Are You Redy for PreClculus? Summer Pcket **Required for ll PreClculus CP nd Honors students** Pge of The PreClculus course prepres students for Clculus nd college science courses. In order to ccomplish this, the course is tught t significntly fster pce thn Algebr, nd students often find it difficult to djust. You will need to spend time this summer prcticing nd reviewing the Algebr nd topics in this pcket! **You will be given Quiz bsed on the contents of this pcket t the beginning of your PreClculus course.** There is formul sheet t the end of the pcket. If you re unsure how to do ny problem, check for online help, such s Khn Acdemy. Here re some other video tutoril sites: http://www.mrmthblog.com/ http://ptrickjmt.com/ http://www.mthispower4u.com/ (Check both Algebr nd Video Librries) A. Evlute using order of opertions: y -. when = -, y = -. - -4 when = - y+ B. Solve equtions:. ( ) 6( ) 4. - + = - - - ( - 9) = - 8( + ) C. Liner Equtions - Sketch grphs, write liner equtions using slope nd intercept:. In which qudrnt is (, -4)? Sketch the grph of the following liner equtions: 6. =- 7. y = Updted My 06
8. y=- + 9. - y= 6 (first solve for y) Pge of 0. Find the slope of (-, ) nd (8, -4) ** (formul sheet t the end). Find the intercepts of -4- y= 6 -intercept: y-intercept:. Rewrite in slope-intercept form: -4- y = slope:. Write n eqution of the line contining (, ) nd (, -). y-intercept: 4. Write n eqution of the line pssing through (7, ) nd hving slope of 0.. Write n eqution of the line hving n undefined slope (no slope) nd pssing through the point (-, ). Updted My 06
Pge of D. Add, Subtrct nd Multiply Polynomils: ( + - ) -( + - ) ( - ) + ( + ) -( -) 6. 4 7. ( ) - + ( 4-7)( + ) 8. 4 9. ( ) 0.. - ( - )( + -) E. Fctoring - Gretest Common Fctor, Trinomils, Difference of Squres: When you 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 by grouping. If you re fctoring trinomil, either fctor by tril nd error, or perhps you remember finding the product nd sum on + b + c, i.e., wht numbers give you product of c nd sum of b? Use those numbers to help you fctor the trinomil. Video: http://tinyurl.com/j6e4en. 49. + 4 4. - 6+ 64. - 6. 7. + 9 4 8. -8 9. 8y- 0y + y 4 Updted My 06
F. Simplify Using Eponent Rules: Pge 4 of 4 0. () (). - 7 9 y.. y 0 (- y) 4 0 4. (- m). y 6 4 y 6. 7. - 4 - y y (- y ) - G. Qudrtic Equtions 8. Solve. (Isolte nd use squre root property) = 8 In #9-40, solve using qudrtic formul nd simplify: 9. + 4 = 0 40. + = In #4-4, fctor to find ll rel solutions: 4. = 0 4. -- 0= 0 Updted My 06
H. Comple (Imginry) Numbers: Pge of Simplify the following: 4. - 9 44. - 7 4. - - 4 46. - - 47. (i) 48. -(i) 49. i 0. 4 i Solve the eqution:. = -9. = -7 Perform the indicted opertion:. (9 + i) + ( 7 i) 4. ( 6i) (8 + i). i( + i) 6. ( + 4i)( + i) I. Rdicls nd Rtionl Eponents: 7. Write in rdicl form nd simplify: 9 8. Write in rtionl eponent form:.) 6 b) 6 9. Simplify, then dd like rdicls: 8 + 8-4 Simplify: 60. 6 7 y 6. 6 Updted My 06
Pge 6 of Solve (check for etrneous solutions): 6. = + 6. = -4 64. - =-7 6. - = 4-7 J. Rtionl Epressions: 66. Divide Rtionl Epressions (Multiply by Reciprocl, Fctor, Simplify) + 6+ 8 + - + 4 + 67. Simplify Comple Frctions using the LCD Method (Video - http://tinyurl.com/z67dhs ) + 68. Simplify Comple Frctions - Multiply by the Reciprocl Method (Video - http://tinyurl.com/jpq7jy ) + + + - Updted My 06
Pge 7 of Section - Common Errors in Algebr Mny lgebr errors come from not mstering the differences between the rules of ddition nd multipliction! Test yourself by doing the following problems. Check your nswers by substituting numbers for the vribles. There my be more thn one correct form of the nswer. I. ERRORS INVOLVING PARENTHESES A. Distributing negtive sign. -( - ) = ) - - b) - c) - + + -. - = ) b) + + + + ( ) + + + + 4.. - = ) b) c) 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 yourself: Does (+ 4) = + 4? II. D. DO NOT distribute when there is only multipliction æ ö. ç ( ) ( b) = ) æ öæ b ö æ ö ç ç b) ç c) d) è ø è øè ø è ø b ( ) b b ERRORS INVOLVING FRACTIONS. Does + b b? Does = + = +? + b b. + = ) b) b + b b+ b. ) b) b = b æ ö 4. ) b) ç = è ø b. ) b) + = + + 6. = ) b) 0 + Updted My 06 +
( + ) 7. = ) b) ( + )( + ) + + Pge 8 of 0 8. Which re possible steps for doing on clcultor? ) 0 b) 0 c) ( )( ) 0 ( ) III. ERRORS INVOLVING EXPONENTS ( ). = ) b) 8.! = ) b). Does 4 - = 4 -( )? 6 9 9 4. ) b) = æ ö ( ) - ç 7. = ) ( ) 7 b) - 6. Which re correct steps for doing on clcultor? ^( ) ) ^ b) - ( ) 7 - è 9 ø! - IV. ERRORS INVOLVING RADICALS. = ) b) c)!. Does + b = + b? Check: Does + 4 = + 4? ( + ) = + ( ). Does b b? Check: Does + 4 = + 4? 4. 64 ) b) = 8 or4. ) b) = 6 4 or 6. Which re correct clcultor steps for + 4? Ù Ù ) 4 b) + ( Ù Ù + 4) ( + ) ( ) c) ^ 4^ ^ d) ^+ 4^ ^( ) Updted My 06
V. ERRORS INVOLVING DIVIDING OUT COMMON FACTORS A. When Simplifying Frctions + b æb ö. = ) + b b) + ç c) è ø + b Pge 9 of +. = ) + b) + ± 4. = ) ± b) ± c) ± 4 ± 4. = ) ± b) ± c) ± 6 4. = ) b) - c) Cn't simplify - 4-4 8 4 6. = ) b) - c) Cn't simplify - 4 - Updted My 06
Pge 0 of Answer Key Are you redy for Algebr /Trig. -7 6» -.7. -4 4. = 8 6.. =. IV 7. 4. y = 4. ( - )( + ) = 0; =, -. = - 6. + - 4. i 44. i 7 7. -4 + 4 + 4. -i 8. 8-6 + 4 46. -i 9. - - 4 0. 4-0 +. - - 9 + 9. ( + 7 )( - 7 ) 47. 48. 49. 0.. 4.. 6. 8. 9. 7. ( + 7 )( - ) ( - 8) ( + 4)( - 4) ( + )( - 4) ( + )( - )( + ) 9i = -9 4. = ±i. = ±i 7. 6 + i 4. -7-7i. 0i + 6i = -6 + 0i 6. 0 + i + 4i = 6 + i 8. ( - )( + + 4) 7. 9. y (6 y - 0 y + ) 8. ) 6 0. 79. 9. + - 4 =. y0. 68 9 = b) (6 ) 60. y 6. 4 6. = + so ( - )( + ) = 0 So = ( ¹ -, etrneous ) - - int : -4. y - int : -6 slope : -4. y - int : - 0. m =. y = - + 4 y y4 6. 7. -8 y 9 8. = ±4. 9. = - ± 7 40. = Updted My 06 6. = - 4 so = - 4. - ± 8 - ± 7 = 6 64. no solution 6. - = 4-7 so = 66. 4( + 4) - 4 + 0 ( 4 + )( - ) 68. ( + )( 4 - ) 67.
4. ( ) - = 0; = 0, Pge 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. b 6. 7. 8. b or c III.. b.. NO!! 4.. b 6. b IV.. c. NO!!. Yes 4. b. b 6. b or d V. A.. b or c. b. b 4.. c 6. Updted My 06
Pge of ALGEBRA II FORMULA SHEET Slope of Line Slope Intercept Form of Line Point Slope Formul Verte Form of Qudrtic m = y - y - y = m + b (y - y ) = m( - ) y = ( - h) + k Qudrtic Formul Discriminnt -coordinte of the Verte of Prbol = -b ± b - 4c = -b b - 4c Pythgoren Theorem Distnce Formul Midpoint Formul Direct Vrition Inverse Vrition Joint Vrition + b = c d = ( - ) + (y - y ) æ è +, y + y y y = k or = k k y = or y = k z = ky ö ø Difference of Two Cubes - b = ( - b)( + b + b ) Sum of Two Cubes + b = ( + b)( - b + b ) Updted My 06