Cambridge Maths Academy

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..

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..

수학 모음 (Maths collection) 전체보기 For a function which depends on two variables $(x,y)$, $$ \textrm f = \textrm f(x,y) $$ we find the critical points by considering 2-dimensional gradient and second-order derivatives. (In 1D, the critical points are usually called the stationary points.) (i) Critical points: $$ \begin{align} \nabla \textrm f = \left( \frac{ \partial \textrm f }{ \partial x }, \frac{..

'영국 교육제도와 수학 공부' 전체보기 Table of contents Edexcel Mathematics (AS level) Edexcel Mathematics (A level) Edexcel Further mathematics (AS level) Edexcel Further mathematics (A level) AQA Mathematics (AS level) AQA Mathematics (A level) AQA Further mathematics (AS level) AQA Further mathematics (A level) OCR Mathematics A (AS level) OCR Mathematics A (A level) OCR Further mathematics A (AS level) OCR ..

'영국 교육제도와 수학 공부' 전체보기 Table of contents 교과서를 충분히 소화했는가 Past papers 활용법 1 - 현재 이해도와 실력 점검 Past papers 활용법 2 - 미리 눈으로 익히기 Past papers 활용법 3 - 복습의 구체적인 예시 Past papers 조심하기 1 - 지나친 의존은 금물 Past papers 조심하기 2 - Past paper가 알려주지 않는 것 이스터 방학 이후의 시간 - 생각보다 빠르게 흘러간다 이스터 방학이 다가오면 학교와 친구들 사이에서 past papers(기출문제) 이야기가 많이 나옵니다. 학교에서도 대개 과목당 1주일에 적어도 1~2개 가량의 past papers를 시도할 것을 권하지요. 여느 시험과 마찬가지로 기출문제는 시험에 어떤 ..