Page of Are You Ready for Algebra /Trigonometry? Summer Packet **Required for all Algebra /Trig CP and Honors students** The Algebra /Trigonometry course prepares students for Calculus and college science courses. In order to accomplish this, the course is taught at a significantly faster pace than Algebra, and students often find it difficult to adjust. To make the transition easier, spend time this summer practicing and reviewing the Algebra topics in this packet! You will be graded on the contents of this packet in the beginning of your Algebra /Trig course. The packet includes sections - Algebra Topics, Algebra Topics, and Common Errors in Algebra. At the end is a formula sheet and answers to the problems. If you are unsure how to do any problem, check the Internet for help. Go to google.com and type Algebra Tutorial, or the words that describe the problem type. Some websites are free, such as http://www.wtamu.edu/academic/anns/mps/math/mathlab/and http://tutorial.math.lamar.edu/sitemap.asp Section - Algebra Topics you are epected to know well A. Evaluate using order of operations: y. when = -, y = -. y + when =. B. Solve equations:. ( ) 6( ). + = ( 9) = 8( + ) C. Linear Equations - Sketch graphs, write linear equations using slope and intercept:. In which quadrant is (, -)? Sketch the graph of the following linear equations: 6. = 7. y = Updated Apr 0
Page of 8. y = + 9. y = 6 0. Find the slope of (-, ) and (8, -). Find the intercepts of y = 6 -intercept: y-intercept:. Rewrite in slope-intercept form: y = slope: y-intercept:. Write an equation of the line containing (, ) and (, -).. Write an equation of the line passing through (7, ) and having a slope of 0.. Write an equation of the line having an undefined slope (no slope) and passing through the point (-, ). Updated Apr 0
Page of D. Add, Subtract and Multiply Polynomials: 6. ( + ) ( + ) 7. ( ) + ( + ) ( ) ( ) + ( 7)( + ) 8. 9. 0. ( ). ( )( + ) E. Factoring- Greatest Common Factor, Trinomials, Difference of Squares:. 9. +. 6+ 6. F. Simplify Using Eponent Rules: 6. () () 7. 7 9 8. y y 9. 0 7 y 0 0. ( m). y 6 y. y y. ( y ) Updated Apr 0
Page of Section - Algebra topics G. Quadratic Equations. Solve 8 =.. Solve using quadratic formula. + = 0 6. Solve using quadratic formula. + = 0 Find all real solutions 7. = 0 8. 0= 0 H. Comple (Imaginary) Numbers: Simplify the following. 9. 9 0. 7... (i). (i). i 6. i Solve the equation. 7. = 9 8. = -7 Updated Apr 0
Page of Perform the indicated operation. 9. (9 + i) + ( 7 i) 0. ( 6i) (8 + i). i( + i). ( + i)( + i) I. Radicals and Rational Eponents:. Write in radical form and simplify: 9. Write in rational eponent form:. Simplify, then add like radicals: 8 + 8 Simplify: 6. 6 7 y 7. 6 Solve: 8. + = 7 9. = 60. = 6. = 7 J. Factoring - Trinomials, Factor by Grouping: 6. 6. + 9 Updated Apr 0
Page 6 of K. Rational Epressions- Perform the operations and simplify: 6. + + + 6 8 + + 8 0 6. + 6 Simplify the comple fractions 66. + 67. + + + Solve: 68. = 69. = 70. + = + 7. = + Updated Apr 0
Page 7 of Section - Common Errors in Algebra Many algebra errors come from not mastering the differences between the rules of addition and multiplication! Test yourself by doing the following problems. Check your answers by substituting numbers for the variables. There may be more than one correct form of the answer. I. ERRORS INVOLVING PARENTHESES A. Distributing a negative sign. ( ) = a) b) c) +. + + = a) + +.. ( + ) + = a) b) + + b) c) + B. Distributing Left and Right ( + ) = a) 8 + 6 b) + c) + 6. ( ) C. DO NOT distribute eponents over addition or subtraction Does ( a+ b) = a + b? Convince yourself: Does ( ) + = +? II. D. DO NOT distribute when there is only multiplication. ( a) ( b) = a) a b b) ab c) ( ab) d) ab ERRORS INVOLVING FRACTIONS. Does a + b a b = +? Does = + a+ b a b. + = a) a b a+ b? b) b + a ab. a b = b a) a b) ab. = a) b) Updated Apr 0
Page 8 of. + = a) + 6. 7. + = + ( + ) = ( + )( + ) b) + a) b) 0 a) + b) + 8. Which are possible steps for doing on a calculator a) 0 b) 0 0 ( )( )? c) 0 ( ) III. ERRORS INVOLVING EXPONENTS. ( ) = a) b) 6. = a) 8 b). Does ( ) =? 9. = a) 9 ( ) b). 7 = 9 a) ( ) 7 b) ( ) 7 6. Which are correct steps for doing on a calculator? a) ^ b) ^( ) IV. ERRORS INVOLVING RADICALS. = a) b) c). Does a + b = a+ b? Check: Does + = +?. Does ( a+ b) = a+ b? Check: Does ( ) + = +?.. 6 = a) b) 8 or = a) 6 b) or Updated Apr 0
Page 9 of 6. Which are correct calculator steps for a) + +? b) ( + ) + ) ( ) c) ( ^ ^ ^ d) ^+ ^ ^( ) V. ERRORS INVOLVING DIVIDING OUT COMMON FACTORS A. When Simplifying Fractions. a + b a = a) + b b) b + a c) + b a. a + a a = a) a + b) +. ± = a) ± b) ± c) ±. ± 6 = a) ± b) ± c) ±. = a) b) - c) Can't simplify 6. 8 = a) b) - c) Can't simplify Updated Apr 0
Page 0 of Answer Key Are you ready for Algebra /Trig 7..7. y =. =. 9i = 9 6...6 6. +. 6.. = 7. + + 7. = ± i 8. =± i 7. =. IV 8. 8 6 + 8 9. 6 + i 6. 9. 0. 7 7i 0. 0+. 0 i+ 6i = 6 + 0i. 9+ 9. 0 + i+ i = 6 + i. ( 7)( 7) 7.. ( 7)( ) 8) Updated Apr 0 +. 9 =. +. + =. ( 6. y 7.. ( + )( ) 8. = so = 6. 79 9. = so = 8. 7. 60. = 0 8. y 6. = 7 so = 9.. 0... 9. 7 6. ( + )( ) 0. 6. ( + )( )( + ) y ( + ). y 6. 6 + 6. ( )(. 66. 9 8 y + 0 + m =. = ± 67. int : y int : 6 slope : y int :. y = +. = ± 7 68. LCD : 6. ( )( ) + = 0; =, ± 8 ± 7 = = 69. Cross Multiply; = 6 = 0; = 0, 70. LC D :( + )( ) 7. ( ) 8. ( )( ) + =0 =, ( )( ) = 0; =, 9. i 0. i 7 7. Cross Multiply; = 0. i. i )
Answers to Common Errors in Algebra Page of I. A.. c. b. a B.. a C. NO!!! D.. b or c or d II.. Yes, No. b. b. b. b 6. a 7. a 8. b or c III.. b. a. NO!!. a. b 6. b IV.. c. NO!!. Yes. b. b 6. b or d V. A.. b or c. b. b. a. c 6. a Updated Apr 0
Page of ALGEBRA II FORMULA SHEET Slope of a Line m = y y Slope Intercept Form of a Line y = m + b Point Slope Formula (y y ) = m( ) Verte Form of a Quadratic y = a( h) + k Quadratic Formula = b ± b ac a Discriminant -coordinate of the Verte of a Parabola b ac = b a Pythagorean Theorem a + b = c Distance Formula d = ( ) + (y y ) Midpoint Formula Direct Variation Inverse Variation Joint Variation +, y + y y y = kor = k k y = ory = k z = ky Difference of Two Cubes a b = ( a b)( a + ab+ b ) Sum of Two Cubes a + b = ( a+ b)( a ab+ b ) Updated Apr 0