Use a probability density function which may be defined piecewise Use the general result E(g(x)) =∫f(x)g(x) dx where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X Understand and use the relationship between the probability density function (PDF) and the cumulative distribution function (CDF), and use either to evaluate probabilities or percentiles Use cumulative distribution functions (CDFs) of related variables in simple cases e.g. given the CDF of a variable X, find the CDF of a related variable Y, and hence its PDF, e.g. where Y = X^ 3.

Use a probability density function which may be defined piecewise Use the general result E(g(x)) =∫f(x)g(x) dx where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X Understand and use the relationship between the probability density function (PDF) and the cumulative distribution function (CDF), and use either to evaluate probabilities or percentiles Use cumulative distribution functions (CDFs) of related variables in simple cases e.g. given the CDF of a variable X, find the CDF of a related variable Y, and hence its PDF, e.g. where Y = X^ 3.

Use a probability density function which may be defined piecewise Use the general result E(g(x)) =∫f(x)g(x) dx where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X Understand and use the relationship between the probability density function (PDF) and the cumulative distribution function (CDF), and use either to evaluate probabilities or percentiles Use cumulative distribution functions (CDFs) of related variables in simple cases e.g. given the CDF of a variable X, find the CDF of a related variable Y, and hence its PDF, e.g. where Y = X^ 3.

Use a probability density function which may be defined piecewise Use the general result E(g(x)) =∫f(x)g(x) dx where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X Understand and use the relationship between the probability density function (PDF) and the cumulative distribution function (CDF), and use either to evaluate probabilities or percentiles Use cumulative distribution functions (CDFs) of related variables in simple cases e.g. given the CDF of a variable X, find the CDF of a related variable Y, and hence its PDF, e.g. where Y = X^ 3.

Use a χ2-test, with the appropriate number of degrees of freedom, to carry out the corresponding goodness of fit analysis

Use a χ2-test, with the appropriate number of degrees of freedom, for independence in a contingency table.

Fit a theoretical distribution, as prescribed by a given hypothesis, to given data Use a χ2-test, with the appropriate number of degrees of freedom, to carry out the corresponding goodness of fit analysis Use a χ2-test, with the appropriate number of degrees of freedom, for independence in a contingency table.

Fit a theoretical distribution, as prescribed by a given hypothesis, to given data Use a χ2-test, with the appropriate number of degrees of freedom, to carry out the corresponding goodness of fit analysis Use a χ2-test, with the appropriate number of degrees of freedom, for independence in a contingency table.

Fit a theoretical distribution, as prescribed by a given hypothesis, to given data Use a χ2-test, with the appropriate number of degrees of freedom, to carry out the corresponding goodness of fit analysis Use a χ2-test, with the appropriate number of degrees of freedom, for independence in a contingency table.

Understand the concept of angular speed for a particle moving in a circle, and use the relation v = rw Understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae r w^2 and v^2/r Solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed Solve problems which can be modelled by the motion of a particle in a vertical circle without loss of energy. Find a normal contact force or the tension in a string, locating points at which these are zero, and conditions for complete circular motion.

Recall Newton’s experimental law and the definition of the coefficient of restitution, the property 0 ≤ e ≤ 1, and the meaning of the terms ‘perfectly elastic’ (e = 1) and ‘inelastic’ (e = 0) Use conservation of linear momentum and/or Newton’s experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.

Recall Newton’s experimental law and the definition of the coefficient of restitution, the property 0 ≤ e ≤ 1, and the meaning of the terms ‘perfectly elastic’ (e = 1) and ‘inelastic’ (e = 0) Use conservation of linear momentum and/or Newton’s experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.

Recall Newton’s experimental law and the definition of the coefficient of restitution, the property 0 ≤ e ≤ 1, and the meaning of the terms ‘perfectly elastic’ (e = 1) and ‘inelastic’ (e = 0) Use conservation of linear momentum and/or Newton’s experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.

Calculate the moment of a force about a point Use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry Use given information about the position of the centre of mass of a triangular lamina and other simple shapes Determine the position of the centre of mass of a composite body by considering an equivalent system of particles Use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this Solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.

Calculate the moment of a force about a point Use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry Use given information about the position of the centre of mass of a triangular lamina and other simple shapes Determine the position of the centre of mass of a composite body by considering an equivalent system of particles Use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this Solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.

Calculate the moment of a force about a point Use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry Use given information about the position of the centre of mass of a triangular lamina and other simple shapes Determine the position of the centre of mass of a composite body by considering an equivalent system of particles Use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this Solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.

Use Hooke’s law as a model relating the force in an elastic string or spring to the extension or compression, and understand the term modulus of elasticity Use the formula for the elastic potential energy stored in a string or spring Solve problems involving forces due to elastic strings or springs, including those where considerations of work and energy are needed

Use Hooke’s law as a model relating the force in an elastic string or spring to the extension or compression, and understand the term modulus of elasticity Use the formula for the elastic potential energy stored in a string or spring Solve problems involving forces due to elastic strings or springs, including those where considerations of work and energy are needed

Use Hooke’s law as a model relating the force in an elastic string or spring to the extension or compression, and understand the term modulus of elasticity Use the formula for the elastic potential energy stored in a string or spring Solve problems involving forces due to elastic strings or springs, including those where considerations of work and energy are needed

Solve problems which can be modelled as the linear motion of a particle under the action of a variable force. Setting up and solving an appropriate differential equation involving variable force.