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====== Algebra ======


[[gcse_maths_notation_vocabulary_manipulation|Notation, vocabulary and manipulation]] \\
[[gcse_maths_graphs|Graphs]] \\
[[gcse_maths_solving_equations_and_inequalities|Solving equations and inequalities]] \\
[[gcse_maths_sequences|Sequences]] \\


=====Notation, vocabulary and manipulation=====


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

ab in place of a × b
3y in place of y + y + y and 3 × y
a² in place of a × a, a³ n place of a × a × a, a²b 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 x² + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax² + 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=====

**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 1 y 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 Pearson Edexcel Level 1/Level 2 GCSE (9 - 1) in Mathematics Specification – Issue 2 – June 2015 © Pearson Education Limited 2015 15

**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=====

**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=====

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


==== Sequences ====

==== Powers and Roots ====

==== Algebra Basics ====

==== Multiplying Out Brackets ====

==== Factorising ====

==== Manipulating Surds ====

==== Solving Equations ====

==== Rearranging Formulas ====

==== Factorising Quadratics ====

==== The Quadratic Formula ====

==== Completing the Square ====

==== Quadratic Equations — Tricky Ones ====

==== Algebraic Fractions ====

==== Inequalities ====

==== Graphical Inequalities ====

==== Trial and Improvement ====

==== Simultaneous Equations and Graphs ====

==== Simultaneous Equations ====

==== Direct and Inverse Proportion ====

==== Proof ====

==== X, Y and Z Coordinates ====

==== Straight-Line Graphs ====

==== Plotting Straight-Line Graphs ====

==== Finding the Gradient ====

==== “y = mx + c” ====

==== Parallel and Perpendicular Lines ====

==== Quadratic Graphs ====

==== Harder Graphs ====

==== Graph Transformations ====

==== Real-Life Graphs ====