Year 13 – Mathematics

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. 

Trigonometric Functions and Identities 

Students will understand and use the standard small angle approximations of sine, cosine and tangent; understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understand their graphs, ranges and domains; understand and use double angle formulae; understand and use rcos(θ ± α) or rsin(θ ± α);  construct proofs involving trigonometric functions and identities; use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Integration 

Students will integrate exponential and trigonometrical functions and their related sums, differences and constant multiples; use a definite integral to find the area between two curves; understand and use integration as the limit of a sum; carry out simple cases of integration by substitution and integration by parts; understand these methods as the inverse processes of the chain and product rules respectively and integrate using partial fractions that are linear in the denominator. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Vectors 

Students will use vectors in three dimensions using both column vectors and i, j, k notation to solve problems including those related to kinematics in up to 2 dimensions, including projectile motion. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Moments 

Students will understand and use moments in simple static contexts. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Forces and Friction 

Students will be able to:  model forces as vectors, resolve forces, be able to answer questions set on an inclined plane or in other contexts that require forces to be resolved; understand that motion may not be restricted to horizontal or vertical and that inclined planes may be used; understand and use addition of forces; resultant forces and the dynamics for motion in a plane. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Projectiles 

Students will model motion under gravity in a vertical plane using vectors. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Application of Forces 

Students will be able to apply their knowledge to solve problems involving smooth pulleys and connected particles. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test. 

Further Kinematics 

Students will be able to use vectors to solve kinematic problems including those requiring the use of calculus.  Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.