Cambridge Maths Academy

Pure mathematics Year 2 Table of contents Edexcel P2 Ch1 Mixed exercise 1 1. Edexcel P2 Ch1 Mixed exercise 1 Question 1. (E/P) Prove by contradiction that $ \sqrt{ \frac12 }$ is an irrational number. [5 marks] (Edexcel 2017 Specifications, P2 Ch1 Mixed exercise 1 Q1.) Solution. Question 2. (P) Prove that if $q^2$ is an irrational number then $q$ is an irrational number. (Edexcel 2017 Specificati..

Pure mathematics Year 2 Table of contents Partial fractions Examples Edexcel P2 Ch1 Exercise 1D 1. Partial fractions In the previous section, P2 §1.2 Algebraic fractions, we learnt how to add and subtract two (or more) fractions, e.g. $$ \frac{2}{x+3} - \frac{1}{x+1} = \frac{x-1}{(x+3)(x+1)} $$ Now, we can perform the reverse. In other words, a single fraction with two distinct linear factors in..

Pure mathematics Year 2 Table of contents Algebraic fractions Multiplication Division Edexcel P2 Ch1 Exercise 1B Addition and subtraction Edexcel P2 Ch1 Exercise 1C 1. Algebraic fractions Algebraic fractions work in the same way as numeric fractions. We can simplify them by cancelling common factors for multiplication and division, and finding common denominators for addition and subtraction. 2...

Core pure mathematics 2 Table of contents First example - the method of separable variables Removing the modulus sign First-order DEs with the method of the integrating factor (I.F.) Second example Two important questions for the integrating factor More examples Exercise 7A First-order differential equations with constant coefficients 1. First example - the method of separable variables If a fir..