# Algebra usually involves replacing numbers with letters and learning ways to solve equations and formulae.

### Tricky stuff.

First, we must find x.

3y + 67 = x  <-----------There it is!

These topics are for GCSE Maths Level.

This theme covers; Expressions, Sequences, nth Term, Index Laws, Equations, Linears, Gradients, Quadratics, Rearranging and Simultaneous Equations.

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## Topics

 Recognise the words: equation, formula, identity and expression D Write the terms of a sequence or a series of diagrams when given the nth term D Draw lines such as y = 2x + 3 using a table of values D Solve equations with unknowns on each side and with brackets D Substitute numbers into formulas D Factorise expressions with one pair of brackets C Multiply out expressions with brackets C Use index notation and index laws for positive and negative powers C Write the nth term of a sequence or a series of diagrams C Find a solution to a problem by forming an equation and solving it C Solve linear equations C Form and solve equations such as x3 + x = 12 using trial and improvement methods C Recognise the equations of straight-line graphs C Find the gradients of straight-line graphs C Draw graphs of quadratic functions by plotting points C Represent solutions to inequalities on a number line C Solve linear inequalities C Understand the difference between a demonstration and a proof C Expand and simplify quadratics B Factorise quadratic expressions B Solve quadratic equations by factorising B Rearrange formulae that include brackets, fractions and square roots B Use and understand y=mx+c B Solve a set of linear inequalities in 2 variables by shading a region of a graph B Solve a pair of simultaneous equations algebraically B Solve simultaneous equations graphically B Complete tables for, and draw graphs of cubic functions and quadratics B Solve proportion problems (direct, inverse, proportional to the square, inversely proportional to the square) A Interpret the graphs of direct and inverse proportion relationships A Rearrange formulae where the new subject appears twice A Understand the gradients of perpendicular straight-line graphs A When given a graph, draw another line to solve an equation A Solve a pair of simultaneous equations where one is linear and the other involves x2 A Solve fractional equations with the unknown in the denominator A* Simplify algebraic fractions A* Solve quadratic equations by using the quadratic formula A* Use the technique of completing the square A* Solve a pair of simultaneous equations where one is linear and the other is a circle A* Solve cubic equations by drawing appropriate lines on graphs A* Transform the graphs of y = f(x), such as linear, quadratic, cubic, sine and cosine functions, using the transformations y = f(x) + a, y = f(x + a), y = f (ax) and y = af(x) A* Recognise and sketch the shapes of graphs of functions A* Derive algebraic proofs using reasoning and logic A* Construct the graphs of loci, including the circle x2 + y2 = r2 A*

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