**Foundation and Higher tier Maths GCSE syllabus.**

Knowing the new topic areas for each tier can be helpful in preparing your child for the summer exams.

With the introduction of the Maths 9-1 GCSE new material was introduced that was not part of the old GCSE syllabus. This change was made to make these exams more challenging. Therefore, it’s good to know which topics your child should be paying extra attention to!

This list can also serve as a useful revision checklist. Clearly laid out are the new topic areas for each tier as well as any new topics that are required learning for both tiers.

**Firstly, you may be wondering, why are there two tiers in the new maths GCSE?**

Each student must either take the higher or the foundation tier. They differ in content, and grading. For the higher tier paper your grade will be in the range 4 to 9.

If you are looking for information on the sample papers and grade boundaries please see our blog ‘New Maths 9-1 GCSE’.

**SO, new topics have been added to the Maths 9-1 GCSE syllabus, but what are they?**

**The Foundation Tier**

Candidates for the new Maths 9-1 GCSE who are sitting the foundation tier are now required to learn content that was previously only a requirement for higher tier students.

New content requirements for foundation students:

- Calculate exactly with multiples of π
- Use standard form
- Round to any number of significant figures (currently 1 s.f. only)
- Expand double brackets
- Factorise quadratics including the difference of two squares
- Solve quadratic equations by factorising
- Know the difference between an equation and identity
- Use y = mx + c to identify parallel lines
- Sketch quadratic, cubic and reciprocal functions
- Problem involving compound interest
- Derive simultaneous equations from real-life situations
- Solve linear simultaneous equations algebraically and graphically
- Perform calculations with density, mass and volume
- Solve problems involving percentage change and reverse percentages
- Use direct and inverse proportion graphically and algebraically
- Find corresponding lengths in similar shapes
- Use the congruence criteria for triangles (SSS, SAS, ASA, RHS)
- Enlarge shapes with fractional scale factors
- Find the areas and perimeters of compound shapes involving circles, and calculate arc lengths and areas of sectors.
- Use the sin, cos and tan trigonometric ratios for right-angled triangles
- Use tree diagrams to solve probability questions
- Infer properties of a population from a sample, while knowing the limitations of sampling.

In addition, foundation students are required to learn extra formulae that will not be on the formulae sheet.

These include

**The Higher Tier**

Some syllabus material that previously was taught at A level will now be a requirement of higher tier students.

New content for higher tier

- Recognise and use the equation of a circle centred at the origin
- Find the equation of a tangent to a circle at a given point.
- Find approximate solutions to equations using iteration
- Solve quadratic inequalities
- Find the nth term of a quadratic sequence
- Recognise and use geometric sequences where the common ratio may be a surd
- Apply the concepts of instantaneous and average rates of change by looking at the gradients of tangents and chords to a curve
- Prove the circle theorems
- Use the probability “AND” and “OR” rules
- Change recurring decimals into their corresponding fractions and vice versa
- Find inverse and composite functions
- Locate turning points of quadratic functions by completing the square
- Sketch y = tan x (in addition to sin and cos)
- Interpret areas under graphs and gradients of graphs in real-life contexts

For the higher tier, additional formulae required to memorise include:

It is also worth knowing there is significant new content that will appear in both the Foundation and Higher tier papers.

- Find the equation of a line through two points or through one point with given gradient
- Recognise and use sequences of triangular, square and cube numbers, Fibonacci type sequences, quadratic sequences and geometric sequences
- Calculate compound measures including pressure in numerical and algebraic contexts
- Express a multiplicative relationship between two quantities as a ratio or a fraction.
- Write a ratio as a linear function
- Set up, solve and interpret growth and decay problems
- Use inequality notation to specify simple error intervals due to truncation or rounding Understand the≠ s symbol
- Use the standard convention for labelling sides and angles of polygons.
- Derive the sum of angles in a triangle
- Work with percentages greater than 100%
- Know the exact values of sin and cos for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan for θ = 0°, 30°, 45° and 60°.
- Consider outliers when calculating the range of distribution.
- Know that correlation does not imply causation.
- Use Venn diagrams.

Its is very important that your child understands what knowledge and skills are required for the tier they are taking. Students studying higher tier, for example, need to know what extra knowledge is required for topics that also appear on the foundation tier.

For this level of insight we recommend a private tutor to provide your child with tailored one-to-one support.

On the Tutorfair website enter your postcode and Tutorfair will show you GCSE Maths tutors in your area, with the top rated tutors!

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