#### 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 7 or A 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. Students will study 1 pure and 1 applied module each year including P1 and M/S in Y12. In Further Maths students study an additional 3 modules each year either in the classroom or online with the Further Maths Network. Class time is currently at 8 periods a fortnight with 2 different teachers splitting the teaching of the 2 modules accordingly.