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- 1.9 The binomial theorem.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Pascal's Triangle Get to know this famous number pattern with some revealing learning activities
- Binomial Theorem Video You may have learnt about the binomial expansion in class some time ago so here's a reminder to bring you up to speed.
- Binomial Theorem Exercises in the process of expanding powers of binomial expressions and finding specific coefficients.

Here are some exam-style questions on this topic:

- "
*If \((x+5)^{10}\) is expanded*" ... more - "
*If \((2x+7)^{6}\) is expanded*" ... more - "
*If you expanded \((2x-3)^{15}\), the term containing \(x^6\) can be written as \(\binom{15}{a}\times(2x)^b\times(-3)^c\)*" ... more - "
*In the expansion of \( (x+j)^{9}\) where \(j \in \mathbb{R}\), the coefficient of the term in \(x^7\) is 144.*" ... more - "
*The constant term in the expansion of \(x^4(2x^2+\frac{m}{x})^7\) is 896*" ... more - "
*Consider the expansion of \( (3x+ \frac{c}{x})^8\) where \( c \gt 0 \).*" ... more - "
*Consider the expansion of \( (7-x^2)^{n-1}\) where \(n \in \mathbb{Z}^+\).*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- Probability Probability is a measure of the weight of evidence, and is arrived at through reasoning and inference. In simple terms it is a measure or estimation of likelihood of the occurrence of an event. The word probability comes from the Latin word probabilitas which is a measure of the authority of a witness in a legal case. Some of the earlier mathematical studies of probability were motivated by the desire to be more profitable when gambling. Today however the practical uses of probability theory go far beyond gambling and are used in many aspects of modern life. We believe that even adults can, in many cases, have a poor intuition regarding the effects of probability. These activities are designed to help pupils calculate but also get a 'feel' for the principles of probability.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.