They range from a request to define n to noticing features of the sequences. These are the questions and observations of a year 9 mixed attainment class. The differences are made up of three consecutive whole numbers in the following pattern:Īs there are two rules to generate the intersecting sequence, there is no single expression for the nth term. This time there are three spaces from one even number to the next. The differences between the pairs of even numbers increase by 12 each time. This could be represented in the following way (where the terms in the sequence are in bold text):Įven (the difference is even) even (the difference is 1 more than the difference before and is, therefore, odd) odd (+2) odd (+3) even (+4) even This means that the differences between the even terms increase by four each time because, firstly, the difference between the terms in in the quadratic sequence increase by one each time and, secondly, there are four spaces from the middle of one pair to the middle of the next. They appear in pairs, each followed by a pair of odd terms. The even numbers in the quadratic sequence form the 'intersecting' sequence. She analysed the mathematical structure of the sequence formed from the common terms. An example comes from a year 9 student who looked at the two sequences below during an online inquiry. One line of inquiry follows the main line of the intersecting sequences prompt. By testing different cases, they come to associate the square with differences that increase (or decrease) by the same amount. In the prompt, students might speculate that there is a link between the constant in the nth term of the quadratic sequence and the fact that the differences between the terms increase by two each time. The terms in the quadratic sequence appear in the linear sequence with an increasing number of terms between them - one number between the first two terms, then two between the second and third, three between the third and the fourth and so on. The prompt contains similar nth terms to draw out features that are the same and different and to address misconceptions, such as 2 n = n 2. It was designed to follow on from the intersecting sequences prompt as a bridge to quadratic sequences later in a scheme of learning. Oxbridge Entrance Help The Ultimate Study Tool For A Level MathsĪlthough the following questions are predominantly from the OCR, OCR MEI and Edexcel exam boards, they are suitable practice for all UK A Level Maths qualifications unless otherwise stated.The prompt links the concepts of linear and quadratic sequences.How To Revise A Level Maths and Further Maths.Bridging the Gap between GCSE and A Level.Cambridge International A Level Maths Exam Papers.Cambridge International A Level Questions By Topic.About the Cambridge International A-Level.How An A Level Maths Tutor Can Help A Student Who Has Fallen Behind.Things To Look For in an A Level Maths Tutor.Finding an A Level Maths Tutor Who Matches Your Needs.Purchase Access to Recordings and Resources (£50).About AS (Year 1) Maths Revision Course.AS Maths (Year 1) Consolidation Course 2021.A Level Further Maths Easter Revision Course 2021.Purchase Access To Recordings and Resources (£50).A Level Maths Easter Revision Course 2021.
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