Grading for the new GCSE 9-1, has become vague and full of jargon.

Make sure you can do as many topics as possible in your foundation or higher syllabus.

Topic questions can be asked in different ways, leading to different levels of difficulty. So practise ‘thinking on your feet’, working out what the question is about before answering them.

For example, the Hannah’s sweets question (2015 Edexcel Maths GCSE paper), is a probability tree question with some algebraic rearrangement. See if you can work it out.

**There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow.**

** Hannah takes a random sweet from the bag. She eats the sweet.**

** Hannah then takes at random another sweet from the bag. She eats the sweet.**

** The probability that Hannah eats two orange sweets is 1/3.**

** Show that n² – n – 90 = 0.**

**A grade 8 pupil can …**

- perform procedures accurately
- interpret and communicate complex information accurately
- make deductions and inferences and draw conclusions
- construct substantial chains of reasoning, including convincing arguments and formal proofs
- generate efficient strategies to solve complex mathematical and non-mathematical problems by translating them into a series of mathematical processes
- make and use connections, which may not be immediately obvious, between different parts of mathematics
- interpret results in the context of the given problem
- critically evaluate methods, arguments, results and the assumptions made

**A grade 5 pupil can …**

- perform routine single- and multi-step procedures effectively by recalling, applying and interpreting notation, terminology, facts, definitions and formulae
- interpret and communicate information effectively
- make deductions, inferences and draw conclusions
- construct chains of reasoning, including arguments
- generate strategies to solve mathematical and non-mathematical problems by translating them into mathematical processes, realising connections between different parts of mathematics
- interpret results in the context of the given problem
- evaluate methods and results

**A grade 2 pupil can …**

- recall and use notation, terminology, facts and definitions; perform routine procedures, including some multi-step procedures
- interpret and communicate basic information; make deductions and use reasoning to obtain results
- solve problems by translating simple mathematical and non-mathematical problems into mathematical processes
- provide basic evaluation of methods or results
- interpret results in the context of the given problem

A grade 4 will be equivalent to a present grade C and a grade 7 will be equivalent to a present grade A.

Foundation covers grades 5, 4, 3, 2, 1 (U) with Higher covering grades 9, 8, 7, 6, 5, 4, (3), (U)

**New Foundation Topics:**

- Index laws
- Compound interest
- Direct and indirect proportion
- Factorising quadratics
- Simultaneous equations
- Cubic and reciprocal graphs
- Trigonometry – the sine, cosine and tangent ratios, including to know the exact values of sin, cos and tan 30°, 60° and 45°
- Arc lengths and sectors of circles
- Vectors
- Density
- Tree Diagrams

**Foundation Formulae to Memorise:**

- Pythagoras Theorem: a² =b² + c²
- Trig. ratios: sinθ=O/H, cosθ=A/H, tanθ=O/A
- Area of a trapezium: ½(a + b)h
- Volume prism: cross sectional area × length

**Geometry Formulae Given:**

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

**New Higher Topics:**

- Expand products of more than two binomials
- Interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’ (using formal function notation)
- Deduce turning points on a quadratic function by completing the square
- Estimating gradients of graphs
- Estimating areas under graphs
- Simple geometric progressions including surds and interpret results in real-life cases
- Nth term of quadratic sequences
- Venn diagrams and conditional probability

**Higher Formulae to Memorise:**

- Quadratic formula, x = (– b ± √(b² – 4ac)) /2a
- Cosine rule: a
^{2}= b^{2}+ c^{2}– 2bcCosA - Sine Rule: \frac{a}{sin A} = \frac{b/}{sin B} = \frac{c}{sin C}
- Area triangle = ½absinC

**Kinematic Formulae Given:**

- v = u + at
- s = ut + ½at
^{2} - v
^{2}= u^{2}+ 2as.

**Edexcel:**

3 papers: 1.5 hour each

NC, 2×C

80 marks each

**AQA**

3 papers: 1.5 hour each

NC, 2×C

80 marks each

**OCR:**

3 papers: 1.5 hour each

NC, 2×C

100 marks each