Before we look at GCSE content it is essential that we look at changes for the younger years, both KS2 and KS3. See the new Key Stage 3 programme of study and From Complete Mathematics a very useful document: Annotated KS3 Curriculum Changes is annotated clearly with changes that were made in this programme of study. Note that you can also find information on changes to the Primary curriculum in this collection of resources; note also with the free resources, the Primary Maths Hokey Cokey. Additionally, see this very clear post from Michael Tidd on 10 things you might not have realised about the new Primary Maths curriculum. and also his article on changes to the Maths and English KS2 Tests. See also KS2 Mathematics 2016 teacher assessment exemplification, and the KS1 version.
A very useful source of ideas, a site I have always found valuable, Kenny’s Pouch which includes many free resources for the new National Curriculum.
Reading various documents on the new GCSE specifications I thought it would be useful to create a simple summary of new content.
Note the very useful general resources at the end of this post.
They will also be expected to know Long Multiplication & Division – Formal Methods
Note the increased emphasis on Problem Solving
Note that another page GCSE Content – Resources lists the resources only.
Structure and Calculation
5. apply systematic listing strategies including use of the product rule for counting
Resources: Combinatorics on Brilliant (create a free account to view)
Systematic Listing Strategies – a collection of problems
Measures and Accuracy
15. round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding
use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b
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Ratio, proportion and rates of change
1. change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts
8. relate ratios to fractions and to linear functions
9. define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics
11. use compound units such as speed, rates of pay, unit pricing, density and pressure
15. interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts
16. set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.
Ratio and Proportion Problems
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Notation, vocabulary and manipulation
4. simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: collecting like terms, multiplying a single term over a bracket, taking out common factors, expanding products of two or more binomials
7. where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’.
9. plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points, or through one point with a given gradient
11. identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
12. recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function, with x ≠ 0, exponential functions and the trigonometric functions (with arguments in degrees) y = sin x , y = cos x and y = tan x for angles of any size
15. calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts
16. recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point.
Expand three brackets
Functions – introduction and further resources: Functions
Use Desmos to explore tangents to a curve
Introducing Calculus – blog post and resources
Use Desmos to explore tangents to circle through given point
Use Desmos to explore circles and tangents
BBC Bitesize – Finding the equation of a tangent to a circle
Circles & tangents – Diagnostic Questions Quiz
Check work on WolframAlpha
Solving equations and inequalities
17. solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph
18. solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph
20. find approximate solutions to equations numerically using iteration
22. solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph
24. recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a rational number > 0 or a surd) and other sequences
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Geometry and measures
Properties and Constructions
2. use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line
8. describe the changes and invariance achieved by combinations of rotations, reflections and translations
Mensuration and calculation
21 know the exact values of sinθ and cosθ for θ = 00, 300, 450, 600 and 900; know the exact value of tanθ for θ = 00, 300, 450 and 600
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1. record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
6. enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
9. calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams.
Resources: Probability – the change in content and further resources
From Nrich Prize Giving and note the Frequency Tree representation
From TES: Frequency Trees
Also on TES: Dave Gale’s excellent Frequency Trees Resource
2 interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use
- AQA GCSE Maths
- AQA Assessment Resources
- AQA Teaching Guidance Extract
- AQA All About Maths – many resources for teachers who offer, or are considering offering AQA maths qualifications.
- AQA Bridging the Gap excellent resources, useful too for ideas to teach KS3.
- AQA Topic Tests
- AQA Exemplar Student Responses for trial of practice papers
- Edexcel GCSE Maths Edexcel Mathematics 9-1
- Edexcel Teacher Support, includes many Practice Papers
- Edexcel Mathematics Emporium – many valuable resources, teachers using any board can register
- Eduqas GCSE (9-1) Mathematics
- Transition Units – Cambridge
- Rich Tasks
- Rich Questions
- From Just Maths: 9-1 Exam questions by topic
- Resourceaholic from Jo Morgan – links to support the teaching of new topics in GCSE Mathematics.