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--- gcse_maths_algebra [2026/02/12 08:39] – created hjb
+++ gcse_maths_algebra [2026/03/02 14:56] (current) – hjb
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-Notation, vocabulary and manipulation
+====== Algebra ======
+[[gcse_maths_notation_vocabulary_manipulation|Notation, vocabulary and manipulation]] \\
-A1 use and interpret algebraic manipulation, including:
+[[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
 y 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
+**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
+**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:
+**A4**
+simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:
 collecting like terms
@@ Line 44: / Line 37: @@
 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
+**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)
-A1 use and interpret algebraic manipulation, including:
-ab in place of a × b
-y 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)
+**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=====
-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
-A8 work with coordinates in all four quadrants
+**A11**
+identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
-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
+**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
-A10 identify and interpret gradients and intercepts of linear functions graphically and algebraically
+**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
-A11 identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
+**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
-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
+**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)
-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
+**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
-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)
+=====Solving equations and inequalities=====
-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
+**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
-A8 work with coordinates in all four quadrants
+**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
-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
+**A19**
+solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph
-A10 identify and interpret gradients and intercepts of linear functions graphically and algebraically
+**A20**
+find approximate solutions to equations numerically using iteration
-A11 identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
+**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
-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
+**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
-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
+=====Sequences=====
-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
+**A23**
+generate terms of a sequence from either a term-to-term or a position-toterm rule
-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)
+**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
-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
+==== Sequences ====
+==== Powers and Roots ====
+==== Algebra Basics ====
+==== Multiplying Out Brackets ====
-Solving equations and inequalities
+==== Factorising ====
+==== Manipulating Surds ====
+==== Solving Equations ====
-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
+==== Rearranging Formulas ====
-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
+==== Factorising Quadratics ====
-A19 solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph
+==== The Quadratic Formula ====
-A20 find approximate solutions to equations numerically using iteration
+==== Completing the Square ====
-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
+==== Quadratic Equations — Tricky Ones ====
-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
+==== Algebraic Fractions ====
-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
+==== Inequalities ====
-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
+==== Graphical Inequalities ====
-A19 solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph
+==== Trial and Improvement ====
-A20 find approximate solutions to equations numerically using iteration
+==== Simultaneous Equations and Graphs ====
-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
+==== Simultaneous Equations ====
-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
+==== Direct and Inverse Proportion ====
-Sequences
+==== Proof ====
+==== X, Y and Z Coordinates ====
+==== Straight-Line Graphs ====
-A23 generate terms of a sequence from either a term-to-term or a position-toterm rule
+==== Plotting Straight-Line Graphs ====
-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
+==== Finding the Gradient ====
+==== “y = mx + c” ====
+==== Parallel and Perpendicular Lines ====
-A23 generate terms of a sequence from either a term-to-term or a position-toterm rule
+==== Quadratic Graphs ====
-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
+==== Harder Graphs ====
+==== Graph Transformations ====
+==== Real-Life Graphs ====