Product rule

Fractional Indices

Simplify surds

Rationalise the denominator

Add and multiply with standard form

Recurring decimals to fractions

Fractions into ratio problems

Use standard units of mass, length, time, money as well as compound units e.g m/s, g/cm³, miles per gallon...

Solving problems with estimation

Error intervals due to truncation or rounding

Limits of accuracy, including upper and lower bounds

Expand triple brackets

Factorise using difference of two squares

Factorise with a coefficient more than 1

Using the quadratic formula

Completing the square

Laws of indices

Changing the subject of the formula

Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs

Inverse functions and composite functions

Draw a straight line when given an equation e.g 2x + 4y = 6

Find the equation of the line through two given points or through one point with a given gradient

Identify and interpret roots, intercepts, turning points of quadratic functions graphically

Deduce roots algebraically and turning points by completing the square

Sketching graphs: linear, quadratic, cubic, exponential, reciprocal, trigonometric (sinx, cosx, tanx)

Sketch translations and reflections of a given function

Distance time graphs and velocity time graph

Equation of a circle and equation of a tangent to a circle

Finding solutions using a graph

Iteration

Nth term of linear and quadratic sequences

Scale factor, scale diagrams and maps

Direct and inverse proportion

Length, area and volume scale factor

Interpret the gradient at a point on a curve as the instantaneous rate of change

Simple and compound interest

Loci problems e.g perpendicular bisector, angle bisector ...

Know the different angle properties (angles at a point, angles at a point on a straight line, vertically opposite angles; angles on parallel lines; angle sum in any polygon 180(n-2)

Congruent triangles

2D and 3D pythagoras' theorem

Transformations: Rotation, enlargement, reflection and translation

Circle Theorems

Plans and elevations of 3D shapes

Area and volume of 3D shapes

Calculate arc lengths, angles and areas of sectors of circles

Trigonometric Ratios: Sin, cos and tan

Exact trig values

Sine rule, cosine rule and area of a triangle 1/2absinC

Vectors

Calculate the probability of independent and dependent combined events, including using tree diagrams

Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

Averages from frequency tables

Histograms