Algebra (2015) foundation

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/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
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