This module consists of constructing and presenting mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction and the use of precise statements involving the correct use of symbols and connecting language.
A Level Mathematics Year 12 & 13
Year 12 & 13 A Level Mathematics Course Modules
This module consists of developing the ability to recognise the underlying mathematical structure in a situation and then simplify and abstract appropriately to enable problems to be solved.
Mathematical modelling involves being able to translate a situation in context into a mathematical model, making any simplifying assumptions.
This module teaches the ability to be able to understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion, disproof by counter example and proof by contradiction.
Detailed and extended work based on the skills already taught at GCSE.
A development of the work at GCSE and the introduction of Parametric Equations and their uses.
This module covers Binomial, Recursive, Arithmetic and Geometric Sequences as well as Sigma Notation.
Radian measure is introduced as are cosec, secant, cotangent, arcsin, arccos and arctan. Trigonometric identities are used to solve trigonometric equations in a given interval. The use of double angle formulae is expected.
A detailed look at exponential and logarithmic functions leading to being able to understand and use exponential growth and decay and their use in modelling (examples may include the use of e in continuous compound interest, radioactive decay, drug concentration decay, exponential growth as a model for population growth). A consideration of limitations and refinements of exponential models is expected.
Differentiation is the related rate of change of one variable with another. Students will be expected to know, understand and be able to use differential calculus to differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions. They will also be expected to differentiate simple functions and relations defined implicitly or parametrically, and construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand).
Students will be expected to know and use the Fundamental Theorem of Calculus, evaluate definite integrals; use a definite integral to find the area under a curve and the area between two curves and understand and use integration as the limit of a sum. The will also be expected to be able to evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions and then interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution; this includes links to kinematics.
Numerical Methods involves uses methods such as Iterative, Recurrence, Newton-Raphson and Trapezium in order to solve problems in context
Students will be expected to be able to calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form. They will also be expected to understand and use position vectors; calculate the distance between two points represented by position vectors and use vectors to solve problems in pure mathematics and in context, including forces and kinematics.
Students will be expected to understand and use fundamental quantities and units in the SI system: length, time, mass, as well as understand and use derived quantities and units such as velocity, acceleration, force, weight and moment.
Students will be expected to understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph. They will also be expected to use calculus in kinematics for motion in a straight line and extend this to 2 dimensions using vectors.
Students will be expected to understand and use Newton’s laws and their application to problems involving smooth pulleys and connected particles. They will also be expected to resolve forces in 2 dimensions; find the equilibrium of a particle under coplanar forces, understand and use addition of forces; resultant forces and dynamics for motion in a plane. In addition, they will understand and use the F ≤ ߤR model for the motion of a body on a rough surface and limiting friction and statics.
Students will be expected to understand and use moments in simple static contexts.
Students will be expected to understand and use the terms ‘population’ and ‘sample’, use samples to make informal inferences about the population, understand and use sampling techniques, including simple random sampling and opportunity sampling and select or critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions about the population.
Students will be expected to interpret measures of central tendency and variation, extending to standard deviation, be able to calculate standard deviation, including from summary statistics and recognise and interpret possible outliers in data sets and statistical diagrams. They will also be able to select or critique data presentation techniques in the context of a statistical problem and be able to clean data, including dealing with missing data, errors and outliers.
Students will be expected to be able to model with probability, including critiquing assumptions made and the likely effect of more realistic assumptions.
Students will be able to understand and use the Normal distribution as a model, find probabilities using the Normal distribution and the link to histograms, mean, standard deviation, points of inflection and the binomial distribution. They will be able to select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate.
Students will be able to conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context.