How to derive and solve a second order differential equation that models simple harmonic motion.

How to derive a second order differential equation for damped oscillations.

The meaning of underdamping, critical damping and overdamping.

How to solve coupled differential equations.

How to calculate the impulse of one object on another in a collision.

How to use the principle of conservation of momentum to model collisions in one dimension.

How to use Newton’s experimental law to model inelastic collisions in one dimension.

How to calculate the work done by a force and the work done against a resistive force.

How to calculate gravitational potential energy and kinetic energy.

How to calculate elastic potential energy.

How to solve problems in which energy is conserved.

How to solve problems in which some energy is lost through work against a dissipative force.

How to calculate power and solve problems involving power.

How to model elastic collision between bodies in two dimensions.

How to model inelastic collision between two bodies in two dimensions.

How to calculate the energy lost in a collision.

How to calculate probability for a Poisson distribution.

How to use the properties of a Poisson distribution.

How to use a Poisson distribution to model a binomial distribution.

How to use a hypothesis test to test for the mean of a Poisson distribution.

How to estimate a population mean from sample data.

How to estimating population variance using the sample variance. How to calculate and interpret the standard error of the mean.

How and when to apply the Central Limit Theorem to the distribution of sample means.

How to use the Central Limit Theorem in probability calculations, using a continuity correction where appropriate.

How to apply the Central Limit Theorem to the sum of n identically distributed independent random variables.

How to conduct a chi-squared test with the appropriate number of degrees of freedom to test for independence in a contingency table and interpret the results of such a test.

How to fit a theoretical distribution, as prescribed by a given hypothesis involving a given ratio, proportion or discrete uniform distribution, to given data.

How to use a chi-squared test with the appropriate number of degrees of freedom to carry out a goodness of fit test.

How to calculate the probability of making a Type I error from tests based on a Poisson or Binomial distribution.

How to calculate probability of making Type I error from tests based on a normal distribution.

How to calculate P(Type II error) and power for a hypothesis test for tests based on a normal, Binomial or a Poisson distribution (or any other A level distribution).