When you get into Year 10, hopefully you are very fluent with number and calculation. This is to say, you are
equally at home calculating with or without a calculator and in handling all number: fractions, decimals and
percentages, converting between these and expressing your answer using any of these forms.
That you are conversant with the arithmetic associative and distributive laws^{1} and competent in handling
algebra, including that involving indeces, using a variety of techniques including expanding and factorising
as well as writing your own expressions and equations in translating word problems into algebraic form. But this
level of fluency is by no means possessed by everyone at this stage and there is often a need to relate the more
complex Mathematics covered in Key Stage 4 back to the underlying arithmetic principles first encountered during
Key Stages 2 and 3 or to cover them again in the light of the new material.

Even if your fluency with Maths is not as good as you would like, you will still be tackling some fairly challenging stuff at GCSE and mastering new concepts, although you will either find yourself revisiting earlier topics or else just muddling through. Fractions, for e.g., is not a topic at GCSE. Lots of students do one or other of these two options.

Maths at GCSE is at the level of *Application*^{2}.
That is, it is using the whole range of your
knowledge and understanding in Maths and applying these to novel situations and problems. Problems which more powerfully
model things in the real world, for example, quadratics, studied in some detail at GCSE, represent a wide range
of real-world phenomena and have very many applications. During Key Stage 4 your work will take on greater integration
- you will make your graphs, equations and diagrams work together,or relate to one another.

- Associative law, EG.: 6 x 9 ÷ 3 = (6 ÷ 3) x 9 = (9 ÷ 3) x 6

Distributive law, EG.: 3(6 + 9) = 18 + 27 - Application: the 3rd level in Bloom's
*Taxonomy of Learning*. Arguably Maths at GCSE includes also some*Analysis*.

GCSE exams taken in 2017 will use the new 1-9 grading system in which grades 4-5 target the old grade 'C'.

New Grade: |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Old Grade: |
G/F |
E |
D |
C |
C/B |
B |
A |
A/A* |
A/A* |

bottom ⅔ of C |
top ⅔ of B |
top 20% of A/A* |
|||||||

Boundaries Foundation: | 40% | 50% | 60% | 70% | 80% | ||||

Boundaries Higher: |
30% | 45% | 55% | 70% | 85% | 90% | |||

Equivalence approximate; boundaries very approximate |

The value of the qualification has been enhanced with the additions at both the Foundation and Higher tiers.
For example the Foundation Level syllabus now includes factorising and solving quadratics in the form x^{2} + bx + c,
compound and reverse percentages, linear simultaneous equations, the lengths of arcs and areas of sectors and
tree diagrams.
The Higher Level syllabus now includes functions and function notation, expanding more than 2 binomials, the
gradients of graphs and the area under a graph, calculating the nth term of a quadratic sequence and the use of
venn diagrams.

The new specification has effectively acquired a new top-level grade which is sometimes called an A**.

Use systematic listing, {and the product rule for counting}.

Working with roots and powers with integer indeces, {and with fractional indeces and estimate powers and roots of any positive number}.

Calculate exactly with fractions and multiples of π {and with surds}.

Working with limits of accuracy, {and upper and lower bounds}.

Understand and use fractional values and ratios in real-world problem solving.

Working with linear graphs and the general form: y = mx + c and with quadratics graphically, identifying intercepts and turning points.

Working with quadratics algebraically, calculating roots using factorisation and the quadratic formula {and roots and turning points by completing the square}.

Working with other algebraic expressions and equations {including those involving surds and including algebraic fractions}.

Interpret simple expressions as functions {and interpret the reverse process as the inverse function and compounded processes as composite functions}.

Recognise and sketch graphs of linear, quadratic and simple cubic functions and the reciprocal
functions (1/x), {the exponential function y = k^{x} and trig. functions} and relate
these to real-world problems {including growth and decay}.

Working with simultaneous equations {including quadratic-linear ones}.

Working with distance-time graphs and velocity-time graphs including using slope {and the area under the graph}.

Working with sequences including arithmetic, Fibonacci-type, quadratic and simple geometric.

Geometric transformation, vectors and loci.

Working with circle theorems, {sine and cosine rule and Area = ½abSinC}.

Presenting and anlysing sets of grouped and ungrouped data, and using a variety of representations.

Working with experimental and theoretical probabilities of single and combined events.

Not a complete list.