Are You Ready for Algebra 3/Trigonometry? Summer Packet **Required for all Algebra 3/Trig CP and Honors students**

Transcription

1 Are You Red for Algebr /Trigonometr? Summer Pcket **Required for ll Algebr /Trig CP nd Honors students** Pge of The Algebr /Trigonometr course prepres students for Clculus nd college science courses. In order to ccomplish this, the course is tught t significntl fster pce thn Algebr, nd students often find it difficult to djust. To mke the trnsition esier, spend time this summer prcticing nd reviewing the Algebr topics in this pcket! **You will be given Quiz bsed on the contents of this pcket t the beginning of our Algebr /Trig course.** There is formul sheet nd nswers to the problems t the end. If ou re unsure how to do n problem, check the Internet for help. Go to google.com nd tpe Algebr Tutoril, or the words tht describe the problem tpe. Some websites re free, such s nd A. Evlute using order of opertions:. when = -, = -. 4 when = - B. Solve equtions:. ( ) 6( ) C. Liner Equtions - Sketch grphs, write liner equtions using slope nd intercept: 5. In which qudrnt is (5, -4)? Sketch the grph of the following liner equtions: Updted M 0

2 (first solve for ) Pge of 0. Find the slope of (-5, ) nd (8, -4) ** (formul sheet t the end). Find the intercepts of 4 6 -intercept: -intercept:. Rewrite in slope-intercept form: 4 slope:. Write n eqution of the line contining (, ) nd (, -). -intercept: 4. Write n eqution of the line pssing through (7, ) nd hving slope of Write n eqution of the line hving n undefined slope (no slope) nd pssing through the point (-, 5). Updted M 0

3 Pge of D. Add, Subtrct nd Multipl Polnomils: E. Fctoring - Gretest Common Fctor, Trinomils, Difference of Squres: When ou fctor, first look for GCF. Then look for specil fctors, like the difference of squres: b ( b)( b ), OR the sum or difference of cubes (formuls re on the lst pge) OR, if there re 4 terms, fctor b grouping. If ou re fctoring trinomil, either fctor b tril nd error, or perhps ou remember finding the product nd sum on b c, ie, wht numbers give ou product of c nd sum of b? Use those numbers to help ou fctor the trinomil Updted M 0

4 F. Simplif Using Eponent Rules: Pge 4 of 0. 4 () () ( 5 m ) ( ) G. Qudrtic Equtions 8. Solve 8. In #9-40, solve using qudrtic formul nd simplif: = = 0 In #4-4, fctor to find ll rel solutions: 4. 5 = Updted M 0

5 H. Comple (Imginr) Numbers: Pge 5 of Simplif the following: (i) 48. (i) 49. i i Solve the eqution: 5. = 9 5. = -7 Perform the indicted opertion: 5. (9 + i) + ( 7 i) 54. ( 6i) (8 + i) 55. i(5 + i) 56. (5 + 4i)( + i) I. Rdicls nd Rtionl Eponents: 57. Write in rdicl form nd simplif: Write in rtionl eponent form:.) 5 6 b) Simplif, then dd like rdicls: Simplif: Updted M 0

6 Solve (check for etrneous solutions): Pge 6 of Section - Common Errors in Algebr Mn lgebr errors come from not mstering the differences between the rules of ddition nd multipliction! Test ourself b doing the following problems. Check our nswers b substituting numbers for the vribles. There m be more thn one correct form of the nswer. I. ERRORS INVOLVING PARENTHESES A. Distributing negtive sign. ( ) b) c) 5. b) b) 5 c) 4 5 B. Distributing Left nd Right. 4( ) 8 6 b) 4 4 c) 4 6 C. DO NOT distribute eponents over ddition or subtrction Does ( b) b? Convince ourself: Does ( 4) 4? D. DO NOT distribute when there is onl multipliction. ( b ) b b) b c) b d) b II. ERRORS INVOLVING FRACTIONS. Does. b b b? Does b b? b b) b b Updted M 0

7 Pge 7 of. b b b) b 4. b) ( ) ( )( ) b) b) 0 b) 8. Which re possible steps for doing on clcultor 50 5? 50 5 b) 50 5 c) 50 5 III. ERRORS INVOLVING EXPONENTS. = 5 b) b) 5. Does 4 4 ( )? b) b) 7 6. Which re correct steps for doing on clcultor ^ b) ^? IV. ERRORS INVOLVING RADICALS. 5 5 b) 5 c) 5. Does. Does b b? Check: Does b b? Check: Does 4 4? 4 4? Updted M 0

8 Pge 8 of b) 8 4 or 5. 6 b) 4 or 6. Which re correct clcultor steps for 4? 4 b) 4 c) ^ 4^ ^ d) ^ 4^ ^( ) V. ERRORS INVOLVING DIVIDING OUT COMMON FACTORS A. When Simplifing Frctions. b b b) b c) b. b). 4 b) c) b) c) b) - c) Cn't simplif b) - c) Cn't simplif Updted M 0

9 Answer Ke Are ou red for Algebr /Trig Updted M i i i IV i i i i i i i 6i 6 0i Pge 9 of 0 i 4i 6 i ( )( 4) (6 0 ) b) 5 5 (6 ) so m so int : 4 5. int : no solution 4 slope : 4 6. int : so ; 0, ; 5,

10 Pge 0 of Answers to Common Errors in Algebr I. A.. c. b. B.. C. NO!!! D.. b or c or d II.. Yes, No. b. b 4. b 5. b b or c III.. b.. NO!! b 6. b IV.. c. NO!!. Yes 4. b 5. b 6. b or d V. A.. b or c. b. b c 6. Updted M 0

11 Pge of ALGEBRA II FORMULA SHEET Slope of Line m Slope Intercept Form of Line m b Point Slope Formul ( ) m( ) Verte Form of Qudrtic ( h) k Qudrtic Formul b b 4c Discriminnt b 4c -coordinte of the Verte of Prbol b Pthgoren Theorem b c Distnce Formul d ( ) ( ) Midpoint Formul Direct Vrition Inverse Vrition, k or k k or k Joint Vrition z k Difference of Two Cubes b ( b)( b b ) Sum of Two Cubes b ( b)( b b ) Updted M 0