Cambridge Maths Academy

Pure mathematics Year 1 Table of contents Introduction Factorial $n!$ and arrangements Permutations (${}_nP_r$) Combination: n choose r An alternative derivation of the formula for 'n choose r' 0! = 1 revisited Pascal's triangle using combinations Examples Edexcel P1 Ch8 Exercise 8B 1. Introduction While Pascal's triangle is a convenient tool, for large values of the index, $n$, it takes a long ..

Pure mathematics Year 1 Here's a short introduction to Pure maths 1 Chapter 8 The Binomial expansion. 8.1 Pascal's triangle: Use Pascal's triangle to identify binomial coefficients and use them to expand simple binomial expressions. 8.2 Factorial notation: Use combinations and factorial notation. 8.3 The binomial expansion: Use the binomial expansion to expand brackets. 8.4 Solving binomial prob..

수학 모음 (Maths collection) 전체보기 Heron's formula calculates the area of a triangle. Here, we will look at two different formulae describing the area of a triangle and then derive the third version, Heron's formula. $A=\frac12ah$ $A=\frac12ab\sin C$ Heron's formula: $A=\sqrt{s(s-a)(s-b)(s-c)}\,$ where $s=\frac{a+b+c}{2}$. s can be thought of as half the perimeter of the triangle. As we will see, the..

Pure mathematics Year 1 Here's a short introduction to Pure maths 1 Chapter 6 Circles. 6.1 Midpoints and perpendicular bisectors: Find the mid-point of a line segment and the equation of the perpendicular bisector to a line segment. 6.2 Equation of a circle: Learn how to find the equation of a circle. 6.3 Intersections of straight lines and circles: Solve geometric problems involving straight li..