Anti-Derivative : An anti-derivative of f x( ) is a function, Fx( ), such that F x f x′( )= ( ). 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. Techniques of Integration 4. 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. 1 0 obj Interactive Development Environment (IDE) or compiler; Statistics . endobj AP Calculus AB is an introductory college-level calculus course. Trigonometric Identities Once you have mastered those fundamental topics of mathematics, you can then build your expertise in calculus. Algebra Review (ACT) 3. Applications of Integration Professor: Dr. Mohammad Shakil C0-Author: Jeongmin Correa Mathematics Department Finding Absolute Extrema To find the absolute extrema of the continuous OneNote will be used for all course materials, including daily agendas, notes, worksheets, assignments, and answer keys. Required. B. Calculus I Formulas MAC 2311 1. %PDF-1.5 min. B. Fundamental Theorem of Calculus Calculus. Basic Properties and Formulas If fx( ) and gx( ) are differentiable functions (the derivative exists), c and n are any real numbers, 1. 11. sin2θ=2sinθcosθ. ab, then there exist numbers c and d so that, 1.,acd b , 2. fc is the abs. 98 0 obj <> endobj stream … endobj �#������(d˸)���JWJ(hIMު�>�|�S= AP Calculus students need to understand this theorem using a variety of approaches and problem-solving techniques. endobj <> 8. sin(A−B) =sin AcosB −sin Bcos. endobj �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:��>'$7� '1����}��g������i�N��Ӈ����i'J�t��er�n[�Ƽ�Oo� %u��z����s:4^��i�}�琝7��t��װ,��@AE�}d�P�j��*c�7U��6U���;�(y�-����Hyjd�G�S����R���>�/��!5=�kt�1O��(��l��M{�Ġ[�'MU�qEى��27^�#�����k,�x��L�V�ƶ*J�FoV�ƌ� �hJϯ��}��+� Traditional Yellow Formula Review Sheet (PDF 81 KB) 1997 AB Exam and FRQs key (PDF 284 KB) Yet another Practice Exam (PDF 419 KB) Sample Exam V (PDF 293 KB) Sample Exam V Key (PDF 424 KB) Sample Exam IV Key (PDF 164 KB) Sample Exam IV (PDF 164 KB) NEED HELP DOWNLOADING: 18 0 obj A. cos. B −sin. <> a`e`�� Ā B,@Q�F� �&py� U2�7Ȝq�ˢ�������ή���U{�J�(���s�J�1?܂��l܂���n'8� CFGGG��`@�@Qq. Calculus AB Home Work.docx . endobj Final Notes . Indefinite Integral :∫f x dx F x c( ) = +( ) where Fx( ) is an anti-derivative of f x( ). b a f xdx Fb Fa, where F(x) is any antiderivative of f(x). This 20 page PDF Calculus guide is a great study resource. x�}Q�N1�#���$v"�JT�Ub嶊 AjYx}|p�V�#Q���� sk���j����v1 ��R��� s�p�Aj��8��æwv���/10�_��T@��O��at�/x��}��G��ͅ8c����/�K���iyS$]W]Cn�/�M0��4,UF��;�L�d�\�e��H�d4ѹH��L�����yB $� 1. AP Calc AB; Welcome to AP Calculus AB! 1+cot θ=csc. 2 Limits with Infinity (at vertical asymptotes): When finding a one-sided limit at a vertical asymptote, the answer is either ±∞. ����H;��֚���QƝ��Vm��3�����7��ΪB�!�+�g;�uOf$J��=��2�����$��� Our Textbook as a PDF file . AP CALCULUS AB and BC . endobj 2. (xn) = nxn−1 dx d 17. dx du dx dy dx dy = × Chain Rule 2. fg fg gf dx d ( ) = ′+ ′ 3. Integrals 5. Year at a Glance. 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 Click here to learn more about the format of the exam: What is the Format of the AP Calculus AB Test?. additional resources, including a PowerPoint version, a Word document in color, as well as AP Calculus BC topics on his website. in ab, . <>/Font<>>>/BBox[ 0 0 77.947 38.009] /Matrix[ 0.9237 0 0 1.8943 0 0] /Filter/FlateDecode/Length 288>> To find these, simply Google "AP Calculus AB formula sheet" and look at your options. stream 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 … 8 0 obj <> <>/XObject<>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> AP CAL AB Reference Sheet.pdf 2 0 obj 4 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�/� <> <> appeared in both the multiple-choice and free-response sections of the AP Calculus Exam for many years. 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 A. cos. B +sin. Summary of Derivative Techniques 3. <> <> 13. θ. θ θ θ cot 1 cos sin A high score (4-5) typically qualifies you to receive college credit or equivalency for one full semester of calculus. 20 0 obj The AP Calculus AB exam is a 3 hour and 15 minute standardized test. endstream Classics Summary. Limits and Derivatives 2. endstream endobj startxref Calculator; Computer Science A. Fundamental Theorem of Calculus: ' x a d F xftdtfx dx where f t is a continuous function on [a, x]. 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) <> 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. absinC Trapezium Area = 1 2 (a +b)h Sector Area = 1 2 r2θ Arc length = rθ Cylinder Volume = !r2h Curved surface area = 2!rh Cone Volume = 1 3!r2h Curved surface area = !rl where l = slant height Sphere Volume = 4 3!r3 Surface area = 4!r2 L3–CALCF 4 Then ( ) (*) 1 lim i b n a n i f x dx f x x →∞ = ∫ =∑ ∆. 12. 2. Before 1997, the AP Calculus questions regarding the FTC considered only a limited number of variations. 1. min. 9 0 obj Video Tutorials. on [ab,]. 5 0 obj in [ab,]. 1. sin θ+cos. Review of elementary functions, limits, differential calculus, and integral calculus. 2. θ. 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. Trigonometric Formulas . A. sin. I also decided to create one myself using after taking a Photoshop class. If f(x) is a rational function given by ( )= ( )),such that ( ) and ( have no common factors, and c … <> <> endobj Applications of Differentiation 4. 19 0 obj "Y���#0i�%Q�S��E�H6�YH2&���͑`�� RQH� �蒏`]�4!�30��` �jW ... 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AP Calculus AB Formulas & Justifications. endobj 14 0 obj <> Calculus AB Calculus BC. 9. cos(A + B) =cos. %PDF-1.6 %���� 1+tan θ=sec. 3. For a quick review check out the following helpful articles. h�bbd```b``6�� �q�d��LK�ls0� x���Ak�0����Cɒ�ƠcMa��Vv*�l����?�MF�������dB͹��˻j�c�ӧw[��\��$B��4g?��I�û�w� 37j(̨��. Includes formulas … calculus review (ab) notes Here are the notes that you will need for the AP CALCULUS exam. Arithmetic Review 2. &%�GS��&���c�k�TѰ��x�+k�~���^�iot�L�+����o���~ �`g�g�;��SKB�ֹ��������*EO�`T1nb�� �IE�1�9֔�Serعu�L�|L����劍*f��:R�_My~��^I�cu�������&X=T� Z}��3�I�Ӌ� D��1���j���@g� endobj Divide [ab,] into n subintervals of width ∆x and choose * x i from each interval. Course Overview. endobj 5. cos(−θ) =cosθ. A. max. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems. Calculus YouTube links by chapter & section.docx . Print out the DERIVATIVE RULES notes ..... this will become your new BEST FRIEND !!!! %���� 15 0 obj After about 20 hours, it is done! 2 ( ) g gf fg g f dx d ′− ′ = 4. f (g(x)) f (g(x))g (x) dx d = ′ ′ 5. x x dx d (sin ) = cos 6. x x dx d (cos ) = −sin 7. x x dx d (tan ) = sec2 8. x x dx d (cot ) = −csc2 9. x x x dx d (sec ) = sec tan 10. x x x dx d (csc ) = −csc cot 11. ex ex dx d ( ) = 12. endobj Read the Course Syllabus . stream Recommended for students typing responses. endobj AB Calculus Facts and Formulae.pdf: File Size: 2865 kb: File Type: pdf: Download File. :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�� 16 0 obj Calculus Honors Home Work.docx. 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 6 0 obj in ab, , 3. fd is the abs. 12 0 obj 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). -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. 17 0 obj Finding Absolute Extrema To find the absolute extrema of the continuous function fx on the interval ab, use the following process. 137 0 obj <>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 2. <>>> %%EOF .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 # ∫ Virtual TBA. endobj 8. x ( ) ( ) 2 32 2 6 6. 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