Mathematics

By the end of Year 13, students will be able to apply and communicate mathematical ideas from across the three main strands of the A Level specification: pure, mechanics and statistics. During the year, students will build on their understanding of pure concepts to extend this to include partial fractions, trigonometric identities, further calculus, parametric equations, differential equations and numerical methods. In the applied part of the course, students revisit the ideas of kinematics and forces in mechanics to expand the application to include two dimensions. In addition, students experiment with the ideas of projectiles, moments and frictional forces. Within the statistics elements of the course students embrace the concept of the normal distribution and deepen their understanding of condition probability. With the introduction of the new specification, they are expected to be able to clean, analyse and draw conclusions from a large data set in a real-life context. Finally, the comprehension part of the assessment is embraced where students need to read an article and interpret mathematical ideas that have been presented. This can include any aspects from the knowledge base that has been developed across their mathematical journey.

Some students continue to study Further Mathematics alongside the A Level Mathematics course. During year 13, students learn the content of the second year of the pure material that forms the 50% of the overall grade when examined. In addition, a third minor module, Numerical Methods, is studied alongside this as the final part of the course. In the pure work completed, students further develop their knowledge of matrices, vectors, proof and series. They also use their newfound mathematical understanding of calculus and complex numbers to learn about hyperbolic functions, polar coordinates, Maclaurin series and differential equations. Within the Numerical Methods work, students revisit some of the methods to solve equations met in the A Level Mathematics course as well as further approaches for numeric integration and differentiation. This compliments several aspects of the year 13 Mathematics course and so supports students in managing the amount of material they need to learn and to be able to successfully apply in the exams at the end of year 13. The content covered in the course provides students with a broad range of knowledge to prepare them for their next steps, whatever this might include.

By the end of Year 12, students will have revisited aspects from their GCSE studies and developed the ability to apply their prior knowledge to more complex problems. In the pure strand of the course, they extend this to include the equation of a circle, polynomial division and the factor theorem, an introduction to calculus, vectors, exponentials and logarithms. They encounter some aspects of probability, data collection and data processing from GCSE but again delve further into related techniques like standard deviation and the formal notation required at A Level. In addition to this, within the statistics element of the course, students meet the idea of the binomial distribution and applying the concept of hypothesis testing to this. At GCSE students will have met the basics of mechanics in the form of the relationships between distance, speed and time as well as velocity, acceleration and displacement. This develops into the knowledge of constant acceleration formulae, variable acceleration and their application in problems. In addition to this, students will meet Newton’s Laws and learn to apply these in one dimension. At the end of the year, students will embrace the first few elements of the second year of the course including sequences, trigonometric equations, radians, proof, functions and more differentiation.

Some students elect to study the Further Mathematics course alongside the A Level Mathematics course. During year 12, students complete the first year of pure content as well as two of the minor units towards the overall qualification, Statistics A and Modelling with Algorithms. The pure module introduces aspects like complex numbers, matrices, sequences, proof and vectors where students must extend their thinking beyond their GCSE studies. All concepts link to prior learning using knowledge of polynomials, rationalising, coordinate geometry and simultaneous equations but in a more abstract manner. Similarly, the Statistics course uses the understanding of probability, averages, scatter diagrams and correlation to analyse and interpret data in a more sophisticated approach. In contrast, the Modelling with Algorithms module develops processes that have not been met before in Mathematics. It allows students to develop methodical approaches to organising information, planning paths and finding optimal solutions to problems that can be expressed mathematically. The pure and the applied modules are learnt concurrently to allow students to develop their knowledge equally and at a sustainable pace.

By the end of Year 11, students will have covered the remaining aspects of the course and revisited each of the six strands covered in year 9 and 10.

For higher students, they will consolidate their understanding of Pythagoras’ Theorem and trigonometry, and extend this to include rules for finding missing sides and angles in any triangle. They will revisit fractions and then consider how these skills can be applied to algebraic fractions, while their knowledge of equations will be extended to include functions and iterations. Work related to graphs will include real-life graphs and considering aspects related to curved graphs both in this context and moving onto circles. The properties and use of vectors will also be explored.

For foundation students, they will revisit their prior learning on linear equations and extend this to both simultaneous equations and linear inequalities. They will focus on the plotting of graphs met previously and apply these skills to quadratics and other curves. At the same time they will develop their algebraic abilities in tackling further factorising and solving of quadratics.

All students will spend time revisiting aspects from throughout the course with a focus on problem solving and application as well as securing a range of methods to apply to the problems faced.

Students in set 1 on the r side, will also continue with their studies towards their Statistics GCSE. In year 11, they will be cover the remaining aspects related to time series, probability which overlaps with the concepts taught in Mathematics, index numbers and probability distributions.

By the end of Year 10, students will have revisited each of the six strands covered in year 9 and built on from here.

For the higher students, number skills are used throughout the material covered but will also be extended to include rules of recurring decimals, indices, surds, counting and limits of accuracy. Geometry is studied further to include Pythagoras’ Theorem, trigonometry in right-angled triangles, similar shapes and circle theorems. Algebra concepts now include straight line graphs, linear and quadratic equations, inequalities and simultaneous equations. Students have their first taste of higher-level probability looking at different ways to calculate with and display probability information including tree diagrams, Venn diagrams and conditional probability. In Statistics, students learn about the use of frequency polygons, cumulative frequency graphs, box plots and histograms. Finally, within the ratio, proportion and rates of change strand, students encounter both direct and inverse proportion where they apply algebraic methods to solve worded problems.

For the foundation students, number skills are not looked at independently this year but are regularly a focus when covering other concepts to ensure that they can be applied in a range of contexts. Geometry has a lot of time dedicated to it across the year. Work is done on perimeter, area, volume and surface area early on in the year before being revisited later when work is done on using Pythagoras’ Theorem and trigonometry in right-angled triangles. Transformations and constructions are also studied during year 10. Algebra is encountered through the solving of equations and exploring sequences and patterns. Foundation students also have their first encounter with more advanced probability here and meet various representations of data in the Statistics elements covered. Finally, within the ratio, proportion and rates of change strand, students encounter both direct and inverse proportion but also have a focus on ratio, compound measures and the use of percentages including in relation to interest.

Students in set 1, will also continue with their studies towards their Statistics GCSE. In year 10, they will be cover the remaining aspects related to time series, probability which overlaps with the concepts taught in Mathematics, index numbers and probability distributions. They will aim to sit their public examination at the end of the academic year.

By the end of Year 9, students will have begun in earnest their GCSE studies. Students start the year working on aspects that provide the foundations for future study. They revisit the basics of number and their properties, including estimation, fractions, decimals and percentages, as well as angle facts, statistical diagrams and averages, and finally working with algebraic expressions and formulae. They will have the chance to recall their knowledge from key stage 3 but will extend this to the requirements of GSCE and put it into practice on examination style questions as well as seeing the real-life applications of each aspect. Moving forwards, students will frequently need to use these skills and apply them to more challenging content as the course progresses.

At this point, students then split into two pathways, either following the higher tier or the foundation tier. The higher students go on to meet sequences, ratio, compound measures, transformations, constructions, areas and volumes. The foundation students work with measurements, 3D shapes, straight line graphs, ratio, proportion and area of 2D shapes. Both groups also complete a recap of the initial algebra work, at the appropriate level, to consolidate and deepen the understanding of this.

Students in set 1, after the tiering decisions have been made, will also embark on studying for GCSE Statistics. In year 9, they will be introduced to the types of data and sampling, to different methods of recording and presenting data and embrace the new ideas of standard deviation and skew while considering summary statistics for data sets.

By the end of Year 8, students will further evolve their understanding of some of the key strands. They expand on the previous year's algebra concepts by attempting to factorise quadratic expressions and further moving onto solving quadratic equations, sequences and finally plotting graphs, both linear, quadratic, reciprocal and cubics. Students will also have to solve simultaneous equations, inequalities, and algebraic fractions which all build on the knowledge gained in Year 7. Students will also progress their knowledge of proportion in Year 8 by extending the idea of direct and inverse proportion wherein they will be plotting graphs and solving algebraically instead of numerically to support with more complex problems. They will also be introduced to the idea of compound measures for the first time in mathematics where they will look at speed, density and pressure which overlaps.

They also develop their number understanding by introducing the ideas of multiples, factors, primes, powers and roots, which have been met at key stage two. They begin to extend these ideas by finding highest common factors and lowest common multiples of larger numbers where prime factor decomposition is necessary. Students are expected to use their understanding of indices to support with this and finally will be presented with standard form.

The students will also enhance their familiarity with geometry by learning about transformations, surface area and volume and plans, elevations and nets which builds upon their knowledge from key stage two whilst tying in the ideas met in Year 7 with regards to area and perimeter of more 2D shapes. Finally, a completely new concept to them will be Pythagoras’ theorem and trigonometry which will encompass many of the skills they have learnt from algebra and geometry in Year 7 and 8.

Once again, they will be continuing to learn about the strand of statistics through the bespoke key stage 3 statistics through excel course we have created. They will by the end of the year, be able to apply statistical tools, using excel and in written form, to complete data sets for them to draw conclusions from and interpret this information in context.

By the end of Year 7, students will have secured their understanding of some key stage 2 concepts across the five primary strands as well as meeting aspects from the sixth secondary strand of probability. In number, this encompasses the fundamental content including the four operations with integers, decimals and fractions, the order of operations, place value, estimating values and calculating with percentages. Throughout the course we expect students to begin to develop their familiarity with algebraic concepts. They start by building on their initial understanding of this content by, more formally, defining algebraic keywords and notation and then continue onto manipulating algebra for the first time. They do this by collecting like terms, substitution, forming expressions, expanding single brackets, and factorising which are the building blocks to algebra.

It is important that students meet algebra again in Year 7 by attempting to formalise the algebraic method to solve linear equations, including, equations with one or two unknowns on each side. Building on from this, students will continue to improve their knowledge of geometry and measures by furthering their understanding of angle facts that they meet in key stage 2 and adding further rules like angles in parallel lines and angles in polygons. As this follows on from solving equations, students can be stretched and challenged by connecting the two strands. Students are also expected to deepen their understanding of perimeter and area of shapes they are familiar with, for instance, parallelograms, triangles, and rectilinear shapes. In addition to this, students will be able to work with areas and perimeters of trapezia, circles, arcs, and sectors by deriving and applying formulae.

Students will also be expected to better their grasp on using and applying ratios and direct and inverse proportion problems. Finally, they will be introduced to the new strand of probability where they will look at calculating simple probabilities both theoretical and experimental, probability diagrams and define key terms from these concepts.

Throughout the year, students will also be experiencing the strand of statistics through a unique course to Ravens Wood which delves into statistics using Microsoft Excel which we feel is an undervalued tool to help with statistical analysis. They will look at finding averages, spreads, creating charts and diagrams (some they have seen in key stage two like bar charts and pictograms) and will begin to understand how to format and use excel efficiently.