I also make them available for a student who wants to do focused independent study on a topic. 0000059369 00000 n { takes good notes that pay attention to detail but still give a holistic picture. h��Vmo�6�+���� (8ɼh; ɖ? Integration and Differentiation Practice Questions Age 16 to 18 Challenge Level: There are a wide variety of techniques that can be used to solve differentiation and integration problems, such as the chain rule, the product rule, the quotient rule, integration by substitution, integration by parts. 0000006437 00000 n (���%�R����z��x����G��x$��x�ˆ2�n�U�X�&Nrh �LK,�Ryᚣʃ �e�[+@��{f@D06�2 ��� k4R�k@�锵D�4ʁ�����cDx�A�Dr�\�w��~�ˆ8�����]�l�b�^f��y�zl��^�ٙ����٪&R�yU6՗p�a=��8�1)?e������A�O�_�6Y��w�{�]4ٺx���uN��gˢ\%���K���M�o~��v�͓�kWl�jG�…]8?�%���2��h�/�c[[�!�)/ڲ�G�� &I����{�o�\}<>� Dr�y���y4�a�1��$��fWU��K4I�zw >�� 0000093956 00000 n It includes six levels: Knowledge 0000105554 00000 n �f�l.�pt���+�w����My��b�_2�0���`w�nXP^�.1rr ��'��xW�0]3�x���sQ�tJo4��������c�1��(;٨��Hf�5q.���8���� ���@���cX��������f�b�6ۀ�Cr$̆�d$��ԓ �n@Jt� #Np�f��A4�� �q��,�@���KP=TG��z��|�pL��=�`�!i5:[�Y. 2 • We have seen two applications: – signal smoothing – root finding • Today we look – differentation – integration • These will form the basis for solving ODEs ��t�"|"��.��d�� @�s�ZG< ���=���΂`�3����y�x��I�v��8I�,�� ާ�h"ëh"�ߢ,���Ƴ@�Y��߂h���c�0�#�(�\D��g�z����{L`dꞿo�O9�1�c�����qy|t�χdE���� +���c�P��T�,�,߇!H��Lj�s;[����,���=����m��0"�a��(�>��jD3�1�~����Q�=�U��$�Ah��i;5i6��w|ڻxDJ\4{�dq޲�ŕ).J�v�g�&� ��OЋ�f�8�ْ�}8�5C���*���eBb ,g������*>�櫂�\rj��,H�X�WH��f��r���p��-֬u�$�"D�^��>�-'�n�O�4��iX�^� �.{�����H{�U��p៝��. Question 2 : Differentiate y = sin x + cos x. Differentiation Formulas – Here we will start introducing some of the differentiation formulas used in a calculus course. Question 9 a) If A x x= −π 2 20 , find the rate of change of A with respect to x. b) If V x x= − 2π 3, find the rate of change of V with respect to x. c) If P at bt= −2, find the rate of change of P with respect to t. d) If 1 W kh h= −6 2 , find the rate of change of W with respect to h. x��Y�n�F}7��#YT��% |M44�S�Z�-�6�ڒR��3�rI��S�x�9;{���4=y��ݔ�m����d�-��"�>=]o�뇿�W����ky{W�ۻu5���g�������ypus|Ă�� K✧���>�������?> S�=��%���� �d�iF�y ��a�����w8�pj���[�;���b @,��[z�������̖�}�n��|�8eclÆ�'p��7� �E6�\>]�b��U�}Z߀����Z�v��;8�)W� stream 0000059042 00000 n 0000005921 00000 n Solution : f(x) = x - 3 sinx. �\#q�j��B��i)����'�w=k(h�f ������x�v��>3%xx:�6��=��� It is important to remember that: A constant disappears when differentiated. 0000107425 00000 n 0000091645 00000 n 0000031360 00000 n It enables the teacher to look at instruction through the lens of challenge. registered in England (Company No 02017289) with its registered office at 26 Red Lion �fʐ��� �8YF����C0�j��� 7+J����P�L���8/+�f���=N�5�q7�w�p�ׁ�`c8 -��|pٷ;�m�)�̺��� �=�����:s:;��ř��nh�v����Q(Wt����2�Z9��{=U��LƽEH�*�c���@}fl$H��i�Z�3��J�&Hs�V��V|%�B���nW��{|o��xF�,��/������Y� 0000060017 00000 n s = 3t4 • Reduce the old power by one and use this as the new power. 0 Differentiate cos³x with respect to x. Differentiate 20x-4 + 9. {�N��Ç��Z�Y�N.8vN�F�G�Rî�N�c�26����ݫ�2a�9I�E��@F����/�)Qi7+x���II��WBN�L2��l}r�B�B� %@AW�����urX�Τ�(n�r! 0000105300 00000 n 0000002854 00000 n %�쏢 startxref A javelin is thrown so that its height, h metres, above the ground is given by the rule: h(t) = 20t-5t2 + 2, where t represents time in seconds. 0000072390 00000 n �M�̅�1��94�X�>ԥ����†a���G�� �w��M�*|4c��ۀ�j)�_��N]0;���nɋ����&�b�tf�+�Gx�:] �f�m_�l�g�s �b��l����lPc�6� 2 0 obj 0000109172 00000 n 452 0 obj <> endobj 0000032693 00000 n 0000071770 00000 n It’s adequate for a district or school leader (or professional developers) to tell or show teachers how to differentiate instruction effectively. 3631 62 0000092955 00000 n endstream endobj 456 0 obj <>stream %%EOF 1 0 obj <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Please welcome Lauren Poinier to the blog today! du 0000094109 00000 n 0000119829 00000 n 461 0 obj <>/Filter/FlateDecode/ID[<2E4C56239E86E34FBA67A222F313302C>]/Index[452 32]/Info 451 0 R/Length 60/Prev 411030/Root 453 0 R/Size 484/Type/XRef/W[1 2 1]>>stream <> Differentiation is a philosophy—a way of thinking about teaching and learning. d���uU�L�l*���2�±�U�غ�x%���&�VN���T|�' ���Pj��lŨ�؇��u$���K�XJ�bKPd�gө&���K�3�\7=/���8���� �~������K}Gj7qW�uG�#O�Хsgb 3�o�ڃl�]��z�]�"Q�we�.7����ٺ�hG%��&��i�w��i �q(�k�E�u���-)��]�d�̟��R�=���gGF{� y’ = d(20x-4)/dx + d(9)/dx. 3692 0 obj<>stream 0000109504 00000 n ���.Aq�=�9��/��st���l��ԓ;?΀�9У�I��]��Q5��{I 2��P�?��{e����1-��е�Ò��g�uZ�",{�Y�APm@c��aAm� ��jz���>pv>�g��`�1�8��ؐ�ꅄ6W��a���炦@�N֒�w�]�n����i�f�UJ�� ?-��` �¦���͞ϲ�X���u�S`� A�+�I�S�pF(��u,Q�@�5h��8�P�k�R���5(��Q�[�?��_ �����xƫN�t�R����X3�R������$�~**�+�YYC^����1��@}� Differentiate cos³x with respect to x. 0000000016 00000 n x��ko���{ �~��4w�|��I�\4@z5pr���iY�#�D�z����s(.��� d����y��W�v��}��'/^\����C�|���>�zu�����Э֛n��n^�L^_�I~�xVI��$��M^gMr�gy��KQfu��r����K����z������[Xy'!����g�`E��TI�TV%� �'+���ų��$�5���ų� ��}�&I�> ����\'�!F#�I��j She's sharing with us her questioning strategies for differentiating instruction and reaching all learners in the classroom. Square 0000108108 00000 n endstream endobj startxref 0000121239 00000 n v���~3N)�a� ���A�@3C cT��"|n_��eTc�`��1a����KKj��2�D�ie� �0�/��� d�1�:q�B�$ ��� Solution: y = 20x-4 + 9. y’ = d(20x-4 + 9)/dx. 0000006073 00000 n 0000032823 00000 n Using the derivatives we just found for u and v gives: Sign in|Recent Site Activity|Report Abuse|Print Page|Powered By Google Sites. Differentiation Formulas – Here we will start introducing some of the differentiation formulas used in a calculus course. ... (12) Differentiation.pdf (13) Integration.pdf (14) Kinematics.pdf (1) Simultaneous, Quadrilaterals and Inequalities (Ans).pdf (2) Surds and Indices (Ans).pdf 0000106170 00000 n x�b```b``�b`c`�x� Ȁ �@1v����40���a>��Q9쀃��� �����;*m0�`�#w��6�f�f�?���\Գv��m�8�n ��-�X|��a"q�����*"���;".noQp������ ��(�ps�? endstream endobj 3691 0 obj<>/Size 3631/Type/XRef>>stream <<76CEE4E94BB2CC4E86DED353515D6867>]>> 0000107957 00000 n Examples. <> 9}��7�n`YOrz�!�j����͞խ�2F��c��Ny3��ʂ����S���dP�)t��<1�T <>>> Product and Quotient Rule – In this section we will took at differentiating products and quotients of functions. x��]ˎ-�q܏�,� 0000106879 00000 n London WC1R 4HQ. 0000110595 00000 n Using the rule for differentiation dy/dx = anx 0-1 = a (0)x-1 = 0 The constant disappears when integrated. 0000120444 00000 n The most challenging questions from the various top school mathematics preliminary examinations were collected, adapted and compiled topically into these legendary sets of question papers. p������ܤF����p�ָh\0�G˃�*:�5��8��g�8a����\����wk�t���F��A� ,�j/W7�ֱ(��Re�{o��W�-�ό^�%x?�I��=$`,Z���1,R���� �T����9{�B��T���p�6�&ʏ�Ըְ��N%K�@]�,a�(Y�vE��V]H9ʌ�όjJf��`��i_�q�9&-���[�_P��T��}�?׃2t_��(M�$%p�ب�֜G%Bw�D�^���� �@�,�^њ��S�x���Q���}B��V�x�n��b�s�%���,a��,��,�س,q*�g)��W�w�2�` D=�

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