How to Prepare for the GCSE Maths Non-calculator Paper

For your GCSE in maths you will sit three papers: two will be calculator-based and one will be non-calculator. Here I will use my experience of over eight years of classroom teaching and tutoring to share tips and suggestions to help you feel fully prepared for the non-calculator paper. 

Why is the GCSE Maths Non-calculator Paper Important?

Calculators are great as they allow us to solve problems involving complicated numbers. However, it is also important that we practise maths problems without using a calculator as this will develop our fluency with numbers and our logical thinking skills. Sometimes the use of a calculator can prevent us from seeing patterns within numbers and it is these patterns that help us generalise rules with algebra.

What are the Key GCSE Maths Non-calculator Paper Topics?

It is important to remember that any topic can appear on any paper. There is no guarantee that the following topics will appear on the non-calculator paper.

Fundamental arithmetic operations

• Basic Arithmetic
  Addition, subtraction, multiplication and division will appear on the non-calculator paper in some form. The examiner may test these skills with whole numbers, decimals and fractions.

• Conversion between Decimals, Fractions and Percentages
  Calculators allow you to convert between decimals, fractions and percentages easily. Therefore if an examiner wants to test this skill it will appear on the non-calculator paper.

• Order of Operations (commonly referred to as BIDMAS)
  Modern calculators automatically apply the order of operations, therefore it is easier for an examiner to test this knowledge when you do not have access to a calculator.

• Estimation
  Some questions will ask you to estimate an answer rather than find the actual answer. The best place for these questions is the non-calculator paper as you will not be tempted to use your calculator and then round the answer.

Algebraic manipulation

• Surds
  Calculators are able to simplify surds and rationalise the denominator of fractions. Therefore these questions tend to appear on the non-calculator paper.

• Roots of Quadratic Equations
  This topic can appear on any paper; however, if an examiner wants to test whether you can use the quadratic formula then the non-calculator paper is the most suitable place to do so. Most modern calculators will solve quadratic equations for you if you type in the coefficients of the terms. I always teach my students how to do this and advise them to use this as a way to check their answers if this type of question appears on a calculator paper.

Geometry and trigonometry

• Exact Lengths, Areas and Volumes
  On the non-calculator paper you may be asked to find the perimeter, area or volume of shapes that involve circles or parts of circles. You will be required to give your answer in terms of π.

• Exact Trigonometric Values
  You need to know the exact values of the trigonometric functions for the angles 0°, 30°, 45°, 60° and 90°. The non-calculator paper is the only place where an examiner can test your knowledge of this.

Ratio, proportion, and percentages

• Percentages of Amounts
  Finding a percentage of an amount is very simple when you have access to a calculator. Therefore it is likely that you will be asked to work with percentages on the non-calculator paper.

• Simplifying Fractions and Ratios
  You can use a calculator to simplify a fraction or a ratio. Therefore this skill is usually tested on the non-calculator paper.

Statistics and probability

• Tree Diagrams
  Questions involving tree diagrams test knowledge of addition and multiplication of fractions, so it is common for examiners to include one of these questions on the non-calculator paper.

Effective Strategies for Success on the Non-calculator Paper

Time-management techniques

My students always used to find the time pressure worse on the non-calculator paper compared with the calculator papers. They told me that it was easy to get bogged down in lengthy calculations and lose track of time.

My best advice is to use the number of marks available as a guide to how many minutes you should spend on a question. If the question is worth 2 marks then spend roughly two minutes on it. After two minutes, if you are still struggling with the calculations then stop. Write down the steps that you need to do to solve the problem and then move on to the next question. You can always come back to it at the end if you have time.

Mental maths tricks and techniques

It is important to be confident with your times tables and types of numbers (primes, squares, cubes, etc.). On the non-calculator paper it is unlikely that you will have to do lots of messy calculations with awkward numbers, so always look for shortcuts. 

If you need to divide by a large number then write the division as a fraction and simplify it. You can then either perform the division with the smaller divisor or leave your answer as a fraction.

Remember that multiplication of numbers can be done in any order. For example, if you need to calculate 25 × 17 × 4 then you can first do 4 × 25 to get 100. The calculation then simplifies to 100 × 17. This trick also works for addition. Consider how you could use it to quickly calculate 243 + 598 + 357.

When multiplying fractions, it is usually easier if you simplify the fractions first to avoid multiplying large numbers unnecessarily. However, if you are calculating a probability using a tree diagram then it is easier to not simplify any fractions until the very end. This is because you will usually need to add fractions together and that is easier to do when they have the same denominators.

Past papers and mock tests

To get better at anything in life you need to practise. This also applies to non-calculator papers. Complete a past paper regularly so that you get used to the style of the questions and to increase the speed at which you can perform the numerical calculations.

As there are two calculator papers, some schools prioritise these when setting mock tests. However, I believe it is just as important to practise non-calculator papers. So, if you are only given a calculator paper for a mock then pick a non-calculator past paper and give yourself an additional mock exam.

Some of my previous students would spend the first five minutes of their exam writing down any tricky times tables and any formulae that they might need. This meant they could remove that information from their short-term memory for the rest of the exam, allowing them to focus on using the facts rather than trying to remember them.

Tips for Enhancing Your Problem-solving Skills

In your exam, you are bound to encounter longer questions that involve problem-solving. Here are my top tips for answering these questions:

• Deal with one sentence at a time

• Pick out the key pieces of information

• See what you can work out from the information you are given

  • Is there a formula or theorem that can help?

• When you have read the whole question, ask yourself:

  • What is the question actually asking for?

  • What information has the question not directly given me?

  • How does the question want the answer to be written?

• Use the number of marks as a guide to how many steps there should be

• Sometimes it helps to ignore the actual question and just work out what you can from the information provided

Revising for the GCSE Maths Non-calculator Paper

If you are studying the Edexcel or AQA specification then the non-calculator paper will be the first maths paper you sit, so you want to be prepared for any topic. For OCR, the non-calculator paper will be the second paper so you will know which topics have already appeared. These topics could appear again, however, so do not completely ignore them when revising, though you might want to prioritise the other topics.

Here are my suggestions for preparing for your GCSE maths non-calculator paper using feedback from my previous students:

• Start revising early 

  • Do not leave it until the night before your exam

• Set yourself weekly study goals

  • Make sure they are realistic and achievable

• Make sure that your calculator is out of reach when revising 

  • This eliminates the temptation to use it

• Practise writing out the times tables as quickly as you can

• Practise recalling the formulae that you are required to learn

• Don’t be scared to ask for help or support from teachers and tutors

• Build your confidence by starting with a small number of topics and master those first

• Try to have a positive mindset

  • If you cannot get to a final answer then you might feel like you have lost a lot of marks

  • However, the final answer to a question is only worth 1 mark – the rest comes from your method

Summary

Use the advice I have given here to help you prepare for your non-calculator paper. Remember there are no topics that are guaranteed to appear in the exam, so it is always best to prepare for anything.

Here at Save My Exams, we have got everything you need to revise for maths in one place. Use the links in the table to access our revision notes and topic questions. Best of luck with your revision.