Summary of Derivative Techniques 3. 2 Limits with Infinity (at vertical asymptotes): When finding a one-sided limit at a vertical asymptote, the answer is either ±∞. Fundamental Theorem of Calculus: () ()v u F x f t dt=∫, then F x f v v f u u′ ′ ′()= −() b () a ∫ f x dx F b F a= −, when F is antiderivative Definition of Continuity: lim () x c f x f c → = If and Only If f is continuous at x = c. Average Rate of Change : Slope of Secant Line (slope between starting and ending point). endstream Calculus Honors Year at a Glance.docx Calculus AB Year at a Glance.docx . Calculus AB Home Work.docx . This 20 page PDF Calculus guide is a great study resource. <> stream Riemann Sums: 11 nn ii ii ca c a 111 nnn ii i i iii ab a b 1 lim ( ) b n n a i f xdx f a i x x n b a x 1 1 n i n 1 (1) OneNote will be used for all course materials, including daily agendas, notes, worksheets, assignments, and answer keys. In general, any formula you use regularly in class is a good one to memorize. AP CALCULUS FORMULA LIST (Unit 4) Average rate of change of ( ) on [ , ] = f b f a f x a b b a _____ Intermediate Value Theorem: If f is continuous on [a, b] and k is any number between f (a) and f (b), then there is at least one number c between a and b such that f (c) = k. Before 1997, the AP Calculus questions regarding the FTC considered only a limited number of variations. If f(x) is a rational function given by ( )= ( ) ( )),such that ( ) and ( have no common factors, and c is a real %PDF-1.6 %���� AP Calculus AB Reference Sheets. B. Basic Properties and Formulas If fx( ) and gx( ) are differentiable functions (the derivative exists), c and n are any real numbers, 1. endobj 1+tan θ=sec. 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B +sin. 19 0 obj 1. sin θ+cos. additional resources, including a PowerPoint version, a Word document in color, as well as AP Calculus BC topics on his website. ¨¸ ©¹ _____ Absolute value: 0 0 x if x x x if x ­ t ® ¯ _____ Definition of the derivative: 0 ( ) lim h f x h f x fx o h c Interactive Development Environment (IDE) or compiler; Statistics . x���Ak�0����Cɒ�ƠcMa��Vv*�l����?�MF�������dB͹��˻j�c�ӧw[��\��$B��4g?��I�û�w� 37j(̨��. B. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems. Calculus Reference Sheets. 2. θ=1. Trigonometric Formulas . I also decided to create one myself using after taking a Photoshop class. I have my students make formula sheet(s) for use during the AP Exam Review Period. endobj A. sin. 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Yellow Formula Review Sheet (PDF 81 KB) 1997 AB Exam and FRQs key (PDF 284 KB) Yet another Practice Exam (PDF 419 KB) Sample Exam V (PDF 293 KB) Sample Exam V Key (PDF 424 KB) Sample Exam IV Key (PDF 164 KB) Sample Exam IV (PDF 164 KB) NEED HELP DOWNLOADING: �C�h�^5�E�L!6Rf��d&���e�� W ���I���?�$Fǂ�U�-�(P�ʂ Zd�0v�:�=|X��K�!�f�5&M�Q�R��h�a���O����|��{���HJI�[d2)�f�9����j�#x"m(h�m��f��d�-Y#w6�#%�-��6:��>'$7� '1����}��g������i�N��Ӈ����i'J�t��er�n[�Ƽ�Oo� %u��z����s:4^��i�}�琝7��t��װ,��@AE�}d�P�j��*c�7U��6U���;�(y�-����Hyjd�G�S����R���>�/��!5=�kt�1O��(��l��M{�Ġ[�'MU�qEى��27^�#�����k,�x��L�V�ƶ*J�FoV�ƌ� �hJϯ��}��+� 1. AP Calculus AB/BC Formula and Concept Cheat Sheet Limit of a Continuous Function If f(x) is a continuous function for all real numbers, then ) lim Limits of Rational Functions A. AP CALCULUS AB and BC . 18 0 obj Required. Arithmetic Review 2. Final Notes . min. … Calculator; Computer Science A. 8 0 obj Read the Course Syllabus . Anti-Derivative : An anti-derivative of f x( ) is a function, Fx( ), such that F x f x′( )= ( ). Click here to learn more about the format of the exam: What is the Format of the AP Calculus AB Test?. .ln ab lna lnb.ln lna lnb == == =+ =− Average Value If the function f(x) is continuous on [a, b] and the first derivative exist on the interval (a, b), then there exists a number x = c on (a, b) such that 1 = () is the average value b a fc f xdx ba fc −−−− ∫∫∫∫ The Fundamental Theorem of Calculus () where '( ) ( ) b a fxdx Fb Fa Fx fx =− ==== ∫∫∫ 2nd Fundamental Theorem of Calculus # ∫ <> AP Calculus AB is an introductory college-level calculus course. endobj Year at a Glance. 3 0 obj <> 6. tan(−θ) =−tanθ. :f㵾ad�ve`7n����q����+[��� Z�������V��Hr��7�����Q��������I�̣ESyC��V��.��e��*w�����~�L��� H藨l�ल|������&��nԥP/��ecj�B��?$`w�GD���-�K1[/~��/0�3�~�kꢦ�ZE9��_��C����N�Y �]��V����q)����>8!Ii��D)�3t�}]���0�� Includes formulas … endobj endobj <> -When we multiply, we add exponenxx xa b ab⋅= + ts: -When we divide, we subtract exponents: a ab b x x x = −, ≠0-When we raise powers, we multiply: ( ) xxa abb = ⋅ 2. Formulas for AP Statistics I. Descriptive Statistics 1 i i x xx nn ∑ =∑= ( ) ( )2 1 2 1 1 i xi xx s xx n n ∑− = ∑− = − − y a bxˆ= + y a bx= + 1 1 ii xy xx y y r n ss −− = ∑− y x s br s = II. 120 0 obj <>/Filter/FlateDecode/ID[<9871803F499FAA0724CEC8496A23EFBB><8A1745348C49E64EA89B685282911FC3>]/Index[98 40]/Info 97 0 R/Length 108/Prev 270482/Root 99 0 R/Size 138/Type/XRef/W[1 3 1]>>stream ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS Proton mass, 1.67 10 kg 27 m p Neutron mass, 1.67 10 kg 27 m n Electron mass, 9.11 10 kg 31 m e Avogadro’s number, 23 1 N 0 6.02 10 mol Universal gas constant, R 8.31 J (mol K) < Boltzmann’s constant, 1.38 10 J K 23 k B Electron charge magnitude, e 1.60 10 C 19 Review of elementary functions, limits, differential calculus, and integral calculus. Classics Summary. A. cos. B +sin. Here you will find the following in this order: 1. endobj 17 0 obj <> Video Tutorials. 8. x ( ) ( ) 2 32 2 6 6. Keyboarding Tip Sheet for 2020 AP Calculus Exams (.pdf/625 KB) Permitted. AP CAL AB Reference Sheet.pdf endobj AP Calculus AB: Assignment Sheet Chapter 2: Differentiation Date SECTION / TOPIC ASSIGNMENT Number A B of problems 9/29 2.2 Basic Differentiation Rules and p143 #1-23 odd, 35, 39, 41, 47, 49, 51, 55, 30 Tu Rates of Change 61, 63, 65, 66, 68, 95, 103, - Power Rule, Sin x, Cos x, and e^x AP#114-117 11 0 obj in ab, . 9 0 obj B. cos. A. <> appeared in both the multiple-choice and free-response sections of the AP Calculus Exam for many years. 7. sin(A + B) =sin. (xn) = nxn−1 dx d 17. dx du dx dy dx dy = × Chain Rule 2. fg fg gf dx d ( ) = ′+ ′ 3. 4. θ. sin(−θ) =−sinθ. Java Quick Reference (.pdf/378.99 KB) Permitted. 2. 3. endobj h�bbd```b``6�� �q�d��LK�ls0� 11. sin2θ=2sinθcosθ. Fundamental Theorem of Calculus: ' x a d F xftdtfx dx where f t is a continuous function on [a, x]. Elaine Cheong’s Calc AB Study Guide. I have been teaching AP Calculus BC for 25 years. Find all critical points of fx in ab, . x��[[o\�~����vQ�_�$�,ǁMc�/VP��U���B�U�������.�#��+if8��7$͎f�}w|v��5?��^�>e����H&;�>����~:�O�w�����q�A�V�+;����hmA{���JozL��>^}��:�qyý̹�x���)c#�ɑ�,f#���\��餜�헳���>�;a�ޢy�wGzv^����b���̑jב^q���s�8=���%w��׋�ͮ���z���݊�]w�oYs �Y���������߰^� 98 0 obj <> endobj Course Overview. 4 0 obj <>/Font<>>>/BBox[ 0 0 83.943 37.009] /Matrix[ 0.85772 0 0 1.9455 0 0] /Filter/FlateDecode/Length 274>> AP Calculus Formula List Math by Mr. Mueller Page 6 of 6 ( ) ( ) ( ) ( ) ( ) 2 2 2 Polar Coordinates and Graphs: For : cos , sin , , tan cos ' sin cos 'sin Slope of a polar curve: sin ' cos sin 'cos Area inside a polar curve y r f x r y r r x y x dy dy d r rf f dx dx d f f r r 14 0 obj It is 2 pages 81/2" x 11" in color in .pdf format. Techniques of Integration 4. Finding Absolute Extrema To find the absolute extrema of the continuous AB Calculus Facts and Formulae 2. Indefinite Integral :∫f x dx F x c( ) = +( ) where Fx( ) is an anti-derivative of f x( ). min. 13 0 obj ��9?z0�'�S.�(�5 ��`�۵b͌�����(wa7`�+u�VW6Ɖ5�Ai���=������j�L멋�!�����'.�h��E����#�*�R��hcAh��ێ]4Z�"ҥ_&�R1|z@Sӛ��T1|z��Q��^��u�{��dܔ�/� Print out the DERIVATIVE RULES notes ..... this will become your new BEST FRIEND !!!! A high score (4-5) typically qualifies you to receive college credit or equivalency for one full semester of calculus. The AP Calculus AB exam is a 3 hour and 15 minute standardized test. Applications of Integration Professor: Dr. Mohammad Shakil C0-Author: Jeongmin Correa Mathematics Department 3 1 3 9. x x x − − − − = = − 1 ( ) 1. Trigonometric Identities Once you have mastered those fundamental topics of mathematics, you can then build your expertise in calculus. 13. θ. θ θ θ cot 1 cos sin Virtual TBA. Calculus YouTube links by chapter & section.docx . 16 0 obj endobj endobj To find these, simply Google "AP Calculus AB formula sheet" and look at your options. !NY�]��`���>��'ĕ��03m =R\�&��'0� #R�=�4Fꂍb#c�G0�Q�`C����mÖ��5 X�������K�&0�g3��>y3�ԃ.�7��c-pj�M������ഐ��h{�p�}S�p�L��]�G��D���aI�U+*6��>���Y���mH(D��5��c�c�=�!�l���r��O���x��� ��9����8�eA�O�m�>d�����l���N|���.l���W��݀�R�C?��PRO^��|��C���QN�ި���؆p ����,��ئq|�5$��ñd�l[��%����)g\��������~�p�6� 12 0 obj <>/XObject<>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> n���I0���y�mdW����b=����;���^�`���"�z� ��z*�A�|�U�ȴZ�&m�%���s.�u�����Fm��\>��>�1I0���s�~���Pa:���v(&��v�s? Calculus I Formulas MAC 2311 1. Traditional "Y���#0i�%Q�S��E�H6�YH2&���͑`�� RQH� �蒏`]�4!�30��` �jW Then ( ) (*) 1 lim i b n a n i f x dx f x x →∞ = ∫ =∑ ∆. on [ab,]. endobj <> 1. 1 1 5 5 25. x x x −= = − ⋅− − ( ) ( ) ( ) 2 8 4 22 8. Calculus Honors Home Work.docx. 5. cos(−θ) =cosθ. For a quick review check out the following helpful articles. ! A. 8. sin(A−B) =sin AcosB −sin Bcos. A. sin. Differentiation rules 3. ab, then there exist numbers c and d so that, 1.,acd b , 2. fc is the abs. 1 0 obj After about 20 hours, it is done! b a f xdx Fb Fa, where F(x) is any antiderivative of f(x). Applications of Differentiation 4. h�b```f`` <> Home Work. 21 0 obj calculus review (ab) notes Here are the notes that you will need for the AP CALCULUS exam. 9. cos(A + B) =cos. AP Calculus AB Cram Sheet Definition of the Derivative Function: f ' (x) = limh 0 ccccccccccccccccf+x h/ccccccccccccccc f+x/ h Definition of Derivative at a Point: f ' (a) = limh 0 ccccccccccccccccf+a h/ cccccccccccccf+a/ h (note: the first definition results in a function, the … <> If f(x) is a rational function given by ( )= ( )),such that ( ) and ( have no common factors, and c … 36 6. 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