Welcome A.P. Calculus Students

Transcription

1 Welcome A.P. Calculus Students Congratulations on your decision to enroll in A.P. Calculus. Electing to take the A.P. course may have been an arduous task; however the intellectual stimulus and challenges that drive the curriculum will be a reward in and of itself, regardless of the outcome in May. To make the transition from Pre-Calculus/Dual Enrollment to A.P. Calculus, our basic mathematics skills: graphing functions, factoring, and trigonometry must be top notch. We have ample timeline (the summer) to accomplish this goal. TI-89 titanium calculators will be used exclusively in class and I ask that you have your own. The mathematics department has some 89 s available for check out but they will be distributed on a first come first served basis the second day of school in August. As a rental fee for using the TI-89 calculator you are expected to bring in a 6 pack of AAA batteries. That usually costs around $0.00. These should be alkaline batteries, not heavy duty. If you have Casio (good choice) but I cannot help you at all. There will be definitely be times we will put the calculators away. So please don t be a calculator baby or become co-dependent. You will be required to purchase a $7.00 practice AP book, for which you can pay me anytime during the first quarter. I will buy them from department funds and you will give me a check for that amount. If you choose not to write in the book you can use it in class and not pay the $7.00. You will also be required to attend a 3-hour afterschool session in April. On this day we will take our final exam and AP practice test. A date will be announced well in advance and an alternate will also be announced.

2 My phone number is , if you need to speak with me over the summer. I will be at the Boot Camp doing my help session for A.P. Calculus. This is what the summer packet includes: 3 Survivor worksheets, a first week schedule, Calculus concept worksheet (parent functions) and formulas which we need to know. The survivor worksheets will be due Friday August 22 th. This is the first Friday of school. Formulas and Theorems: Parent Functions: Know These Know: Domain & Range, Key Points, Shape Calculus Concepts WS FIRST WEEK SCHEDULE DAY ONE QUIZ Day Two Day Three Day Four DAY FIVE QUIZ! TrigonometryFunctionValues(NoCalc) % " DaddyCurvesWithTranslations & $ Formulas ' Begin discussion on Summer Homework Check out Calculators and Texts Questions on summer work Book Work assignments Questions on summer work Book Work and calculator assignments Questions on Summer Work, Book Work SUMMER WORK QUIZ ALL WORK DUE, Summer Packet and Book Work But be prepared to roll with the above schedule, unless otherwise notified. Call me for questions. Summer Packets are also on the web site. I am looking for students willing to do homework every night and be detailed oriented. Ms. Imperatore

3 Would you like to be an AP Calculus Survivor? With there skill as lifelines you are sure to make a 5. ON YOUR OWN PAPER. Factor out monomial factors. (A) 3x 4 + 4x 3! x 2 = x 2 (...) (E) x 2! 6x2 = x(...) (B) 2 x + 6x 3 2 = x 2 (...) (F) sin x + tan x = sin x(...) (C) e!x! xe!x + 2x 2 e!x = e!x (...) (D) x!! 2 + x = x! (...) 2. Factor these. (G) 2x 2 + 4x = x (...) (A) x 3 " 27 = (B) x 4 " 25 = 3. Factor completely by grouping. (A) x 3 + 4x 2! 2x!8 = (B) x 3 + 2x 2 + 3x + 6 = 4. Use synthetic division to factor. p q (A) x 3! 4x 2 + 2x += (B) x 4! 3x 3 + x 2 + x + 2 = (C) 4x 4 + 3x 2!=

4 5. Factor as indicated. DO NOT MULTIPLY THESE OUT (A) (x!) 3 (x)! (x!) 2 = (B) 3(x 2 + 4)(x 2 +)+ 6(x 2 + 4) 2 = x 2 (C) x 2 +! x 2 + = (D) (x! 3) 3 (x + 2)! 2(x! 3) 2 (x + 2) 2 = (E) (2x +) 3 2 (x 2 )+ (2x +) 5 2 (x! 2 ) = 6. Reduce each expression to lowest terms. DO NOT MULTIPLY OUT. (A) 3x + 9 6x (D) x 2! x 3 x 6 (B) x2 x 2 (E) x! + (x!) 3 2 x! (C) (x +) 3 (x! 2)+ 3(x +) 2 (x +) 4 (F)! (sin x + cos x)2 2sin x 7. Solve using the quadratic formula (if you don t remember this, use a lifeline-call a friend). Equation (A) x 2! 4x!= 0 (B) 2x 2 + x! 3 = 0 solve for x x 8. Factor there quadratic expressions. (A) x 2! 3x + 2 = (B) x 2! 9 = (C) x 2 + 5x! 6 = (D) x 2 + 5x + 6 = (E) 2x 2 + 5x! 3 = (F) e 2 x e!2 x = (G) x 4! 7x 2 +2 = (H)! sin 2 x =

5 9. Factor these polynomials completely. p/q (A) x3! 2x 2! 5x + 6 = (B) 2x3!7x 2 + 9x!8 = (C) 4x 4! 7x 2! 5x!= (D) 3x 3! x 2! 22x + 24 = 0. Simplify (your life) and these expressions. (A) (x +)(x + 3)! (x +)2 x + (D) x +! x!! 2 x 2! (B) x 2 +! ( x 2 + ) x 2 + (E) x(!2x) 2! x 2 +! x2 +! x 2 (C) x2! 5x + 6 x 2! 4x + 4. Rational the denominator. Use a conjugate. 2 (A) (C)! cos x x + x 2 + (B) x! x 2 +

6 Calculus Name: Graphing Worksheet It is important to be able to visualize mentally the graphical image of a function when given an algebraic description. Without your calculator, graph each function. Clearly label the units. Be able to identify key points and domain and range.. f (x) = x 2. f (x) = x 2 3. f (x) = x 3 4. f (x) = x 5. f (x) = [x] 6. f (x) = sin x 7. f (x) = cos x 8. f (x) = tan x 9. f (x) = sec x 0. f (x) = e x. f (x) = ln x 2. f (x) = x 3. f (x) = x 2 4. f (x) = x 5. f (x) = a2! x 2

7 FORMULAS AND THEOREMS.Quadratic formula 5. Area and Volume Formulas: ax 2 + bx + c = 0 (a! 0) FIGURE AREA FORMLA x =!b ± b2! 4ac 2a 2.Distance formula Trapezoid 2 [base + base 2 ](height) Parallelogram (base)(height) d = (x 2! x ) 2 + (y 2! y ) 2 3.Equation of a Circle x 2 + y 2 = r 2 center at (0,0) and radius = r Equilateral Triangle Circle s 2 3 4!r 2 (circumference = 2!r) 4.Equation of an Ellipse x 2 a + y2 2 b 2 = center at (0,0) (x! h) 2 (y! k)2 + = a 2 b 2 center at (h,k) Solid Volume Surface Area Sphere 4 4!r2!r3 3 Right Circular!r 2 h 2!rh Cylinder Right Circular Cone 3!r2 b Lateral S.A:!r r 2 + b 2 Total S.A. Special Angles Function 0 30º π/6 45º π/4 60º π/3 90º π/2 80º π 270º 3π/2 360º 2π Sin 0 / Cos 3 2 ½ Tan Undefined 0 Undefined 0 3 Pythagorean Identities: sin 2 x + cos 2 x = + tan 2 x = sec 2 x + cot 2 x = csc 2 x