Welcome to Accelerated PreCalculus! I look forward to getting to know you and working with you during the 06 07 school year. While you are enjoying your summer, please take time out to complete the attached assignments. This packet is designed to help make the transition into this challenging course as smooth as possible (and to keep your math skills from deteriorating from lack of use). One thing is for sure the more you do over the summer, the easier it will be when school starts and the more comfortable you will feel with the pace of the class. Your summer assignment consists of problems that cover the following concepts: Part : Prerequisite Skills Eponent Rules, The Quadratic Formula, Factoring and Polynomials Part : Domain, Range, Functions and Inverses Part : Logarithms Part : Triangles Part : Conic Sections You should recognize these concepts from Algebra II and Geometry. It is very important that you complete the summer work. Packets WILL BE COLLECTED on the FIRST day of school. A completion grade will be assigned to all students. At that point, if you have not completed the majority of the assignment, you have to work that much harder to earn the grade that you desire. We will spend some time in class reviewing the prerequisite skills covered in this packet, but we will NOT complete problems from this packet, as they are your responsibility to complete over the summer. You will be tested on this material within the first week of school. We will be building on all of these concepts for the rest of the year. These foundational skills and practice are very important!! Notes related to each concept area are posted below. If you need help, please use the resources that I have posted for you and venture out and discover on your own. Answers are attached at the end of this packet so you can check your solutions as you work. This does not mean copy the answers to complete the assignment. No work no credit!!! If you have questions or concerns, you can reach me by email at saffol@fultonschools.org I will respond, but please understand that I do not check my email as frequently in the summer as I do during the school year. I will still do my best to answer your question as quickly as possible. Give me your best work while giving yourself the opportunity to get off to a great start! I look forward to meeting you in August! ~ Mrs. Saffo The solutions are located in the attachment!! Make sure you check your work as you go! Summer Assignment Notes
Accelerated PreCalculus Summer Packet!! *Please complete ALL work on a separate sheet of paper and ALWAYS show ALL work to support your answer!!* Part : Prerequisite Skills Eponent Rules, The Quadratic Formula Factoring and Solving Polynomials Simplify using eponent rules. Assume that no variable equals zero. Write all eponents as POSITIVE. 8 6 y my... a c ac y 9my. a 7 bc. 7m n m n Solve each equation using the quadratic formula. 6. 8 y y y. 0. 0 9. 6. 90. 7. 9 6. 8 8 8. 8 Solve each equation by factoring. 9. (n )(n) 0. n 8 9n 0. m m0. 7v v. (n)( n) 0. ( n )(n ) 0 6. 7. k k v v v 6v. k 7 k Solve each polynomial. 8. f ( ) 9 0 0. f ( ) 8 9. f ( ) 9. f ( ) 0. f ( ) 6 8. f ( ) 9 7. f ( ) 7 0
Find the domain of each function. Part : Domain, Functions and Inverses. h( ). g( ) 8... f( ) f( ) g ( ) ( ) 6. h ( ) 660 7. g ( ) 8. f ( ) 9. h ( ) 0. f( ). g ( ). h ( ). j ( ). f( ) 9 0 8 Find f g (), f g (), g () f f, and (), given the following: g. f( ), g( ) 7 6. f ( ), g ( ) 7. f( ), g ( ) Find f g( ) for each f( ) and g ( ). Also state the domain of the composition. 8. f ( ) and g ( ) 9. f( ) and g ( ) 0. f( ) and g ( ). f ( ) 6 and g( ) Inverses: Find the inverse of each function.. f ( ). h( ). w ( ). g ( ), for 0 6. r ( ) Showing Inverses by Composition: For each problem, find f(g()) and g(f()). Then determine whether f and g are inverses. 7. f ( ), g( ) 8. f ( ), g( ) 9. f( ), g ( ) 0. f ( ), g ( )
Part : Logarithmic Functions Evaluate each epression. Work on a separate sheet of paper. Make sure to show the eponential equation. Leave your answer in simplest fraction form, if necessary.. log. log 6. log. log9 7. log 8 log 6. 7 Solve each equation. Work on a separate sheet of paper. Show all work. Leave your answer in simplest fraction form, if necessary. 7. log9 8. log 9. log0 0. log ( ). log 6( ). log ( ). log 8( ) Solve each equation. Work on a separate sheet of paper. Show all work. Leave you answer in simplest fraction form, if necessary. Important: When no base is shown, the base is 0.. log 6( ) log 6 log 6. log( ) log log 6. log log ( ) 7. log ( ) log ( ) 8. log log( ) log 9. log( ) log log( ) 0. log log( 6) log 9. log ( 7) log. log ( ) log ( ). log( ) log( ). log(7 ) log( ). log ( ) log () 6. log (y) log ( y) 7. log( c ) log( c ) log log log log 7 8. 7 7 7 7 9. 0. log 6(9 ) log 6( ) log ( 9) 6 0
Part : Trigonometry, Law of Sines and Law of Cosines Right Triangle Trigonometry: Find the values of sine, cosine and tangent of for. Write your answer in simplest fraction and/or radical form (rationalize your denominator!!) Write an equation involving sine, cosine or tangent that can be used to find. Then solve the equation. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. Solve for all missing parts of triangle ABC using the given measurements. Round measures of the sides to the nearest tenth and measures of the angles to the nearest degree. 0. A =, a =. B = 7, b =. B = 6, c = 8. a =, b = 7. A = 7, c =.. b =, c = 9 Use Trigonometry, Law of Sines, or Law of Cosines to solve each triangle. Round to the nearest tenth. 6. B = 70, C = 8, a = 8 7. c = 8, C = 9, B = 7 8. A =, b = 0, c = 9. B = 9, a =, c = 6 0. B =, C = 90, c =. a =, b = 7, c = 8. a = 7, b = 9, B = 70. b =, c = 0, A = 0
Circles Part : Conic Sections Write the standard form of the equation of the circle with radius r and center (h, k).. r = ; (h, k) = (0, 0). r = ; (h, k) = (, ). Find the equation of a circle in standard form where C(6, -) and D(-, ) are endpoints of a diameter. Find the center (h, k) and radius r of the circle with the given equation.. + y = 6. ( + ) + (y - 9) = 6. + + 6 + (y - 7) = 9 7. + + + y - 6y + 9 = 6 Find the general form of the equation of the circle. 8. Center at (-, -); containing the point (-, ) 9. Center at (, -); containing the point (, -) Parabolas Find the verte, focus and directri given the equation of the parabola. 0. y. y 8. ( y) ( ). y y 0. y 6 0. y 8 8 Find the equation of the parabola given the following information. 6. verte at (0, ), passes through the point (, ). 7. verte at (, ), passes through the point (, ). 8. verte at (0, -), passes through the point (, 0) Ellipse Find the vertices and foci given the equation of the ellipse. 9. y 0. y. 9 y. 9 y 6 Hyperbola Find the center, transverse ais, vertices, foci and asymptotes for each equation.. y. 9 y. y 9 9 6. ( ) ( y) 6 9