- Perform essential manipulations of algebra, use the laws of indices, manipulate surds, solve quadratics equations and work with quadratic graphs, solve simultaneous equations, solve linear and quadratic inequalities including using graphs, use graphs of functions and sketch simple transformations of graphs.
- Solve problems with coordinate geometry in the (x, y) plane by understanding the equation of a straight line, parallel and perpendicular lines, find lengths and areas using equations of straight lines, find the midpoint of a line segment, understand and use the equation of a circle and be able to use the properties of chords and tangents.
- Use further algebraic skills to complete algebraic division, know how to apply the factor theorem, fully factorise a cubic expression, understand proof and solve problems using the binomial expansion.
- Use vectors in two dimensions, calculate the magnitude and direction, add vectors diagrammatically and multiply by scalars, understand position vectors and find the distance between two points.
- Differentiate including from first principles, apply differentiation to find gradients, tangents and normal, maxima and minima and stationary points and where functions are increasing or decreasing.
- Calculate with trigonometry using right angled trigonometry rules, the sine and cosine rules, finding the area of triangles, understand trigonometric graphs and understand and use trigonometric identities and equations.
- Integrate xn and related sums, differences and constant multiples, evaluate definite integrals and use then to find the area under a curve.
- Use exponentials including the function ex and its graph, know how to use the definition of logarithms and understand the laws of logarithms.
- Recall statistical sampling terminology and know the advantages and disadvantages of sampling over a census, understand and use sampling techniques and compare sampling techniques in context.
- Present and interpret data by calculating measures of location and measures of variation, understand and use coding, interpret diagrams for single-variable data, interpret scatter diagrams and regression lines, recognise and interpret outliers and draw simple conclusions from statistical problems
- Understand and use fundamental quantities and units in the S.I. system (length, times & mass) and understand derived quantities and units (velocity, acceleration, force, displacement & weight).
- Explain the concept of a force and understand and use Newton’s first, second and third laws to draw force diagrams and solve problems in equilibrium including with smooth pulleys.
- Understand and use mutually exclusive and independent events when calculating probability.
- Use discrete statistical distributions to model real-world situations, identify the discrete uniform distribution, calculate probabilities using the binomial distribution.
- Understand and use the language of kinematics, be able to represent them graphically, use a derive the formula for constant acceleration for motion in a straight line and understand and use weight and motion in a straight line under gravity.
- Use calculus (differentiation and integration) in kinematics for motion in a straight line where there is variable acceleration.
- Understand and be able to apply the language of hypothesis testing, including significance levels developed through a binomial model and then carry out hypothesis tests.