X - 2 = ± 4 Square Root Property x = 6 or x = - 2 Solve each equation. The solution set is {6, -2}. Find the value ofc that makes each trinomial a perfect square. Then write the trinomial as a perfect square x 2 - lox + c 3. x - ax + c x + 2x + c Solve each equation by completing.the square. 10.2x 2 - ax + 1 = x x - 9 = 0

8 --_.. ".._..._,,'...,,-"" This page is for students entering Precalculus Honors. Refer to the indicated lesson in the Algebra 2 textbook for help. Practice Monomials Simplify. Assume that no variable equals G. Rational Exponents Write each expression in radical form m 8 y 6-9my " 5. V5i Write each radical using rational exponents. -27%8(-%7) Vi (4w- 3 z- 5 )(8w)2 15. (fd2f4)4(-fd5f)8 Evaluate each expression. (3x-2y 3 X5xy-8) 17. (x-3)4y-2 Simplify each expression. 12 s 17.c 6. c 6 s IS i Study Guide and Intervention J. Y 2 28'-1 ji Radical Equations and Inequalities!SOlve each equation xv3 ;:: v'Sx = 15 S.8+Vx+l=2 v'x2 + 7x = v'7x - 9 IG.4V2x = 10

9 Name: -...:Precalculus Summer Work Answer Sheet Write the answer to each specified problem on the indicated line on this answer sheet. The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part ofthe complete packet. Submit the packet to your Precalculus teacher by September 7,2010. If your Precalculus class is scheduled for second semester, you must submit the packet to Mr. Perkins or Mr. Corbett in the Green Math office by September 7,2010. Packets will not be accepted after this date. Please note that the last page is part ofthe packet for Honors level only. Algebra 1 Lesson Lesson Lesson Lesson Geometry Lesson Lesson

10 ll 12. Lesson Lesson Lesson Algebra 1 Lesson

11 5. J 10 x Lesson Lesson Lesson 5-6 Lesson

12 The following problems are for Honors level only. Lesson Lesson 5p Lesson