**Differentiation **

Students will differentiate exponential and trigonometric functions, related sums, differences, and constant multiples; understand and use the derivative of ln x; apply differentiation to find points of inflection; differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Parametric Equations **

Students will understand and use the parametric equations of curves and conversion between Cartesian and parametric forms; use parametric equations in modelling in a variety of contexts; differentiate simple functions and relations defined parametrically. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Numerical Methods **

Students will locate roots of f(x) = 0 by considering changes of sign of f(x); understand how change of sign methods can fail; solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams; solve equations using the Newton-Raphson method and other recurrence and use numerical methods to solve problems in context. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Differential Equations **

Students will construct simple differential equations in pure mathematics and in context; evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions; interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Probability **

Students will understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables; understand and use conditional probability formulae; model with probability, including critiquing assumptions made and the likely effect of more realistic assumptions. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Normal Distribution **

Students will understand and use the Normal distribution as a model; find probabilities using the Normal distribution; select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Hypothesis Testing **

Students will extend their previous work on Hypothesis Testing to enable them to: carry out a hypothesis test for a product moment correlation coefficient, conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.