1 / 12

Example of a past paper question (June 12): 1) Why is this a Binomial Expansion question?

C4 – Algebra(Ch 7): Binomial Expansion. Example of a past paper question (June 12): 1) Why is this a Binomial Expansion question? 2) Do you spot something which is new compared to C1?. C4 – Algebra(Ch 7): Binomial Expansion. Crucial point to be successful in this topic:

merton
Download Presentation

Example of a past paper question (June 12): 1) Why is this a Binomial Expansion question?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. C4 – Algebra(Ch 7): Binomial Expansion Example of a past paper question (June 12): 1) Why is this a Binomial Expansion question? 2) Do you spot something which is new compared to C1?

  2. C4 – Algebra(Ch 7): Binomial Expansion Crucial point to be successful in this topic: • Binomial expansion knowledge from C1 • Great care required when dealing with fractions, signs • Make sure that you know the validity of your expansion

  3. C4 – Algebra(Ch 7): Binomial Expansion In AS we dealt with the binomial expansions with n In A2 we deal with binomial expansions with n is any real number! • ....BUT – there are two important differences to note when n : • The series is infinite (i.e. Non-terminating) and we only use a certain number of terms as approximation • The expansion of (1+x)n is only valid if

  4. C4 – Algebra(Ch 7): Binomial Expansion Example 1: 1) Expand (1 + x) -3 up to the term x3. 2) state the values of x for which the expansion is valid. -> answer

  5. C4 – Algebra(Ch 7): Binomial Expansion Example: 1) Expand (1 + x) -3 up to the term x3. 2) state the values of x for which the expansion is valid. Solution: 1) 2)

  6. C4 – Algebra(Ch 7): Binomial Expansion Example 2: Find the first four terms in the binomial expansion State the set of values of x for which the expansion is valid.

  7. C4 – Algebra(Ch 7): Binomial Expansion Example 2: Find the first four terms in the binomial expansion State the set of values of x for which the expansion is valid. Ex 7A: Q1 :a – c on examples i) – iv), Q2

  8. C4 – Algebra(Ch 7): Binomial Expansion What’s the problem ?: Find the first four terms in the binomial expansion (4 + x)1/2

  9. C4 – Algebra(Ch 7): Binomial Expansion Sometimes we need to use a Binomial Expansion to approximate expressions like(a + x)n. In order to use our formula we needto take a outside the brackets: This expansion is hence valid for

  10. C4 – Algebra(Ch 7): Binomial Expansion Example Binomial Expansion of form (a + x)n: Find the first four terms in the binomial expansion Valid for ?

  11. C4 – Algebra(Ch 7): Binomial Expansion Why bother? • Historically, the Binomial series has been used to approximate calculations w/o calculator – the more terms you calculate the better the approximation.(try √2 as (1+1)^1/2) • A series can only be used to approximate if the terms decrease • When І x І < 1, the magnitude of x, x2, x3, x4, ... Form a decreasing geometric sequence • Hence, the expansion of (1+x)n is only valid if І x І < 1.

  12. Homework (due Tue, 24/09): • Ex 7A: Q1 :a – d on examples i) – iv) + Q3,4, 5*, 6* • -> warning: your homework may include questions like • Use ICT resources: • DESMOS to plot the graph • Wolframalpha to get more terms of the series and see how it changes the approximation • This is homework for two lessons (there is no lesson on Friday 20th!)

More Related