3 The binomial expansion Understand and use the binomial B6 manipulate polynomials The binomial expansion is 1.3 – expansion of algebraically used in Chapter 13 Ex 1.3A Students are introduced to the binomial D1 binomial expansion Probability and statistical – expansion formula as a way of any distributions for binomial binomial expansion, they should state distributions which formula they are using at the start of any answer. Manipulate polynomials 4 Factorisation B6 manipulate polynomials Factorisation is used in 1.4 – algebraically including: algebraically Chapter 2 Algebra and Ex 1.4A Students factorise different sorts of factorisation functions 2: Equations and expressions including quadratics. They inequalities when working also factorise a difference of two squares. with quadratic equations Some questions are given in relation to and in Chapter 3 Algebra real life problems to show how and functions 3: Sketching factorisation is used. curves 5 Algebraic division Manipulate polynomials B6 manipulate polynomials Link algebraic division to 1.5 – algebraically including: algebraically, including expanding numerical division Ex 1.5A expanding brackets and All the skills are then combined to write brackets, collecting like simplifying by collecting like algebraic fractions in their simplest form. factorisation and simple algebraic terms Students work through the factor division; use of the factor theorem factorisation theorem. Students then divide simple algebraic division polynomials by an expression make it – use of the factor theorem clear to students that they use the same method as they do for numerical long division. 6 Laws of indices, manipulating surds Understand and use the laws of A1 mathematical proof Builds on GCSE skills 1.6 – indices for all rational exponents B1 understand and use the laws Laws of indices is used in 1.7 – Students questions using the laws of Use and manipulate surds of indices for all rational Chapter 7 Exponentials Ex 1.6A indices, including negative and fractional exponents and logarithms, section 7.2 Ex 1.7A indexes. They are reminded that surds are B2 - use and manipulate surds, Manipulation of indices roots of rational numbers and simplify including rationalising the and surds is used in expressions involving surds. denominator Chapter 8 Differentiation and Chapter 9 Integration 7 Rationalising the denominator Use and manipulate surds, including A1 mathematical 1.8 – rationalising the denominator Ex 1.8A
3 The binomial expansion Students are introduced to the binomial expansion formula as a way of any binomial expansion, they should state which formula they are using at the start of any answer. Understand and use the binomial expansion of B6 – manipulate polynomials algebraically D1 – binomial expansion The binomial expansion is used in Chapter 13 Probability and statistical distributions for binomial distributions 1.3 Ex 1.3A 4 Factorisation Students factorise different sorts of expressions including quadratics. They also factorise a difference of two squares. Some questions are given in relation to real life problems to show how factorisation is used. Manipulate polynomials algebraically including: factorisation B6 – manipulate polynomials algebraically Factorisation is used in Chapter 2 Algebra and functions 2: Equations and inequalities when working with quadratic equations and in Chapter 3 Algebra and functions 3: Sketching curves 1.4 Ex 1.4A 5 Algebraic division All the skills are then combined to write algebraic fractions in their simplest form. Students work through the factor theorem. Students then divide polynomials by an expression – make it clear to students that they use the same method as they do for numerical long division. Manipulate polynomials algebraically including: expanding brackets and simplifying by collecting like terms factorisation simple algebraic division use of the factor theorem B6 – manipulate polynomials algebraically, including expanding brackets, collecting like factorisation and simple algebraic division; use of the factor theorem Link algebraic division to numerical division 1.5 Ex 1.5A 6 Laws of indices, manipulating surds Students questions using the laws of indices, including negative and fractional indexes. They are reminded that surds are roots of rational numbers and simplify expressions involving surds. Understand and use the laws of indices for all rational exponents Use and manipulate surds A1 – mathematical proof B1 – understand and use the laws of indices for all rational exponents B2 - use and manipulate surds, including rationalising the denominator Builds on GCSE skills Laws of indices is used in Chapter 7 Exponentials and logarithms, section 7.2 Manipulation of indices and surds is used in Chapter 8 Differentiation and Chapter 9 Integration 1.6 1.7 Ex 1.6A Ex 1.7A 7 Rationalising the denominator Use and manipulate surds, including rationalising the denominator A1 – mathematical 1.8 Ex 1.8A