GCSE Maths


New GCSE Grading System

The GCSE grading system is being changed. When English and maths results are announced in 2017, and when the results of other examinations are announced the following year, instead of getting A*, A, B, C, D, E, F or G, papers will be given a 9, 8, 7, 6, 5, 4, 3, 2 or 1 grading. The top three grades (9, 8 and 7) will replace the current top two (A* and A).


·        Maths will be tiered with an overlapping tiers model


·        Foundation tier covers grades 5, 4, 3, 2, 1 (U)


·        Higher tier covers grades 9, 8, 7, 6, 5, 4, (3), (U)


·        Overlap at grades 5 and 4


·        Higher tier also to include a grade 3, for candidates a ‘small number of

            marks’ below grade 4.

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

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 and 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


GCSE Exam Tuition:

The Maths GCSE exam covers a large number and variety of topics so a student will on average need up to seven to ten tutorial revision sessions to cover all the exam topics. This number however can vary dependent on the student's individual ability. From the beginning of the tuition the student will need to do one set of mock papers or past papers (one calculator and one none calculator) at the students appropriate exam level. This will enable me to identify the student’s weakness and topics they have difficulty with. The following tuition will then concentrate on these identified topics with the aim to boost the student's confidence for the real exam. The student will also complete a minimum of five set of past papers throughout the series of tuition sessions to ensure they feel comfortable with the exam questions prior to the real thing.


Exam Tips

The following list is by no means complete but these are some points to bear in mind when answering examination questions.

How to avoid common mistake

Always read the question

How often students don't read a question. They see a diagram and ignore any comments about it or any earlier notes and rush straight in. It can often be a good idea to highlight or tick off each point as it is read, so that you don't miss anything.


Rounding Errors

When a question involves several stages of working where answers end in long decimals, DO NOT round up. If you use the rounded value again in another part of the question it will cause the next answer to be slightly out. Instead write answers at any stage as un-rounded values so if the calculator gives an answer such as 23.456782314 simply write 23.4567. Use this or your calculator value in further calculations to avoid rounding errors.


Always check after you finish a question that you are giving the answer to required degree of accuracy that was asked for. It may be 3 significant figures, 1 decimal place etc. Why lose an accuracy mark unnecessarily?

Cumulative frequency graphs

Always plot points based on the upper bounds of any class intervals, NOT midpoints.

Inverse percentage questions

These are questions where you have to calculate the original value before an increase or decrease has taken place. These can be tricky but you should be able to tell if you have made a mistake as the answers are almost always a clean answer. Get a long decimal that needs rounding and the chances are you have made a mistake.


When calculating the mean from a set of data makes sure your answer lies between the lowest and highest values of the set of data. If it is outside this range it must be wrong.

Pythagoras' Theorem

When finding a shorter side of a right angled triangle checks that the answer is smaller than the hypotenuse. If not then the chances are you added rather than subtracted the squares of the two other sides.


When calculating a probability, check that your answer always lies between 0 and 1. 0 means the event will never happen and 1 that it is guaranteed to happen. I am still surprised how many times I see students give answers more than 1 and are quite happy to accept it.

Solving Quadratic Equations

When a question says solve the following quadratic giving answers to 3 significant figures or several decimal places then do not waste time trying to factorise it. It will not factorise. Instead, use the quadratic formula.

Simultaneous equations

Most questions that are set will give nice answers, usually integer values. If you get horrible decimals then suspect your answer and check again. It is quite likely that you have made a mistake somewhere.


When calculating a side of a right angled triangle. Check that it looks sensible. If it is a smaller side it should not be larger than the hypotenuse.

Bold Print Comments in a Question

If a question contains bold print then take care as it is trying to draw your attention to a specific point where it may be very easy to trip up. For example it is common to see the following question on cumulative probability. Find the number of people less than 150 cm tall. You would simply read off the value. However, find the number of people who are more than 150 cm tall requires a little more care. Take your answer for how many are less than 150 cm away from the total number of people.

Materials Required For Examination

Tracing Paper

Get some tracing paper. Most exam boards allow you to take this in to the exam. It is often overlooked and can be useful for rotating shapes about a point.

Setting out your work

Try to write reasonably small as there is often very little space to show your working. Always show working, as this is likely to give you method marks. No working and you could be throwing away marks. Try not to write down what may appear to be random calculations. The following statements mean nothing 50x2 = 100 100-3 = 97 Instead, try to give an introduction to a calculation, such as Area of rectangle = 50x2 = 100 cm squares Set work out in columns if possible, drawing a line between columns to separate your working.