**Algebra**

*Notation, vocabulary and manipulation*

What students need to learn:

**A1 **use and interpret algebraic manipulation, including:

– ab in place of a × b

– 3y in place of y + y + y and 3 × y

– a to the power of 2 in place of a × a, a to the power of 3 in place of a × a × a, a(to the power of 2) b in place of a × a × b

– a/b in place of a ÷ b

– coefficients written as fractions rather than as decimals

– brackets

**A2 **substitute numerical values into formulae and expressions, including scientific formulae

** A3 **understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

● collecting like terms

● multiplying a single term over a bracket

● taking out common factors

● expanding products of two binomials

● factorising quadratic expressions of the form x^2+ bx + c, including the difference of two squares;

● simplifying expressions involving sums, products and powers, including the laws of indices

**A5 **understand and use standard mathematical formulae; rearrange formulae to change the subject

** A6 **know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

** A7 **where appropriate, interpret simple expressions as functions with inputs and outputs.

* Graphs*

What students need to learn:

** A8** work with coordinates in all four quadrants

**A9** plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points or through one point with a

given gradient

**A10** identify and interpret gradients and intercepts of linear functions graphically and algebraically

**A11** identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically

**A12** recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y=1/x with

x ≠ 0

** A14** plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

*Solving equations and inequalities*

What students need to learn:

** A17** solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph

**A18** solve quadratic equations algebraically by factorising; find approximate solutions using a graph

**A19** solve two simultaneous equations in two variables (linear/linear algebraically; find approximate solutions using a graph

**A21** translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution

**A22** solve linear inequalities in one variable; represent the solution set on a number line

*Sequences*

What students need to learn:

**A23** generate terms of a sequence from either a term-to-term or a position-to-term rule

**A24** recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r^n where n is an integer, and r is a rational number > 0)

**A25** deduce expressions to calculate the nth term of linear sequences

To see the split between Higher and Foundation please see the full specification **Edexcel GCSE 2015 Specification**