9 Solve quadratic equations arising from algebraic fractions Know how to use a composite function Estimate area under a quadratic graph by dividing it into trapezia Estimate the gradient of a quadratic or non-linear graph at a given point by sketching the tangent Find the equation of a tangent to a circle at a given point Interpret coordinates for trigonometric graphs Plot graphs of the exponential function y = 〖ab〗^x Use iteration with simple converging sequences 8 Find the inverse of a linear function Plot graphs of exponential functions Recognise, sketch and interpret graphs of trigonometric functions Know how to transform graphs Find the gradient of the radius that meets the circle at a given point Find the nth term of a quadratic sequence Solve linear/x²+y²=r² simultaneous equations 7 Solve quadratic equations by using the quadratic formula Expand two or more brackets Factorise harder quadratics, including difference of two squares Use function notation Deduce turning points by completing the square Sketch a graph of a quadratic Find the equation of the line through two given points Find the equation of the line through one point with a given gradient Find the gradient of perpendicular lines Give equations of lines parallel and perpendicular to the given line Solve quadratic inequalities Manipulate algebraic expressions with surds and algebraic fractions Solve linear/quadratic simultaneous equations Solve linear/non-linear simultaneous equations graphically Set up equations to solve direct or inverse proportion problems 6 Solve linear equations with fractional coefficients Solve quadratics by completing the square Expand double brackets (ax ± b)(cx ± d) Change the subject of a more complex formula (square roots and fractions) Identify and interpret gradient from an equation in the form ax+b=c Recognise, sketch and interpret cubic and reciprocal graphs Find the midpoint of a line using a formula Solve linear inequalities graphically Solve two simultaneous inequalities algebraically Answer simple proof and ‘show that’ questions Continue a quadratic sequence and use the nth term to generate terms Continue geometric progression and find term to term rule, including negative, fraction and decimal terms Simplify expressions involving brackets and powers Use expressions of the form y ∝ x² Identify direct proportion from a table of values 5 Solve quadratic equations by factorising Change the subject of a formula (including subject on both sides) Find the equation of a straight-line from its graph Interpret distance-time graphs and calculate speed Interpret gradient as rate of change Identify and interpret roots, intercepts and turning points of a quadratic graph Given the coordinates of points A and B, calculate the length of AB Plot and draw graphs of straight lines without using a table of values Solve more complex linear inequalities Use algebra to support and construct arguments Recognise and use simple geometric progressions Use function machines to find terms of sequence Solve linear simultaneous equations algebraically and graphically Write a ratio as a linear function 4 Solve more complex equations (including negatives and division) Use systematic trial and improvement Form and solve an equation Expand double brackets Understand the meaning of an identity and use the ≠ sign Find an unknown that is not the subject of the formula Rearrange simple equations Find the gradient of a line Identify parallel lines from their equations Plot the graphs of linear functions in the form y=mx+c Plot and recognise quadratics Solve simple linear inequalities Find and use the nth term of an arithmetic sequence Simplify simple expressions involving index notation Understand and use compound measures (density, speed, pressure) Solve problems involving variables in direct and inverse proportion 3 Solve equations with ‘x’s on both sides Solve equations involving brackets Expand and simplify a single bracket Substitute positive integers into expressions involving small powers Identify an Identity Factorise linear expressions Change the subject of a formula in one step Know what is meant by the gradient of a straight line Draw velocity-time graphs Find the coordinates of the midpoint of a line from a given graph Recognise that equations of the form y=mx+c lead to straight line graphs Write down whole number values that satisfy an inequality Use algebra to describe the nth term in an arithmetic sequence. Understand the use of small, positive powers in algebra 2 Solve two-step equations Construct equations from real life situations Substitute into more complex formulae (involving brackets and more than one operation) Substitute positive and negative integers into simple formulae Select an expression/ equation/ formula from a list Generate coordinates from functions Use graphs to solve distance-time problems. Interpret information from a complex real life graph Find the coordinates required to complete a shape Plot and draw graphs of straight lines using a table of values Draw the next term in a pattern sequence Recognise cube numbers and Fibonacci-type sequences Know how to find the nth term for linear sequences 1 Substitute integers into equations and formulae Construct expressions from worded descriptions Multiply a single positive term over a bracket Create expressions from worded examples Complete a number machine Plot a simple distance-time graph Read coordinates in all four quadrants Draw graphs of y=a, x=a, y=x and y=-x Show inequalities on a number line Generate terms in a sequence given term-to-term rule or position-to-term rule Use arithmetic operations with algebra Multiply together two simple algebraic expressions W3 Substitute into simple formulae Use function machines Simplify by collecting like terms Find inputs and outputs of functions Interpret line graphs Read values from straight-line graphs Draw, label and scale axes Use inequality notation >, <, ≥, and ≤ Generate terms of a simple sequence Know square and triangle numbers W2 Find outputs of simple functions Read coordinates in the first quadrant