Cambridge Maths Academy

Pure mathematics Year 2 Here's a short introduction to Pure maths 2 Chapter 2 Functions and graphs. 2.1 The modulus function: Understand and use the modulus function. 2.2 Functions and mappings: Understand mappings and functions, and use domain and range. 2.3 Composite functions: Combine two or more functions to make a composite function. 2.4 Inverse functions: Know how to find the inverse of a ..

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 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 Table of contents Disproof by counter-example Proof by deduction Proof by exhaustion Proof by contradiction 1. Disproof by counter-example Examples Exercise - 2. Proof by deduction Examples Exercise - 3. Proof by exhaution Examples Exercise - 4. Proof by contradiction A contradiction is a disagreement between two statements, which means that both cannot be true. There are..