Mathematics

Mathematical thinking is important for all members of a modern society as a habit of mind for use in the workplace, business and financial worlds, and for personal decision-making.  Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics.  It is essential in public decision-making and for participation in the knowledge economy.

Mathematics equips students with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all students when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Students who are functional in Mathematics and financially capable are able to think independently in applied and abstract ways, can reason, solve problems and assess risk.  Mathematics is a creative discipline.  The language of Mathematics is international. The subject transcends cultural boundaries and its importance is universally recognised. Mathematics has developed over time as a means of solving problems and also for its own sake.

Students sit three written exams. Each paper is 1 hour 30 minutes and are equally weighted towards the final grade. Paper 1 is a non-calculator paper, Paper 2 and Paper 3 are calculator papers.

The exam board for GCSE Maths at Glyn is AQA.

Students are required to have a scientific calculator for GCSE Maths. The following models from Casio are recommended: fx-85GT CW, fx-83GT CW, fx-991 CW (for those intending to study Maths at A Level).

Mathematics GCSE leads on to A Level Mathematics or Further Mathematics. These A Levels open the door to a large number of degree courses including Mathematics, Engineering, Computer Science, Physics, Finance and Economics.

If you have a particular interest in Mathematics, you could consider careers in Engineering, Financial Services, Teaching, Market Research, Economics, Accountancy or Quantity Surveying.

Half Term 1 - Directed Number and Sequences, Number Sense (Directed Number, Types of Sequences, Compare and Order Numbers, Rounding and Error Intervals, Order of Operations)

Our students’ maths curriculum begins with work on negative numbers, ensuring that students have a firm understanding of how to perform calculations across zero. We then  introduce sequences through pattern spotting and recognising term-to-term rules in a variety of sequences, including the famous Fibonacci sequence. Following this students explore the relationships between numbers, comparing and ordering numbers including those involving decimals and negatives as well as looking at the impact that rounding numbers has. Finally, students extend their understanding of the order of operations from primary school to more complex calculations involving decimals and negative numbers.

Half Term 2 - Algebraic Systems and Numerical Methods (Operations from Expressions, Equations and Equivalence, Factors and Multiples, Prime Factors)

Students begin the second half term with an introduction to algebra, a core concept that will be used throughout their time at Glyn. They are introduced to algebraic notation and terminology, and learn to simplify expressions, substitute values into expressions and solve linear equations. Students then recap and extend their understanding of types of numbers including factors, multiples and primes, including applications with algebraic expressions.

Half Term 3 - Arithmetic Applications (Fractions, Decimals and Percentages, Addition and Subtraction)

A comprehensive review of students’ prior knowledge of fractions ensures that students can fluently convert between a wide range of fractions, decimals and percentages. This extends to more complex numbers and considers strategies both with and without a calculator. The concept of recurring decimals is introduced and explored here as well. Students then practice formal methods of addition and subtraction with a focus on applied problems, including concepts such as financial maths, time and calendar problems, perimeter of compound shapes and interpreting data representations. Mental strategies for addition and subtraction are also discussed to support students’ mental arithmetic.

Half Term 4 - Arithmetic and Geometric Applications (2D Shapes, Multiplication and Division, Fractions and Percentages of Amounts, Area of 2D Shapes and Addition and Subtraction of Fractions)

Concepts related to shapes such as parallel and perpendicular lines, and regular and irregular shapes are discussed to ensure that students have a firm understanding of the properties of 2D shapes.  Students then extend their knowledge of multiplication and division to include calculations with decimals. This allows students to reflect on the common misconception that ‘multiplication always makes something bigger’, which students learn is not always the case… Division leads students into working out fractions and percentage of amounts, including amounts more than a whole (for example, finding 150% of a quantity). Students solve problems involving the area of various shapes, including trapeziums and compound shapes. Finally, students review their understanding of addition and subtraction with fractions, extending this to more complex calculations, including those involving simple algebraic fractions. 

Half Term 5 - Geometric Applications and Algebraic Systems (Angles, Expanding and Factorising Brackets, Multiplication and Division of Fractions)

Formal conventions of labelling angles and lines are introduced before students practice using construction equipment such as protractors and pairs of compasses to construct a variety of shapes. Use of protractors leads nicely into studying pie charts, where students learn to construct accurate representations of data. A fundamental skill of expanding and factorising with brackets is introduced, with students being exposed to a variety of representations and methods to support their fundamental understanding. Multiplication and division of fractions then leads onto the concept of reciprocals and students develop their ability to perform any calculation that involves fractions and mixed numbers. Finally, students solve a range of complex problems involving angles, applying their knowledge of angle facts and algebra to form and solve equations.

Half Term 6 - Probability and Working in the Cartesian Plane

Students round out the year looking at sets and probability, a concept that is no longer taught at Key Stage 2. They are introduced to key terms such as the intersection, union and complements of sets and explore how to interpret Venn diagrams (popularised by John Venn in the 1880s). Vocabulary of basic probability is introduced, as are some fundamental concepts about calculating simple probabilities. The final topic of the year explores work in the Cartesian Plane, where students extend their knowledge of coordinates to explore the links between the equations of straight lines and their gradients.

Half Term 1 - Algebraic and Numerical Techniques (Indices, Brackets and Equations, Inequalities, Multiplying and Dividing Fractions)

Students begin the year by using algebraic notation to solve problems with indices, which will be applied to new concepts throughout the next few topics. This leads on to expansion and factorisation using brackets where students will be able to work with higher powers of variables. Students recap and extend their knowledge of solving equations to solving inequalities, including representing solutions on a number line using inequality notation. Students finish the half term by recapping addition and subtraction of fractions from Year 7 before multiplying and dividing fractions. Students learn about the concept of reciprocals and apply their current knowledge of fractions in algebraic contexts.

Half Term 2 - Representations and Reasoning with Data (Representing Data, The Data Handling Cycle)

Students build on their knowledge of bar charts, pictograms and tables from Key Stage 2 and extend this to other representations such as scatter graphs, pie charts, frequency tables and two-way tables. Various types of data are introduced along with deciding which representations are most appropriate for different types of data. Concepts such as correlation vs causation allow for interesting discussions of how data can sometimes be misleading. With little exposure to data handling at Key Stage 2 this topic allows students to investigate the data handling cycle, design questionnaires and choose how best to represent their results.

Half Term 3 - Proportional Reasoning (Tables and Probability, Sequences, Ratio and Multiplicative Change)

Having looked at representations of data in the previous half term, students consider how to calculate probabilities from sample spaces, two way tables and Venn diagrams. Students then extend their understanding of sequences that began in Year 7, including generating both linear and non linear sequences from algebraic rules before working out the nth term of linear sequences. Following this, students are introduced to ratio notation, understanding the multiplicative links between quantities and using proportional reasoning to solve problems. Graphical representations of variables in direct proportion, including currency conversions, link students' knowledge of the Cartesian Plane with ratio and multiplicative change. 

Half Term 4 - Developing Geometry (Fractions and Percentages, Area and Perimeter, Angles in Parallel Lines, Angles in Polygons)

After briefly studying further calculations involving fractions and percentages, including increasing and decreasing quantities by a fraction or percentages, students recap and review the concepts of perimeter and area. This involves more complex shapes than previously studied, including the exploration of circles and an understanding of the value of π. This provides a lovely opportunity to extend beyond the curriculum with investigations of the area and circumference of circles alongside discussing the history of π seen through the centuries. Students extend their knowledge of angles to solve problems involving parallel lines and polygons beyond triangles and quadrilaterals. An emphasis on using correct mathematical terminology is important here and students explore the meaning of terms such as corresponding, alternate and co-interior angles as well as polygons, regular vs irregular shapes and the names of 2D shapes. Properties of special quadrilaterals are also explored, including concepts of symmetry that will be further explored later in the year.

Half Term 5 - Developing Number, Algebra and Data (Standard Index Form, Further Linear Equations, Measures of Location and Spread)

Students are taught standard index form which builds on from indices studied earlier in the year. The use of context is important to help students make sense of the need for the notation and when it is useful, including looking at incredibly large and incredibly small objects within our universe. Students then move onto application of equations which builds on from one and two step equations to solving equations with unknowns on both sides and with expansion of brackets taught earlier this year. This leads on to forming and solving equations using contextual problems such as area and perimeter, sequences and angles in parallel lines and polygons. Students complete the half term by looking at measures of location and spread which is built on from Year 7, recapping mean, median and range and introducing the mode, while also looking at why and when each average should be used. 

Half Term 6 - 2D and 3D Geometry (Line Symmetry and Reflection, 3D Shapes, Volume and Surface Area)

Students finish Year 8 with a focus on shapes. Concepts of symmetry and reflection from Key Stage 2 are reviewed and extended to make use of students’ understanding of the Cartesian Plane. Knowledge of 2D shapes is extended to 3D shapes, allowing students to name and identify properties of 3D shapes. Plans, elevations and nets of 3D shapes are explored using a mixture of concrete and digital resources to support students’ understanding and visualisation. Finally, students calculate the volume and surface area of cuboids, prisms and cylinders, including considering problems linked with capacity.

Half Term 1 - Reasoning with Algebra (Equations and Inequalities, Rearranging Formulae, Straight Line Graphs)

Students revisit forming and solving multi-step equations and inequalities, bringing together knowledge of expanding brackets and solving equations with unknowns on both sides. This topic is extended to use of negative coefficients for inequalities and applications to concepts such as measures of location and spread and volume and surface area. Use of inverse operations to solve equations is linked to rearranging formulae, ahead of rearranging equations of straight line graphs to decide if lines are parallel, perpendicular or neither.

Straight line graphs are extended from plotting graphs using y=mx+c to quantifying and interpreting the meaning of gradients and intercepts. Students work out the equation of lines from a graph and explore links between parallel lines and perpendicular lines in preparation for working out the equation of parallel and perpendicular lines in Year 10. 

Students begin the year reviewing their ability to use construction equipment from year 7 and build towards introducing the concept of congruence. Other types of constructions are introduced, including the idea that a perpendicular is the shortest distance from a point to a line. These constructions also form the basis of solving loci problems in year 10. Students then compare and contrast the ideas of congruence and similarity through learning how to enlarge shapes using positive, negative and fractional scale factors. The idea of proportion in similar shapes leads nicely into further study of ratio and proportion, applying this to new contexts such as best buy problems, graphs and algebra.

Half Term 2 - Constructions and Proportional Reasoning (Constructions, Congruence, Enlargement and Similarity, Rotation and Translation, Geometric Reasoning)

A review of constructions from Year 7 begins this half term, with students extending their ability to use equipment to construct perpendiculars and angle bisectors. Constructing triangles leads nicely into congruence, where students explore the conditions for which triangles can be congruent. Congruence is then further extended to similarity, where students learn to enlarge shapes by a given scale factor. More transformations of shapes, namely rotations and translations, are explored so that students have now seen all four transformations, including reflections seen in Year 8. The half term rounds off with an emphasis on recapping and proving geometric results.

Half Term 3 - Reasoning with Number and Proportion (Types of Numbers, Ratio and Multiplicative Change)

The term begins with a recap of fundamental number skills and concepts including fractions, decimals, directed numbers, factors, multiples and primes. Students’ understanding of types of numbers is then extended to explore the idea of real numbers and rational vs irrational numbers, including the term surds which will be studied in greater depth in Year 10. Students then study proportional reasoning, building on their knowledge from Year 8 to solve more advanced problems. The concept of inverse proportion is introduced in contrast to direct proportion problems students have seen to this point.  

Half Term 4 - Reasoning with Proportion and Right-Angled Triangles (Rates and Compound Measures, Pythagoras’ Theorem, Introduction to Trigonometry)

Students continue their reasoning with proportion to look at rates and compound measures such as speed-distance-time and density-mass-volume problems. Proportional reasoning is used to help students convert between units of measure, recapping metric conversions before converting more difficult compound units, for example converting between m/s and kph. Following this, students get to know one of history’s most famous mathematicians, Pythagoras, as they are introduced to his famous theorem about right-angled triangles. Alongside learning about the man, students investigate why the theorem works before becoming fluent in using it to solve problems. This study of right-angled triangles is extended to an introduction to trigonometry and the ratio between sides using sine, cosine and tangent. This will be explored in greater depth in Year 10. 

Half Term 5 - Reasoning with Number (Rounding and Estimation, Using Percentages, Maths and Money)

Students explore the value of rounding and estimation in real life, discussing how this can be appropriate at certain times when an exact answer is not required (for example, when working out an estimated total when shopping). Rounding, taught in previous years, is extended to concepts of upper and lower bounds as well as truncation. Percentage calculations, such as reverse percentages, is studied before leading into a fascinating insight into applications of maths in money including tax rates, mortgages, rent, inflation, bank statements and budgeting. Students also spend time developing their understanding of spreadsheet tools to support these concepts to prepare them for managing their finances in adulthood.

Half Term 6 - Delving into Data (Probability, Measures of Location and Spread)

Students recap their understanding of probability from previous years before discussing the difference between theoretical and experimental probabilities. An appreciation that probabilities based on large sample sizes are increasingly reliable is discussed as well as how many times we expect outcomes to happen based on their probability and number of trials. Students then review how to calculate measures of location and spread, extending their knowledge from Year 8 to calculate measures from ungrouped and grouped frequency tables. A discussion about why we can only make estimates from grouped data rounds out the year.

Half Term 1 - Developing Algebra (Equations and Inequalities, Straight Line Graphs, Quadratics, Simultaneous Equations)

Year 10 begins with an important review of students’ ability to solve equations and inequalities, including representing inequalities and regions on graphs. Working with graphs leads students into working out the equations of straight lines given gradients and coordinates on a line. Students extend their understanding of expansion and factorisation with single brackets to now work with quadratic expressions and equations, which involves students understanding that an equation can have multiple solutions. The half term finishes with solving simultaneous equations, building on the work completed on linear and quadratic equations and again supporting students’ understanding of different types of solutions to equations, this time with more than one type of variable.

Half Term 2 - Similarity and Trigonometry (Congruence, Similarity and Enlargement, Pythagoras and Trigonometry)

Students recall their knowledge of similarity and congruence from Year 9 and build on this to construct proofs for whether or not shapes are congruent. Alongside this, students extend ideas of similarity to areas and volumes of shapes. A review of Pythagoras and Trigonometry covered in Year 9 is provided to ensure students are fluent in their calculations, while students are then encouraged to interpret questions to decide which formula is needed in each case to support their depth of understanding.

Half Term 3 - Proportions and Proportional Change (Loci, Percentages and Interest, Advanced Ratio, Direct and Inverse Proportion)

The half term begins with an extension of constructions covered in Year 8 and Year 9 into the concept of loci, which allows students to apply their ability to construct to solve problems. Students then recap a variety of percentages calculations, including simple and compound interest, before extending this to repeated percentage changes such as with growth and decay. More advanced ratio problems are then studied, including combining ratios and linking ratio and algebra to solve more complex problems. A more algebraic approach to direct and inverse proportion is then taught, where students are encouraged to form and solve proportion equations including powers and roots.

Half Term 4 - Geometry (Volume and Surface Area, Angles and Bearings, Vectors)

Volume and surface area links back to similar shapes and ratios but also introduces new shapes such as pyramids, cones and spheres. Angles and bearings provide the students with an opportunity to recall their understanding of angles in parallel lines as well as exploring Pythagoras’ theorem and trigonometry in different contexts. An exploration of where bearings are used in real life, and the history behind why they are given as three-figure bearings provides an interesting discussion. The concept of a vector, in contrast to scalars that students have thus far used, broadens students’ understanding. Representing vectors visually and performing calculations with them builds on vector notation covered when studying translations and extends further to vector geometry problems.

Half Term 5 - Further Data (Collecting, Representing and Interpreting Data, Probability)

Collecting, representing and interpreting data builds on Key Stage 3 topics including bar charts, pie charts and scatter graphs by enabling students to understand how data is collected, including sampling methods, and introduces more representations of data such as cumulative frequency diagrams and box plots. Students review their understanding of probability and then look at using probability tree diagrams to calculate probabilities of successive independent events and explore tree diagrams as another representation of outcomes.

Half Term 6 - Using Number and Transformations of Shapes (Non Calculator Methods/Recurring Decimals and Surds, Types of Sequences, Indices and Roots, Transformations of Shapes)

Students explore the number line outside rational numbers, and the concept of using exact values as solutions. At foundation level this is consolidated with working with non-calculator problems such as exact trigonometric values and problems involving pi. At the higher tier this extends to working with surds and recurring decimals. Students then review their knowledge of sequences, building from linear sequences to look at geometric and quadratic sequences and finding nth term of quadratic sequences at the higher tier. Students also explore the golden ratio and its links to the Fibonacci sequence. Indices and roots build on squares, cubes, roots and rules of indices as well as standard index form by working on negative and non-integer powers, including the concept of raising a term to the power of zero. Finally, students review their knowledge of transformations of shapes with a greater emphasis on describing transformations using appropriate mathematical terminology. 

Half Term 1 - Advanced Algebra (Quadratics, Simultaneous Equations, Inequalities)

Students review their key algebra skills including expanding, simplifying, factorising and rearranging in the area of quadratics. This extends to forming quadratic equations and using quadratic graphs to find approximate solutions. Higher students learn ways of solving quadratic equations that do not factorise, by completing the square and using the quadratic formula. Next, students review their understanding of solutions from linear graphs into solving simultaneous equations, a concept first seen in Year 10. The focus here will be on students forming and then solving simultaneous equations from various contexts. Students move on to recapping inequalities before solving more complex inequalities than seen previously, including quadratic inequalities for the higher tier. 

Half Term 2 - Geometry and Probability (Working with Circles, Probability)

Students spend a large amount of time working with circles, beginning with a recap of prior knowledge about area and circumference. These calculations are extended to sectors of circles, where students work out arc lengths and areas. At the higher tier, students study circle theorems, including exploring some proofs of why these are always true. Students also study the equations of circles centred around the origin and equations of tangents to circles.

Students then move onto probability, with a focus on Venn diagrams, including use of set notation and terminology, as well as independent, dependent and conditional probability. Students at foundation tier also spend some time reviewing their understanding of straight line graphs in order to develop their fluency and understanding.

Half Term 3 - Geometry and Algebra (Trigonometry, Non Linear Graphs, Algebraic Fractions)

Students consolidate their understanding of trigonometry learnt in previous years, with higher tier students extending this to trigonometry involving non right-angled triangles. These new skills are also linked with other topics such as bearings and working out the areas of segments of circles. Students explore non linear graphs, building on their knowledge of straight line graphs and quadratics to look at cubic, reciprocal, exponential and trigonometric graphs. Higher tier students then work with more complex algebraic fractions, applying their understanding from numbers to use the four operations with algebraic fractions and simplifying through factorisation. A recap of solving quadratic equations is taught through the context of forming said equations from algebraic fractions.

Half Term 4 - Algebra, Graphs and Proof (Functions, Iteration, Transformations of Graphs, Real Life Graphs, Proof)

Students consider algebraic functions, moving from basic function machines to using function notation. Composite and inverse functions extend students’ algebraic thinking and test their fluency with a number of algebraic skills. Iteration provides a recap of substitution while also helping students consider ways of solving equations when other methods fail. Higher tier students then move onto transformations of graphs, including translations and reflections, working with a variety of non linear graphs seen previously. All students study real life graphs, including distance-time graphs and speed-time graphs, using these to work out missing information such as distance covered, acceleration etc. At the higher tier, students also look at estimating areas and gradients of non linear graphs and interpret results in a variety of contexts. During this half term, students are taught how to construct proofs, with a focus on reasoning and correct mathematical notation. 

Half Term 5 - Histograms and Revision

Students studying the higher tier will recap their understanding of data, especially cumulative frequency and box plots, before studying their final representation of data; histograms. A variety of problems will be tackled in order to develop students' fluency and understanding of histograms and continuous data, including using histograms to work out estimates for the mean and comparing distributions using a variety of representations.

All students at this stage will be preparing towards their GCSE Exams: practising their exam techniques and applying their knowledge and skills into a broad range of questions. 

Half Term 6 - Exams

Students sit their GCSE Exams during this half term. All that waits is to receive results in the summer and, for many, to complete summer induction material in preparation for studying A Level mathematics.

First year teaching (Year 1)

Half Term 1 (AS topics)

Baseline Test and submission of summer transition work.

Algebraic expression; Quadratics; Equations and inequalities; Graphs and transformations; Straight line graphs; Circles (geometry); Data collection (LDS).

Why we sequence the scheme of work this way

Revisit, consolidate and extend algebraic techniques, concepts, skills and processes from GCSE.

Teach and encourage the use of mathematical notations and symbols in presenting solutions and arguments.

Deepen understanding of 2D spaces, and geometry.

Introduce statistical sampling techniques and the large data set for familiarisation. This aspect of statistics is embedded throughout the statistics course - introducing it early enables regular revisiting and retrieval and familiarisation. 

Additionally, there are more Statistics content in Year 1, compared to Year 2 (the reverse for Mechanics). Teaching statistics early allows for interleaving of topics: Pure and Applied; and opportunities for retrieval, and revisiting topics (if needed).

Half Term 2 (AS topics)

Algebraic methods; Vectors; Measures of location and spread; Representation of data; Modelling with mechanics; Constant acceleration.

Why we sequence the scheme of work this way

Revisit, consolidate and extend concepts, skills and processes from GCSE.

Formalise and deepen methods for mathematical proofs.

Encourage and apply higher-order thinking and reasoning in logic, sense of proportion and use of powerful statistical representations.

Encourage higher order spatial awareness through the study of vectors and motion graphs (kinematics).

Develop understanding for modelling and assumptions for modelling in mathematics: pure and applied - an essential skill and assessment objective embedded throughout the course.

Assessment 1

Half Term 3 (AS topics)

Binomial expansion; Trig ratios; Trig identities and equations; Exponentials and logs; Correlation.

Pre-public examination 1.

Why we sequence the scheme of work this way

Revisit, consolidate and extend concepts, skills and processes from GCSE.

Introduce new concepts such as binomial theorem, exponentials and logarithms.

Connecting concepts e.g. mathematical approximations and estimations with mathematical models e.g. abstractions of real-world problems.

Half Term 4 (AS topics)

Trig identities and equations; Exponentials and logs; Differentiation; Probability; Statistical distribution; Forces and motion. 

Why we sequence the scheme of work this way

Continuation of topics taught in Half Term 3 e.g. Trig identities and equations etc.

Extend concepts from GCSE e.g. pre-calculus (gradient of curve)

Connect and apply  more mathematical concepts, skills and processes with mathematical and scientific models and phenomena through the study of statistical distributions; forces and motion. 

Consolidate and further develop mathematical modelling skills.

Half Term 5 (AS topics)

Differentiation; Integration; Statistical distribution; Hypothesis testing; Variable acceleration.

Why we sequence the scheme of work this way

Continuation of topics taught in Half Term 4 e.g. Differentiation etc

Extend concepts from GCSE e.g. pre-calculus (gradient of curve and area under graph).

Further develop analytical reasoning; and proof through the study of calculus.

Apply calculus (rates of change) in the study of kinematics in mechanics.

Prepare students for pre-public examinations (exam literacy and resilience); Prepare students for A level content in Year 2.

Half Term 6 (A level topics)

Conditional probability; Forces and friction.

Why we sequence the scheme of work this way

Teaching of A level applied content: Teaching A level applied topics early allows for interleaving of topics: Pure and Applied; and opportunities for retrieval, and revisiting topics (if needed). 

There are more mechanics content to be taught than Statistics in Year 2 - practically, prioritising teaching applied content enables coverage of the whole course in time by Half Term 5 (all of Pure by Half Term 4) in the following year.

Second year teaching (Year 2)

Half Term 1 (A level topics)

Baseline test and submission of summer transition work.

Algebraic methods; Functions and graphs; Sequences and series; Radians; Moments.

Assessment 1.

Why we sequence the scheme of work this way

Extend and apply Year 1’s knowledge and processes.

Develop more advanced algebraic techniques; concepts in geometry and trigonometry.

There are more mechanics content to be taught than Statistics in Year 2 - practically, prioritising teaching applied content enables coverage of the whole course in time by Half Term 5 (all of Pure by Half Term 4) in the following year. 

Half Term 2 (A level Pure topics)

Sequences and series; Binomial expansion; Vectors; Trig functions; Trig and modelling.

Pre-public examination 1.

Why we sequence the scheme of work this way

Continuation of topics taught in Half Term 1 e.g. Sequences and series etc

Extend and apply Year 1’s knowledge, processes, more advanced algebraic techniques and concepts. 

No Year 2 applied content taught in this term; however, students are encouraged to revisit Year 1 and some Year 2 content taught regularly.

Prioritising completion of Pure content by Half Term 4 for students to be assessed on two-thirds of the A level paper (Pure).

Half Term 3 (A level Pure topics) 

Trig and modelling; Parametric equations; Differentiation; Numerical methods; Integration.

Why we sequence the scheme of work this way

Continuation of topics taught in Half Term 2 e.g. Trig and modelling etc

Extend and apply the previous terms’ and/or year’s knowledge, skills and processes.

No Year 2 applied content taught in this term; however, students are encouraged to revisit Year 1 and some Year 2 content taught regularly.

Prioritising completion of Pure content by Half Term 4 for students to be assessed on two-thirds of the A level paper (Pure).

Prepare students for pre-public examination 2.

Half Term 4 (A level Topics)

Differentiation; Integration; Regression and correlation; The normal distribution; Projectiles; Application of forces.

Pre-public examinations 

Why we sequence the scheme of work this way

Extend and apply the previous terms’ and/or year’s knowledge, skills and processes.

Year 2 applied content taught in this term: opportunity to revisit and extend knowledge from Year 1 applied content.

Prioritising completion of Pure content by Half Term 4 for students to be assessed on two-thirds of the A level paper (Pure).

Half Term 5 (A level Applied topics)

The normal distribution; Application of forces; Further kinematics/

Why we sequence the scheme of work this way

Extend and apply the previous terms’ and/or year’s knowledge, skills and processes.

Year 2 applied content taught in this term: opportunity to revisit and extend knowledge from Year 1 and 2 applied content.

Completion of A level applied topics, thus, the whole course for the last stage of exam preparation and A level examinations.

Half Term 6

A Level Examinations

Why we sequence the scheme of work this way

The topics are sequenced based on students’ prior knowledge, in order of difficulty and complexity, and exposure to relevant mathematical concepts, skills and processes in order to promote coherence and depth in understanding, fluency in skills and processes, retrieval of knowledge and better problem solvers and mathematical modellers.

A Level Mathematics Curriculum Sequencing

Consecutive Delivery: A Level Mathematics in the first year 

(Topics listed match the Pearson Edexcel Textbook for Year 1 and 2)

Half Term 1 (AS topics) 

Baseline Test and submission of summer transition work

Algebraic expressions; Quadratics; Equations and inequalities; Graphs and transformations; Straight line graphs; Circles; Vectors; Data collection (LDS); Measures of location and spread; Representation of data; Correlation; Modelling with mechanics; Constant acceleration.

Half Term 2 (AS and A level topics)

Algebraic methods; Binomial expansion; Trig ratios; Trig identities and equations; Differentiation; Integration; Exponentials and logs; Correlation; Probability; Conditional probability; Statistical distribution; Hypothesis testing; Forces and friction. 

Assessment 1

Half Term 3 (AS and A level topics)

Integration; Algebraic methods; Functions and graphs; Sequences and series; Radians; Differentiation; Regression, correlation and hypothesis testing; Variable acceleration; Forces and friction; Moments.

Pre-public examination 1

Half Term 4 (A level topics)

Functions and graphs; Sequences and series; the binomial expansion; Trig functions; Trig modelling; Parametric equations; Differentiation; Integration; The normal distribution; Projectiles; Application of forces.

Half Term 5 (A level topics)

Numerical methods; Integration; Vectors; The normal distribution; Application of forces; Further kinematics.

Half Term 6 (A level further topics)

Pre-public examination 2.

Complex Numbers (Core Pure 1); Series(Core Pure 1); Poisson and Binomial Distributions; (Further Statistics 1); Momentum and Impulse (Further Mechanics 1).

Why we sequence the scheme of work this way

Further maths builds and extends from A Level maths. We adopt the consecutive delivery path: further maths being taught after maths, because most content in maths is prerequisite knowledge; and establishes foundational understanding for further maths. This better promotes coherence and in-depth understanding, retrieval and association of essential knowledge, fluency in skills and processes. 

Consecutive Delivery: A Level Further Mathematics in the second year 

(Topics listed match the Pearson Edexcel Textbook for Core Pure, Further Statistics 1, and Further Mechanics 1)

Half Term 1 (A level further topics)

Baseline Test and submission of summer transition work.

Argand diagrams; Roots of polynomials; Volumes of revolution; Matrices; Linear transformations (matrices); Vectors; Discrete random variables; Geometric and negative binomial distribution; Hypothesis testing; The central limit theorem; Work, energy, and power; Elastic strings and springs.

Assessment 1

Half Term 2 (A level further topics)

Proof by induction; Vectors; Complex numbers; Series; Volumes of revolution; Chi-squared test; Elastic collisions in 1D’ Elastic collisions in 2D.

Pre-public examination 1.

Half Term 3 (A level further topics)

Polar coordinates; Hyperbolic functions; Methods in calculus; Methods in differential equations; Modelling with differential equations;  Probability generating functions; Quality of tests; Elastic collisions in 2D.

Half Term 4 (A level further topics)

Review of A level Mathematics and Further Mathematics;  Preparation for PPE 2.

Pre-public examination 2.

Half Term 5 (A level further topics) 

Review of A level mathematics and further mathematics; Preparation for A level examinations

Half Term 6

A level examinations.

Why we sequence the scheme of work this way

Most of the Core Pure, Further Statistics 1 and Mechanics 1 topics are built on, and extended from the A Level maths.

The further maths content/topics are sequenced in order of complexity and difficulty that builds from either the A Level maths or the previous topics. This aims to promote coherence and depth in understanding, precision in performing algebraic, numerical and graphical analyses, retrieval in knowledge, fluency in skills and processes for students to be better problem-solvers, and modellers in mathematics.

A Level Further Mathematics Curriculum Sequencing