Cambridge Maths Academy

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..

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 Table of contents Binomial, trinomial and polynomial Binomial expansion Pascal's triangle Examples Edexcel P1 Ch8 Exercise 8A 1. Binomial, trinomial and polynomial The binomial expansion tells us how to expand $(a+b)^n$. The word 'bi-nomial' means 'two terms' - here, they are $a$ and $b$. Similarly, monomial means 'one term', trinomial means 'three terms' and polynomial m..

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..

Pure mathematics Year 1 Table of contents Introduction Tangent properties Chord properties Edexcel P1 Ch6 Exercise 6E 1. Introduction We can use the properties of tangents and chords within circles to solve geometric problems. 2. Tangent properties A tangent to a circle is a straight line that intersects the circle at only one point. A tangent to a circle is perpendicular to the radius of the ci..

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..