Cambridge Maths Academy

Pure mathematics Year 2 Table of contents Edexcel P2 Review exercise 1 Q1-10 1. Edexcel P2 Review exercise 1 Q1-10 Question 1. (E/P) Prove by contradiction that there are infinitely many prime numbers. [4 marks] (Relevant section: P2 §1.1 Proof by contradiction.) (Edexcel 2017 Specifications, P2 Review exercise 1 Q1.) Solution. Question 2. (E/P) Prove that the equation $x^2 - 2=0$ has no rationa..

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 Algebraic division Examples Edexcel P2 Ch1 Exercise 1F Improper fractions in partial fractions Edexcel P2 Ch1 Exercise 1G 1. Algebraic division An improper algebraic fraction is one whose numerator has a degree equal to or larger than the denominator. The degree of a polynomial is the largest exponent in the expression. For example, $x^3 + 5x - 9$ has d..

Pure mathematics Year 2 Table of contents Partial fractions revisited Partial fractions with repeated factors Examples Edexcel P2 Ch1 Exercise 1E The main task of this section is to understand partial fractions with repeated factors. In order to do so, we need to consider and understand some general form of fractions. 1. Partial fractions revisited In the previous section, P2 §1.3 Partial fracti..

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 Here's a short introduction to Pure maths 2 Chapter 1 Algebraic methods. 1.1 Proof by contradition: Use proof by contradiction to prove true statements. 1.2 Algebraic fractions: Multiply and divide two or more algebraic fractions; Add or subtract two or more algebraic fractions. 1.3 Partial fractions: Convert an expression with linear factors in the denominator into parti..