Cambridge Maths Academy

케임브리지 대학교 수학 전공 선생님과 A-level Maths, Further maths 온라인 수업(1:1/그룹) 진행 중입니다. 자세한 수업 내용과 선생님 이력은 아래 사진을 참조해 주시기 바랍니다. ★ 선생님 약력: (사진 참조) - 케임브리지 대학교 수학과 학부, 석사 졸업. 박사과정 수료 (전액장학금 수여) - 10년 이상 A-level 수학 지도 - A-level Maths A* (594/600), Further maths A* (597/600), Physics A* (596/600), Chemistry A* (565/600) - STEP I, II, III Outstanding(S) - British Maths Olympiad: Gold medal (Top 50 in the nation Aw..

Further statistics 1 Table of contents Probability density functions Moment generating functions Moments Edexcel FS1 Ch Exercise 1. Probability density functions The probability dentity function for a normal distribution, $ X \sim \textrm N \left( \mu, \sigma^2 \right) $, is $$ \begin{align} \textrm f(x) = \frac{1}{ \sqrt{2\pi} \sigma} \textrm e^{ - \frac12 \left( \frac{ x - \mu }{ \sigma } \rig..

Further statistics 1 Table of contents Probability mass function Probability generating function Moment generating function Moments Using moment generating function Central moments Standardised moments Edexcel FS1 Ch Exercise (under construction) 1. Probability mass function The probability mass function for a geometric distribution, $ X \sim \textrm{Geo}(p)$, is $$ \begin{align} \mathbb P(x) = ..

Pure mathematics Year 1 Here's a short introduction to Pure maths 1 Chapter 1 Algebraic expressions. 1.1 Index laws: Multiply and divide integer powers. 1.2 Expanding brackets: Expand a single term over brackets and collect like terms. Expand the product of two or three expressions. 1.3 Factorising: Factorise linear, quadratic and simple cubic expressions. 1.4 Negative and fractional indices: Kn..

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..