====== 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 ====