Algebra (2015) higher

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