**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^2in place of a × a, a^3 in place of a × a × a, a^2b 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

**A4** simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:

● collecting like terms

● multiplying a single term over a bracket

● taking out common factors

● expanding products of two or more binomials

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

form ax^2 + bx + c

● 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 and proofs

**A7** where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’;

interpret the succession of two functions as a ‘composite function’ (the use of formal function notation is expected)

*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 and

perpendicular 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 and turning points by completing the square

**A12** recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y=1/x with x ≠ 0, exponential functions y = kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size

**A13** sketch translations and reflections of a given function

**A14** plot and interpret graphs (including reciprocal graphs and exponential 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

**A15** calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret

results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts (this does not include calculus)

**A16** recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point

*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 (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph

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

**A20** find approximate solutions to equations numerically using iteration

**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 or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line,

using set notation and on a graph

*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 or a surd) and other sequences

**A25** deduce expressions to calculate the nth term of linear and quadratic

sequences

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