#### The new GCSE Maths syllabus is bigger than the old GCSE syllabus and requires more teaching time

“*The new mathematics GCSE will demand deeper and broader mathematical understanding … it will be more demanding and we anticipate that schools will want to increase the time spent teaching mathematics. On average, secondary schools in England spend only 116 hours per year teaching mathematics, which international studies show is far less time than that spent on this vital subject by our competitors. Just one extra lesson each week would put England closer to countries like Australia or Singapore who teach 143 and 138 hours a year of mathematics respectively. We announced on 14 October that mathematics, alongside English, will be double weighted in secondary school performance measures from 2016. This will also provide a strong incentive for schools to ensure that they are strengthening their mathematics provision.*”

Michael Gove, former Education Secretary

#### Some Higher Tier Maths topics have been moved into the Foundation Tier, a few A-Level Maths topics have been introduced into the Higher Tier

The additional topics moved from the Higher Tier to the Foundation Tier are listed below (topics in bold are completely new):

Number

- Index laws: zero and negative powers (but not fractional powers)
- Standard Form
- Compound interest and reverse percentages
- Direct and inverse proportion
- Multiples of π
**Use inequality notation to specify simple error intervals due to truncation or rounding**

Algebra

- Selecting identities from a list
- Expanding the product of 2 linear expressions
- Factorise quadratic expressions (
*x*only), including the difference of two squares. Solve quadratic equations.^{2}+ bx + c - Simplify and manipulate algebraic expressions including surds
- Simultaneous equations (find exact solutions, use elimination/substitution, interpret graphically, set up and solve)
- Change the subject of the formula where the subject appears on both sides, or with a power of the subject
- Find and analyse gradients for graphs in the form
*y = mx + c*, interpret and analyse straight-line graphs, find the equation of the line through two given points or through one point with a given gradient, gradients of parallel lines but not perpendicular lines - Plot cubic and reciprocal graphs, recognise the shapes of quadratic and cubic graphs (but not exponential or trigonometric functions)
- Select mathematical techniques to draw quadratics
**Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically****Fibonacci type sequences, quadratic sequences, and simple geometric progressions (***r*where^{n}*n*is an integer, and*r*is a rational number > 0)

Ratio, Proportion and Rates of Change

**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) specifically in algebraic contexts****Express a multiplicative relationship between two quantities as a ratio or a fraction****Relate ratios to linear functions****Interpret the gradient of a straight line graph as a rate of change**

Geometry and Measures

- Using basic angle properties in more complex problems
- Understand and use congruence and similarity
- Using the trigonometric ratios in right-angled triangles to solve problems, angles of elevation and depression (but not 3D problems)
- Fractional scale factors in transformations (but not negative scale factors)
- Know that the perpendicular distance from a point to a line is the shortest distance to the line
- Perimeter, area and surface area of compound shapes (other than triangles and rectangles)
- Lengths of arcs and areas of sectors of circles, including answers in terms of π
- Solve mensuration problems involving more complex shapes and solids (segments of circles, frustrums, surface area and volume of spheres, pyramids, cones and composite solids, real-life solids, area of a segment of a circle)
- Vector notation, sum and difference of vectors, scalar multiple and resultant of vectors (but not geometric proofs)
- Compound measures: density
**Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°**

Statistics and Probability

- Sources of bias and sampling
- Design an experiment/survey, justify a sampling scheme, stratified sampling
- Explain an isolated point on a scatter graph
- Using other than lines of best fit to predict values (maybe a non-linear relationship), and appreciating correlation as measure of the strength of association between two variables
- Probability: understand selection with or without replacement
- Tree diagrams (not conditional probability)
**Record, describe and analyse the frequency of outcomes of probability experiments using frequency trees****Enumerate sets and combinations of sets systematically, using Venn diagrams**

#### New maths topics introduced in the new syllabus from 2015, assessed in Higher Tier only:

Number

- Use of the product rule for counting (i.e. if there are
*m*ways of doing one task and for each of these, there are*n*ways of doing another task, then the total number of ways the two tasks can be done is*m × n*ways) - Estimate powers and roots of any given positive number

Algebra

- Expanding products of more than two binomials
- Interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’ (the use of formal function notation is expected)
- Deduce turning points (of quadratics) by completing the square
- 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 (this does not include calculus – draw a tangent to a curve to estimate the gradient, approximate the area under a curve using trapeziums)
- Find approximate solutions to equations numerically using iteration
- Solve quadratic inequalities in one variable
- Recognize and use simple geometric progressions (
*r*where^{n}*n*is an integer, and*r*is is a surd) and other sequences - Recognize and use quadratic sequences

Ratio, Proportion and Rates of Change

- 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 (this does not include calculus)

Statistics and Probability

- Calculate and interpret conditional probabilities through representation using expected frequencies with Venn diagrams

#### Omitted Content

- Writing numbers in words and writing numbers as words
- Recognising odd/even numbers
- Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals
- Systematic trial and improvement
- Tessellations
- Using isometric grids
- Know rough metric equivalents of pounds, feet, miles, pints and gallons
- Design/criticise a question for a questionnaire
- 2D and 3D co-ordinates
- Rotation and enlargement of functions expressed algebraically

#### The formulae provided have been reduced so students need to memorize more formulae

It looks like the formulae sheet at the start of each exam paper is being removed. The following formulae will still be given in specific questions if relevant:

- Volume of sphere
- Surface area of sphere
- Volume of cone
- Curved surface area of cone

From the diagram below you can see that the following have been removed:

- Volume of prism
- Area of trapezium
- Quadratic equation
- Sine/Cosine rules
- Area of triangle

**There are now 3 exam papers not 2**

- The new exam format consists of 1 non-calculator paper and 2 calculator papers.
- Each is 1 hour 30 minutes long and is worth 80 marks.
- All content domains will be assessed in roughly the same proportions across all three papers.

#### There is a new grading system of numbers from 1-9 instead of letters G-A*

The diagram above shows that the new grading system of numbers 1-9 does not directly correlate to the old grading system of letters A* – G.

According to Ofqual :

- Grade 1 is slightly beyond the G grade.
- Grade 4 = Grade C
**Only the top third of students achieving a grade C will be awarded a grade 5****Critically, a grade 5 will become the new “good” pass for GCSE Mathematics**- Grade 7 = Grade A
- Grade 9 is beyond the A* grade. Only the top 20% of students achieving grades A and above will be awarded a grade 9

“*We do need to caution against direct comparisons and overly simplistic descriptions of the approach. For example, it is not right to say simply that a new grade 4 will equal a current grade C. The read across is at the bottom of each grade, so that broadly the same proportion of students will get 4 and above as currently get C and above. A subtle but important difference.*

*From our formal consultation and conversations with teachers and parents, we know some people may not have fully comprehended our plans for grade 5 and international comparisons. To try and clarify this, it is not about putting in place any direct links or ties to any grades set elsewhere. Rather, where grade 5 sits within the grading scale will place it above a current grade C, and broadly in line with what the best available evidence tells us is the average performance of 16-year-olds in high performing countries.*“

Glenys Stacey, Ofqual CEO

#### Exam papers have changed in structure, with fewer lower grade questions in each tier and more higher grade questions

Foundation Tier | Higher Tier |
---|---|

50% of the exam targets grades 1-3 50% of the exam targets grades 3-5 | 50% of the exam targets grades 4-6 50% of the exam targets grades 7-9 |

Topics | Weighting of marks | |
---|---|---|

Foundation Tier | Higher Tier | |

Number | 25% | 15% |

Algebra | 20% | 30% |

Ratio, proportion and rates of change | 25% | 20% |

Geometry and measures | 15% | 20% |

Probability and statistics | 15% | 15% |

- There is a greater emphasis on ratio, proportion and rates of change at Foundation tier.
- There is a greater emphasis on algebra at Higher tier to bridge the gap between GCSE and A-level Mathematics.
- Mathematical problem solving, reasoning and communication is being assessed more.
- There is no longer a requirement to assess quality of written communication.

#### More rules around exam entries

Exams are only available in May/June each year, with an option for exams in November if the following condition is satisfied:

- Students need to be aged 16 and above by 31st August that calendar year if they want to take exams in November.

**Conclusion: the new GCSE is much tougher**