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 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...

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..