hsn higher maths sequences

0000038425 00000 n endstream endobj 575 0 obj <. Higher Mathematics Functions and Graphs . a. and . endstream endobj startxref Free Higher Maths HSN Theory Guides. – Thank you. 0000038580 00000 n 0000011960 00000 n For example: u u n +1 = + n 2, u 0 =4. Unit 1 Summary. This is a standard argument, but not necessarily obvious at first sight, and proceeds as follows. hsn.uk.net. a, a + d , … Thanks to the SQA for making the excellent resources below freely available. Course Summary. 164 0 obj <>stream All videos can be found at www.m4ths.com and www.astarmaths.comThese videos were donated to the channel by Steve Blades of maths247 'fame'. 0000011367 00000 n 623 0 obj <>stream Sequences. Vectors. Mathematics. Exponentials & Logs – Videos, Theory, Mind Maps & Worksheets. Advanced Higher Notes (Unit 3) Further Sequences and Series M Patel (April 2012) 6 St. Machar Academy As the original series converges, it remains to show that 1 1 ( 1) n n n ∞ + = ∑− diverges. Higher Mathematics Unit 2 – Integration hsn.uk.net Page 95 HSN22200 4 Definite Integrals If F x( ) is an integral of f x( ), then we define: ∫b ( ) ( )= = −[ ]b ( ) ( ) a a f x dx F x F b F a where a and b are called the limits of the integral. xref Karen – March 2018 Search for: Search. Two sequences are generated by the recurrence relations un+1 = aun+10 and vn+1 = a 2v n+16. Past Paper Question Breakdown by topic. Stated simply: Work out the integral as normal, leaving out the constant of integration. A sequence is defined by the recurrence relation u ku kn n+1 = + 2 and the first term is u0. PLP PLP-for-Higher Maths. Online tests. ��d��)�yF� ��T�u�RE[��v��ﭷ�Zo��$9��{{��p9^�p�ܹ��lX���)�A�Cb㳒"�=��R\v��)��t��N75�ӌӯ�=��y��ͷ�MM�'��]��,�]��K|��,�,&5*�7T��!%:5=-5=236f��gII�!��2|Cb3b��7_�⛐�雙��X��s�臃q8S��8�a��g9��f.�:'�đsz8?ppӹw_ Study at Advanced Higher Maths level will provide excellent preparation for your studies when at university. Straight Lines. 7 [SQA] 47. Free Higher Maths notes. 2001 Paper : 2001 Solutions. %PDF-1.5 %�� 4. So easy just to direct students to your amazing site! In maths, a sequence is an ordered set of numbers. 2002 Paper : 2002 Solutions. 0000031330 00000 n Notes covering the new Curriculum for Excellence Higher Mathematics course. %%EOF 0000037723 00000 n To properly define a sequence using a recurrence relation, we must specify the initial value . Page 2 CfE Edition . Having topic by topic past paper questions, HSN notes and SQA papers all on one site is wonderful. i�+�� cS'>�^�m��c�0פO'ݝ�`��e�˕S�)[�tO]5�|�#��VM�?�j�،��|��x 0000038062 00000 n Note . Free Higher Maths Essential Skills. of order one. -��+�C��.T��襟�kc��"c'��K.��G8�L�l��-0fxE[��8��~Xk!�I X*�̐�J9֝ C�/ 0000002846 00000 n Higher Maths SQA Past & Practice Papers. Trigonometry. Differentiation – Videos, Theory, Mind Maps & Worksheets. %%EOF For example $1,5,9,13,17$.. For this sequence, the rule is add four. Recurrence Relations Sequences based on recurrence relations. 0 Study at Advanced Higher Maths level will provide excellent preparation for your studies when at university. The nth term is given by an d+−(1). is a geometric sequence. Polynomials and Quadratics. New Higher. 0000031839 00000 n Solutions for Higher Maths exams from 2006 to 2013. Circles – Videos, Theory, Mind Maps & Worksheets. ��pP�p��:��)��R�~�7P��tuE��8߄p��˾�� ;��24��4@�kiz�W�)u��xXQ�.�nJ��Rf� P�]�qk�ws�#��͊�N��jYZ��852 lH��l�X�Ɋ��_�6�]�O+��=Ҭ��V �ľ�Q6�y�6��㏞F��^�v��mZ�|h�K9��ihB��q$�̰��Uɓ��$��$Նp��j�I�6x2��F"sIy��ȎQ?`�`��_��\� ِˁ��Zq��oMM\��_��{�w�^z��bg{�P�Bg�J]s�P�S�l�%i��o8��M�x骩��p��,d��A��R�x��HW��.q�=��Դ� Higher Maths. ��q�Ly�p �Q�Zma?x ��w Firstly, as you will be aware if you read the blogs on factorising quadratic expressions ( foundation tier and higher tier ), quadratics are expressions in which the highest power of x is an x 2 term. hsn.uk.net. Content Answer U3 OC1 (a) 3 C CR G16 1992 P2 Q2 (b) 2 C CR G16 (c) 3 C CR G27 (d) 5 C CR G28 hsn.uk.net Page 4 Questions marked ‘[SQA]’ c SQA All others c Higher Still Notes These are called . Proof by Contrapositive Welcome to advancedhighermaths.co.uk A sound understanding of Proof by Contrapositive is essential to ensure exam success. 0000018727 00000 n %PDF-1.4 %�� trailer h�b```�� cc`a�q��a�� ,�_˫�f; �uR��,$�V�1)��Ԉ_�� ?r42o�Ȩ�Xy+~K�T�KA��Y�t��v*�eI��2m��˰�7,�.�݋2�%�C]'͛r~��ׅ�3�tmlty��_g��Ұ��s��jG ��!�o 0000000976 00000 n Other useful resources: Past Paper Solutions from 2006 to 2013; Online tests Writing out the last series mentioned, 1 + 1 2 + 1 3 Integration. Circles. 0000028354 00000 n Differentiation. Unit 1 Specimen NAB Assessment. b귩��Vq 0000027413 00000 n 4 (b) Hence ﬁnd the value of t, where 0 ≤ t≤ 2, for which Zt 0 (3cosx+5sinx) dx= 3. 0000033294 00000 n u au b. nn +1 = + where . Please find below: 1. 0000002548 00000 n endstream endobj 132 0 obj <> endobj 133 0 obj <> endobj 134 0 obj <>/Font<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 135 0 obj <> endobj 136 0 obj <> endobj 137 0 obj <> endobj 138 0 obj [/ICCBased 163 0 R] endobj 139 0 obj <>stream Functions and Graphs. Another way to define a sequence is with a . b. are any real numbers and . Calculate the values of Rand a. 131 34 Free Heinemann Text Book Worked Solutions. Determining a recurrence relation from given information and using it to calculate a required term 0000028721 00000 n recurrence relation. Practice multiple choice questions with instant feedback. Higher Maths Theory Guides Thanks to HSN for making the excellent Higher Maths Theory Guides freely available for all to use. 4. EXAMPLES . ... Sequences. . Advanced Higher Mathematics Course Summary hsn.uk.net Page 5 HSN21000 Sequences and Series 1 Arithmetic Sequences An arithmetic sequence has the form aa da da d,,2,3,+ ++K where a is the first term and d is the common difference. 0000004097 00000 n 0000002688 00000 n 1. 0000018649 00000 n Determine the value of aand evaluate the limit. Given that the limit of the sequence is 27, find the value of k. The limit is given by 2 1 1 b k a k = − −, and so ( ) 27 29 2 27 1 27 1 2 29 27. k k k k k k = − − = = = Some universities may require you to gain a … Continue reading → 0000033821 00000 n Higher Mathematics Sequences . ``0� FA%e��h`RR/��BJJ�0I�{��R�� 9��c�&)ƻ�@Z��6e�g��!u��̩L|�djx'��:Ao��_0+�:�~`��4?�,��z�ę�Զh1pH0�G��6�� Restrictions on the Domain The domain is the set of all possible inputs to a function, so it must be possible to evaluate the function for any element of the domain. h�|X TS�N��ը��9��ֶ�֡�Z�� 'fDF! 1. Quadratic sequences (higher tier only) This is the most difficult type of sequence you will see in GCSE maths. Arithmetic Sequences An arithmetic sequence has the form. (a) The expression 3sinx−5cosxcan be written in the form Rsin(x+a) where R> 0 and 0 ≤ a< 2π. 0000002463 00000 n 0. 131 0 obj <> endobj 0000004718 00000 n )� ��N��l�'��.9� �� &{��RX0�"{~ewk�ꡡ�ư��B�3��"��Fc�i�`t�h��č�qa ��${��=��7��H,��($)��B@��1��8>��Ŀ��!�h�آ~n��n�ѷ��uȑ�bo��0Ƅ�魆��S0^�_��ݻ�H�*��X2 z��'�5��К�u��t�B^��}��"��,�Q�e��l��4��: Higher Mathematics 46. Buy the books direcly from us! A In Higher, we will deal with recurrence relations of the form . >. Advanced Higher Notes (Unit 2) Sequences and Series M Patel (April 2012) 8 St. Machar Academy Geometric Sequences and Series Definition: A geometric sequence is one in which the ratio (aka common ratio r ) of any 2 successive terms is the same, r def = n1 n u u + Example 13 Verify that 3, 6, 12, 24, 48, . We hope you find this website useful and wish you the very best of success with your Higher Maths course in 2021. <<933B2D16E304BF439DEBAFB294BEEC38>]>> . says “the first term () u 0 is 4, and each other term is 2 more than the previous 0000033218 00000 n 0 ... Sequences, Rem Theorem & Integration BP14 Trig, Diff, RR & Integration ... HSN Queen Anne High School Millburn Academy. Free Higher Maths Videos & Worksheets. Higher Maths Resources. Higher Mathematics Unit 1 – Sequences hsn.uk.net Page 60 HSN21400 2 Linear Recurrence Relations In Higher, we will deal with recurrence relations of the form u au bn n+1 = + where a and b are any real numbers and u0 is specified. For teachers. xڜUkPWބ�HBx6hAc�! New Higher. 0000018039 00000 n 0000000016 00000 n Sequences & Series Welcome to advancedhighermaths.co.uk A sound understanding of Sequences & Series is essential to ensure exam success. hsn.uk.net. 0000011716 00000 n Part Marks Level Calc. Higher Mathematics Unit 1 – Sequences hsn.uk.net Page 63 HSN21400 2. 0000017621 00000 n 0000032911 00000 n The two sequences approach the same limit as n→ ∞. 2. (08Mp��6� ��R�:��『6k�e�J��Q��:j��Z;ڎ2A�}U��8ӻ�("��o��=�;��Y�� p}�7�A� ��-��7�q��nd�s D_ �,B��x'rpF�o�U��,��1�48�L?z�XWU��u��n!h�~��#�į�;�j�c,Zع�.�s�]e��5��.z��V�68Ɍ��ܣ��y��?ԣ�� W�Q�j�e�z�] �Q� 574 0 obj <> endobj Formulae List (Exam) Formulae used in the course. 0000027974 00000 n 0000004755 00000 n Revision Resources Higher-Revision-Pack-1 Higher-Revision-Pack-2. These are called linear recurrence relations of order one. 0. is specified. 0000003473 00000 n ��@Z��I�H�KA�ʘ�ɷ�� t 2004 Paper : 2004 Solutions. Exponentials and Logarithms. Higher Mathematics [SQA] 7. 0000010927 00000 n Later we will see that integration is a useful tool for evaluating areas and solving a special type of equation. I��V��2Z��Q;�s;��n��+6��Y��>�B��X- ��&g��֊@6o��1��:g�U ��=ԉtQy%�Y���64\]0#ye�e��з��k�� Note To properly define a sequence using a recurrence relation, we must specify the initial … 2. Higher Mathematics recurrencelimits [SQA] 1. T��/jK��/�4�er��"qZYK'_�ҶY�ge�o��X��ۉJ��s�M�*a�I��a�v:�¿G�Z��v�+@��9:IE�'�W��g�̠��*��k C�*��! Recurrence Relations . 3. Higher Mathematics Unit 1 – Straight Lines hsn.uk.net Page 4 HSN21100 3 Gradients Consider a straight line passing through the points (x y1 1,) and (x y2 2,): The gradient m of the line through (x y1 1,) and (x y2 2,) is 2 1 1 2 2 1 change in vertical height for change in horizontal distance y y m x x x x − = = ≠ −. Some universities may require you to gain a … Continue reading → 605 0 obj <>/Filter/FlateDecode/ID[<71B48A02B318EB47848B9ED0153BEB74><34F03517BEFC904F956E5850B570CAA0>]/Index[574 50]/Info 573 0 R/Length 130/Prev 151290/Root 575 0 R/Size 624/Type/XRef/W[1 2 1]>>stream startxref u. 2 Geometric Sequences A geometric sequence has the form aarar ar,, , ,23K Just a HUGE thank you from me – I’ve been teaching Higher Maths for about 20 years and your site has made this so much easier. Also, since 2 1 2 1 Opposite tan HSN extra provides resources exclusively for teachers. 0000018413 00000 n 5 Part Marks Level Calc. Holy Cross Hamilton Tweets by @@holycrossham. Click HERE for all available Online Maths Courses. 0000032628 00000 n u. $��$䀄�^ �tH�� )�A�E�H��0012��HM�?�� t� hsn.uk.net Page 3 CfE Edition . 2 Linear Recurrence Relations . This is a rule which defines each term of a sequence using previous terms. ... Advanced Higher Mathematics. Sequences and Series 1. We are free to choose the domain, provided that the function is defined for all elements in it. Higher Mathematics Unit 2 – Integration hsn.uk.net Page 89 HSN22000 OUTCOME 2 Integration 1 Indefinite Integrals In integration, our aim is to “undo” the process of differentiation. h�bbd``b`~ $W ��@�- ĺ"��x ��D�)��f��[A�*�"�@�) �( �` Advanced Higher. These will prove a fantastic resource in helping you consolidate your understanding of Higher Maths. linear recurrence relations. Old Higher: Unit 2. 2003 Paper : 2003 Solutions.

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