#### CONTENT MOVING FROM HIGHER TO FOUNDATION

- Use standard form
- Calculate exactly with multiples of pi
- Expand double brackets, factorise quadratics including difference of 2 squares.Solve quadratics by factorising
- Know the difference between an equation and an identity
- Use y=mx+c to identify parallel lines
- Sketch quadratic, cubic and reciprocal functions
- Derive simultaneous equations from real life situations; solve simultaneous equations algebraically and graphically
- Perform calculations with density, mass and volume
- Solve problems involving reverse percentages
- Use direct and inverse proportion graphically and algebraically
- Solve problems involving compound interest
- Find corresponding lengths in similar shapes
- Use congruence criteria for triangles (SSS, SAS, ASA and RHS)
- Enlarge shapes using fractional scale factors
- Find the area and perimeters of compound shapes involving circles and calculate arc length and areas of sectors
- Use the sin, cos and tan trigonometric ratios for right-angled triangles
- Use tree diagrams to solve probability questions
- Infer properties of a population from a sample, while knowing the limitations of sampling

#### NEW CONTENT AT FOUNDATION AND HIGHER

- Find the equation of a line through two point or through one point with given gradient
- Recognise and use sequences of triangular, square and cubic numbers, Fibonacci type sequences and geometric sequences
- Calculate compound measures including pressure in numerical and algebraic contexts
- Express a multiplicative relationship between two quantities as a ratio or a fraction
- Write a ratio as a linear function
- Set up, solve and interpret growth and decay problems
- Use inequality notation to specify error intervals due to rounding
- Understand the “not equal” symbol
- Use the standard convention for labelling sides and angles of polygons
- Derive the sum of angles in a triangle (note the use of the word derive!)
- Know the exact values of sin, cos and tan at key angles (0, 30, 45, 60 and 90 degrees)
- Use Venn diagrams
- Consider outliers when calculating the range of a distribution
- Know that correlation does not imply causation.

#### NEW CONTENT AT HIGHER ONLY

- Recognise and use the equation of a circle centred at the origin
- Find the equation of a tangent to a circle at a given point, using the fact that it is perpendicular to the radius
- Find approximate solutions using iteration (trial and improvement?)
- Solve quadratic inequalities
- Find the nth term of a quadratic sequence
- Recognise and use geometric sequences where the common ratio may be a surd

now the difference between an equation and an identity - Apply the concepts of instantaneous and average rates of changes by looking at the gradients of tangents and chords to a curve
- Prove the circle theorems
- Find inverse and composite functions
- Locate turning points of quadratic functions by completing the square

Sketch y = tan x (in addition to sin and cos) - Interpret areas under graphs and gradients of graphs in real-life contexts (eg recognise that the area under a velocity/time graph represents displacement)
- Use the probability “AND” and “OR”

#### KS5 – A-Level

When students have chosen to pursue Maths, and potentially Further Maths, in Y12 they are advised to have achieved a grade 6 or B equivalent at GCSE previously. Further Maths students are advised that a grade 8 or A* equivalent is advised at GCSE. Edexcel is followed here as well as at GCSE with the current qualification split into AS and A2 modules. Students will study two core and one applied module each year including C1, C2 and either S1 or D1 in Y12. In Further Maths students study an additional three modules each year either in the classroom or online with the Further Maths Network. Class time is currently at eight periods a fortnight with two different teachers splitting the teaching of the three modules accordingly.