Exam questions recurrence relationships examsolutions. Higher mathematics psfrag replacements o x y recurrence relations objective 1 1. Page 59 hsn21400 recurrence relations another way to define a sequence is with a recurrence relation. Determine if the following recurrence relations are linear homogeneous recurrence relations with constant coefficients. Set out in stages of try then check the worked solution to each part of the question. Linear recurrence relation can be written in the form. Given that the limit of the sequence is 27, find the value of k. Given a recurrence relation for a sequence with initial conditions. The two equations above mean exactly the same thing. Series expansion for general solution of 2nd order linear differential higher maths past papers and answers. Discrete mathematics recurrence relation in this chapter, we will discuss how recursive techniques can derive sequences and be used for solving counting problems. This is a practice set based on the actual format of the question met in the assessment. Discrete mathematics recurrence relations 523 examples and nonexamples i which of these are linear homogenous recurrence relations with constant coe cients. The site is still under development and will be updated on a regular basis.
Discrete mathematics recurrence relation tutorialspoint. Higher skills list number algebra continued algebra. Past papers should be used towards the end of the course to give yourself practice of various topics. Limits sequences higher maths revision bbc bitesize. Recurrence relations section a revision section this section will help you revise previous learning which is required in this topic.
A in higher, we will deal with recurrence relations of the form. Higher past papers this page has lots of resources for studying higher maths. We would like to show you a description here but the site wont allow us. Provides information on the performance of candidates which is useful to teachers, lecturers and assessors in their preparation of candidates for future assessment. Higher mathematics psfrag replacements o x y recurrence rel. If both sequences have the same limit, express p in term of q. Fp1 proof by induction for recurrence relations how to find sum to infinity of recurrence relationships alevel maths. A recurrence relationship is defined as u n 1 au n b. Higher mathematics course overview and resources sqa. Notice that the limit is not dependent on the value of or. A nab national assessment bank is provided by the sqa as a test of questions based at level c and is the minimum competence, in other words has to be passed by each candidate in order for them to sit the final examination.
To ensure your success in 202021 there is a wealth of fantastic additional n5 maths exam focused resources for less than the cost of a text book. Powered by create your own unique website with customizable templates. Jul 09, 2012 test 4 out of 14 on recurrence relations for unit 1 of the higher mathematics course objective and extended questions. A recurrence relation is an equation that uses recursion to relate terms in a sequence or elements in an array. Higher test 4 recurrence relations teaching resources. Instructional exercise for outcome 4 of the sqa higher mathematics unit 1 assessment. Attached is a ppt i made for my year 11s to introduce them to recurrence relation notation that is in the new gcses. Past papers unit 1 outcome 4 multiple choice questions each correct answer in this section is worth two marks. Higher mathematics unit 1 official mathematics revision. Recurrence relations objective 1 dornoch mathematics.
R1 i have revised percentage appreciation and depreciation questions using real life examples. It is a way to define a sequence or array in terms of itself. Higher practice papers hillhead larbert youtube videos. Make yn the subject of the above recurrence formula. The format of the external examination has varied over the years but the content has remained consistent. Includes some simple examples and some questions for them to try in their books. Includes some simple examples and some questions for. Sep 02, 20 instructional exercise for outcome 4 of the sqa higher mathematics unit 1 assessment. Recurrence relations have applications in many areas of mathematics. Recurrence relations after these four outcomes candidates are then ready to sit their nab. Jan 15, 20 instructional exercise consisting of question 3 from paper 2 of the 2011 sqa higher mathematics exam. Recurrence relationsharder sequences for new gcse teaching. Learn how to create and use recurrence relations to find nextprevious terms, missing coefficients and its limit for higher maths. A linear recurrence relation is defined by or the above relation tends to a limit as, if and only if to find the limit we use the formula.
Design and interpret mathematical models of situations involving recurrence relations. Recurrence relations solving linear recurrence relations divideandconquer rrs recurrence relations recurrence relations a recurrence relation for the sequence fa ngis an equation that expresses a n in terms of one or more of the previous terms a 0. Sep 25, 2016 attached is a ppt i made for my year 11s to introduce them to recurrence relation notation that is in the new gcses. To properly define a sequence using a recurrence relation, we must specify the initial value. From session 201819, the higher mathematics exam will be extended in length. This website is primarily a free maths resource for pupils, adult learners, parents and teachers. Browse other questions tagged recurrence relations or ask your own question. All help appreciated, if you can only answer one part but not the other, thats still fine, i would prefer it if all parts are answered though. Higher test 4 recurrence relations test 4 out of 14 on recurrence relations for unit 1 of the higher mathematics course objective and extended questions. The higher mathematics course is assessed by means of an external exam completed in the may diet of sqa examinations. This is a rule which defines each term of a sequence using previous terms. It often happens that, in studying a sequence of numbers an, a connection between an and an. A recurrence relation describes a sequence in which each term is a function of previous terms. Discrete mathematics recurrences saad mneimneh 1 what is a recurrence.
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