A: Algebra

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A1

use and interpret algebraic manipulation, including:

• ab in place of a × b

• 3y in place of y+y+y and 3×y

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

• 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

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)

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 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 = k^x 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)