<> endobj endobj B. <>/Font<>>>/BBox[ 0 0 83.943 37.009] /Matrix[ 0.85772 0 0 1.9455 0 0] /Filter/FlateDecode/Length 274>> %PDF-1.5 calculus review (ab) notes Here are the notes that you will need for the AP CALCULUS exam. Traditional Algebra Review (ACT) 3. Arithmetic Review 2. min. 137 0 obj <>stream So it’s really important to do well on the test if you want a jump start on your college career. AP Calculus AB Formulas & Justifications. <> endobj endobj :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�� 4. θ. sin(−θ) =−sinθ. First and foremost, you must be you must know arithmetic, algebra, and trigonometry inside-out. B. The AP Calculus AB exam is a 3 hour and 15 minute standardized test. endobj A. 2. 2 0 obj Finding Absolute Extrema To find the absolute extrema of the continuous function fx on the interval ab, use the following process. 3 0 obj Techniques of Integration 4. Trigonometric Identities Once you have mastered those fundamental topics of mathematics, you can then build your expertise in calculus. 1 0 obj <> 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 ab, then there exist numbers c and d so that, 1.,acd b , 2. fc is the abs. n���I0���y�mdW����b=����;���^�`���"�z� ��z*�A�|�U�ȴZ�&m�%���s.�u�����Fm��\>��>�1I0���s�~���Pa:���v(&��v�s? A. cos. B +sin. Elaine Cheong’s Calc AB Study Guide. 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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: Calculus YouTube links by chapter & section.docx . To find these, simply Google "AP Calculus AB formula sheet" and look at your options. Required. 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. AB Calculus Facts and Formulae 2. Calculus Honors Year at a Glance.docx Calculus AB Year at a Glance.docx . 5�J�%)�"]Xel�S ) A. sin. This 20 page PDF Calculus guide is a great study resource. ¨¸ ©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 2. Before 1997, the AP Calculus questions regarding the FTC considered only a limited number of variations. <> Required. After about 20 hours, it is done! Easily printable. 14 0 obj <> b a f xdx Fb Fa, where F(x) is any antiderivative of f(x). 5. cos(−θ) =cosθ. endobj In general, any formula you use regularly in class is a good one to memorize. <> <> Video Tutorials. AP Calc AB; Welcome to AP Calculus AB! <> <> endobj A high score (4-5) typically qualifies you to receive college credit or equivalency for one full semester of calculus. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems. If f(x) is a rational function given by ( )= ( ) ( )),such that ( ) and ( have no common factors, and c is a real 2. θ. Home Work. 9. cos(A + B) =cos. additional resources, including a PowerPoint version, a Word document in color, as well as AP Calculus BC topics on his website. in ab, , 3. fd is the abs. .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 # ∫ -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. endstream %%EOF in [ab,]. Anti-Derivative : An anti-derivative of f x( ) is a function, Fx( ), such that F x f x′( )= ( ). Calculus Summary Formulas Differentiation Formulas 1. endobj endobj ����H;��֚���QƝ��Vm��3�����7��ΪB�!�+�g;�uOf$J��=��2�����$��� 36 6. h�b```f`` Calculus AB Home Work.docx . 8 0 obj Fundamental Theorem of Calculus: ' x a d F xftdtfx dx where f t is a continuous function on [a, x]. Trigonometric Formulas . Review of elementary functions, limits, differential calculus, and integral calculus. 6 0 obj endstream endobj 10. cos(A − B) =cos. 11. sin2θ=2sinθcosθ. 19 0 obj Calculus Reference Sheets. 1+tan θ=sec. Applications of Integration Professor: Dr. Mohammad Shakil C0-Author: Jeongmin Correa Mathematics Department endobj Limits and Derivatives 2. x�}Q�N1�#���$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 $� AP Calculus AB/BC Formula and Concept Cheat Sheet Limit of a Continuous Function If f(x) is a continuous function for all real numbers, then ) lim Limits of Rational Functions A. It is 2 pages 81/2" x 11" in color in .pdf format. A. cos. B −sin. 11 0 obj (xn) = nxn−1 dx d 17. dx du dx dy dx dy = × Chain Rule 2. fg fg gf dx d ( ) = ′+ ′ 3. 8. x ( ) ( ) 2 32 2 6 6. 4 0 obj ! "Y���#0i�%Q�S��E�H6�YH2&���͑`�� RQH� �蒏`]�4!�30��` �jW Calculus AB Calculus BC. <>/Font<>>>/BBox[ 0 0 77.947 38.009] /Matrix[ 0.9237 0 0 1.8943 0 0] /Filter/FlateDecode/Length 288>> Course Overview. 7 0 obj 3. Riemann Sums: 11 nn ii ii ca c a 111 nnn ii i i iii ab a b 1 lim ( ) b n n a i f xdx f a i x x n b a x 1 1 n i n 1 (1) Calculus Formula Sheets.pdf . 7. sin(A + B) =sin. Fundamental Theorem of Calculus Divide [ab,] into n subintervals of width ∆x and choose * x i from each interval. AP Calculus AB Cram Sheet Definition of the Derivative Function: f ' (x) = limh 0 ccccccccccccccccf+x h/ccccccccccccccc f+x/ h Definition of Derivative at a Point: f ' (a) = limh 0 ccccccccccccccccf+a h/ cccccccccccccf+a/ h (note: the first definition results in a function, the … �#������(d˸)���JWJ(hIMު�>�|�S= 6. tan(−θ) =−tanθ. 1 Limits at Infinity: To find lim ( ) x. f x. think Top Heavy ⇒limit is ±∞ Bottom Heavy ⇒limit is 0 Equal ⇒limit is ratio of coefficients. 20 0 obj stream Basic Properties and Formulas If fx( ) and gx( ) are differentiable functions (the derivative exists), c and n are any real numbers, 1. AP Calculus AB is an introductory college-level calculus course. [ 18 0 R] endobj For a quick review check out the following helpful articles. !NY�]��`���>��'ĕ��03m =R\�&��'0� #R�=�4Fꂍb#c�G0�Q�`C����mÖ��5 X�������K�&0�g3��>y3�ԃ.�7��c-pj�M������ഐ��h{�p�}S�p�L��]�G��D���aI�U+*6��>���Y���mH(D��5��c�c�=�!�l���r��O���x��� ��9����8�eA�O�m�>d�����l���N|���.l���W��݀�R�C?��PRO^��|��C���QN�ި���؆p ����,��ئq|�5$��ñd�l[��%����)g\��������~�p�6� stream Final Notes . 12. endobj If f(x) is a rational function given by ( )= ( )),such that ( ) and ( have no common factors, and c … 13. θ. θ θ θ cot 1 cos sin Summary of Derivative Techniques 3. 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 OneNote will be used for all course materials, including daily agendas, notes, worksheets, assignments, and answer keys. AP CAL AB Reference Sheet.pdf ... [ab,], 3. fd( ) is the abs. 1. sin θ+cos. I have my students make formula sheet(s) for use during the AP Exam Review Period. 1+cot θ=csc. 10 0 obj Calculus Honors Home Work.docx. Classics Summary. ��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�/� 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 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 18 0 obj 2. Recommended for students typing responses. 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 . 2. θ=1. 8. sin(A−B) =sin AcosB −sin Bcos. 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���������߰^� 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. I also decided to create one myself using after taking a Photoshop class. 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 endobj Here you will find the following in this order: 1. 3 1 3 9. x x x − − − − = = − 1 ( ) 1. Central Bucks High School East. h�bbd```b``6�� �q�d��LK�ls0� Then ( ) (*) 1 lim i b n a n i f x dx f x x →∞ = ∫ =∑ ∆. appeared in both the multiple-choice and free-response sections of the AP Calculus Exam for many years. 1. Includes formulas … 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). Integrals 5. x���Ak�0����Cɒ�ƠcMa��Vv*�l����?�MF�������dB��˻j�c�ӧw[��\��$B��4g?��I�û�w� 37j(̨��. endobj <>>> Java Quick Reference (.pdf/378.99 KB) Permitted. endobj %���� 2. θ. Print out the DERIVATIVE RULES notes ..... this will become your new BEST FRIEND !!!! on [ab,]. <>/XObject<>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> endobj stream Virtual TBA. Interactive Development Environment (IDE) or compiler; Statistics . Our Textbook as a PDF file . 5 0 obj Finding Absolute Extrema To find the absolute extrema of the continuous B. cos. A. max. endstream endobj startxref endobj AP Calculus students need to understand this theorem using a variety of approaches and problem-solving techniques. Calculator; Computer Science A. 16 0 obj <> <> 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. A. cos. B +sin. 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