Improve Your Grade – GCSE Maths

Chapter 1: Introduction to Year 11 Maths

Welcome to Paro Tuition’s Year 11 Maths Guide!

This guide will begin by outlining the general structure of Year 11 Maths GCSE. Section 2 will then address how to achieve the highest mark possible for specific grades, how to prepare for the mock exam, and how to revise for the GCSE papers.

Why is GCSE Maths so important?

Literacy and numeracy are the cornerstones of the British education system. Further and Higher Education institutions, training providers and employers all look to a person’s GCSE Maths grade for a general indication of intelligence and academic competence.

GCSE Maths is one of the most important examinations a teenager will ever take. As such, it is vitally important to ensure that learners are fully prepared and possess a thorough understanding of the course material.

Assessment format and structure

Whether taking the Foundation tier or the Higher tier, learners sit 4.5 hours of exams, spread across 3 papers.

Exams typically run from the third week of May to early June:

1. Grading, Tiers and Exam Boards

The new grading system

In 2017, the UK Government introduced a new grading system for Maths GCSE. Previously, learners were graded A* to U. Pupils are now awarded a grade between 9 and 1, with 9 being the highest:

Foundation tier

Learners on the Foundation tier can achieve a maximum grade of 5 (a low B/high C on the old system).

Higher tier

In the Higher tier, grades go from 4 to 9. Around 20% of learners who achieve a Grade 7 (or higher) are awarded a Grade 9.

Exam boards

  • AQA – An independent education charity who cater for around 50% of GCSE Maths examinations in England
  • OCR – The Oxford, Cambridge & RSA exam board
  • Edexcel – A privately-owned exam board, operated by Pearson

1.2 Foundation Topics and Skills

Grades 1-3 topics and skills

Geometry and measures:




Ratio, proportion and rates of change:



Grades 4-5 topics and skills

Geometry and measures:



Ratio, proportion and rates of change:



1.3 Higher Topics and Skills

Grades 6-7 topics and skills

Geometry and measures:



Ratio, proportion and rates of change:



Grades 8-9 topics and skills

1.4 General Format of the Year

The end of lessons

Each school will have its own specific timetable, but generally most schools will finish all of the teaching for the course between January and March.

Following this, schools prepare Year 11 pupils for the upcoming GCSEs using a combination of mock exams, classroom revision, after school clubs and independent revision plans.

Mock exams

After lessons stop, most Year 11 pupils sit a series of mock exams, usually commencing in the middle of January. Some may sit two sets of mocks with the first set occurring earlier in the year (October time).

Mock exams have been a staple of the British education system for decades. Essentially, they are an additional form of assessment, alongside classroom testing, that allows a school to gauge each pupil’s ability level, how prepared they are for the real exam, and what topics they need to focus on during revision.

Mock exams are designed to provide learners with experience of an official GCSE examination. For many pupils, sitting a mock exam can be a stressful experience, but it is important to remember that mock results are for internal use only.

Exam period and study leave

Some schools will give students study leave as they approach their exam period. If given, this will typically be around the end of May. During study leave, students are allowed to study and prepare for their exams at home, coming to school only when they actually have an exam to sit.

Most schools have actually stopped giving study leave as there were cases of students carrying out no revision or even going on holiday. Some schools now give a hybrid format of study leave which requires students to be at school but allows them to spend their day revising how they see fit.

2. Achieving the Highest Grade Possible

2.1 General Tips on Improving Your Grade

Pupils often make the mistake of thinking that to obtain a high mark on a Maths GCSE paper, they merely have to possess a solid understanding of the various topics and skills taught. Whilst this is undoubtedly a major part of achieving a good grade, there are also other important factors to consider:

  • Pertinent revision, with a well-organised study planner (i.e. focusing on parts a learner struggles to understand the most or has forgotten)
  • Plenty of practice answering exam questions
  • Sound problem solving skills

Repeat and redo

Numerous academic studies have shown that learners who test their knowledge by independently repeating difficult topics and tackling progressively more difficult questions cultivate a much better understanding of what is being taught to them. It’s not enough to simply be understanding something that’s been taught or explained, students must be able to do it themselves independently at a later date!

The simplest way to do this is to redo any questions that answered incorrectly in class, homework, assessments or exam practice. It may mean doing the same question a few times over but this method is brutally effective.

2.2 Targeting Grade 4

To achieve a Grade 4 (a C in the previous system), it is vitally important that learners have a comprehensive understanding of the topics and skills listed above for Grades 1-3.

It is not enough that learners are adept in one or two major areas, or even a majority of topics. Pupils need to have a good grasp of all low-level foundational topics, and their associated skills. These areas represent the building blocks of the modern Maths GCSE curriculum, and need to be mastered in their entirety before a pupil can begin to think about targeting mid-to-high level grades. Learners should be able to recall all the basic principles they contain, and understand how they relate to one another where applicable.

Students must also be able to problem solve with these areas and understand how to apply these skills in different ways.

2.3 Targeting Grade 5

Key to achieving Grade 5 is having a sound grasp of the Grade 4/5 ‘crossover’ topics – these are questions that are common to both the Foundation and Higher papers. Crossover topics represent the most difficult questions a learner will face on the Foundation paper, where Grade 5 is the highest grade achievable. Study guides often break down GCSE Maths into Foundation, crossover and Higher questions.

Common problem areas:

  • Forming and solving equations
  • Simultaneous equations
  • Trigonometry
  • Equations of lines
  • Vectors
  • Compound measures
  • Reverse percentages
  • Polygons

With these topics, a particular emphasis needs to be placed on problem solving as questions are almost always asked in an unorthodox way.

2.4 Targeting Grade 6

When targeting Grade 6, pupils should ensure a good understanding of the Grade 4/5 crossover topics (above) and revise simpler topics from the Higher tier.

These include:

  • Similar shapes with area/volume
  • Cumulative frequency
  • Box plots
  • Expanding three brackets
  • Harder indices
  • Using the quadratic formula
  • Recurring decimals to fractions
  • Tree diagrams
  • Histograms
  • Graphical inequalities

As pupils revise each topic, it is important that they do not automatically move onto the next topic once their study planner demands it, if they feel they haven’t fully understood what they are learning. Recall should be improved by covering an area until a learner is comfortable with answering questions on a topic (within reason and not to the detriment of other topics), or is at least able to understand how to answer a question on it.

The good thing is that most of these topics don’t often have much problem solving, making the questions quite repetitive and predictable.

2.5 Targeting Grade 7

Before aiming for Grade 7, pupils need to possess a thorough understanding of all the lower-end Grade 6 topics, along with a sound grasp of the crossover topics.

Once pupils are comfortable with these areas of study, they can move onto topics for Grade 7 (see section 1.3), especially Algebra, Number and Geometry.

It is also useful to revise some of the easier topics from Grade 8, or even Grade 9, to advance their knowledge of the principles learned in Grade 7.

Suitable topics to study include:

  • Inverse/direct proportion
  • Advanced trigonometry
  • Functions
  • Iteration
  • Transformations of graphs
  • Surds
  • Completing the square
  • Circle theorems
  • Algebraic fractions
  • 3D trigonometry
  • Pythagoras

Problem solving is of huge importance when students get to this stage. Many of these topics have a lot of variation in their question style so a broad range of exam style questions need to be tackled. It’s also important to work on exam technique and question interpretation as sometimes just understanding the question can be difficult.

To tackle these harder questions, students should break them down by underlining key words, circling numbers and trying to see what they can work out using the information provided. After enough practise, they’ll start to see some of the same patterns appearing in other questions.

2.6 Targeting Grade 8 and Above

Grades 8 and 9 represent the most difficult topics taught on the Maths GCSE curriculum.

Pupils who are aiming for these grades must first demonstrate a comprehensive understanding of all Grade 6 and Grade 7 topics, and should be able to easily recall the skills and techniques they have learned throughout secondary school.

Pupils who target these grades should immerse themselves in independent revision and consult with their teacher on how to structure a study guide. Revision should be focused on Grade 7,8 and 9 topics, with occasional sessions dedicated to lower grade questions.

Not all Grade 8 or 9 topics are included in the exam, making them slightly harder to revise for, but revisiting some of the hardest topics from the course will stand pupils in good stead for whatever does appear on the exam paper.

These include:

  • Quadratic simultaneous equations
  • Vectors
  • Quadratic inequalities
  • Turning points

It must be noted, that students need to have excellent problem solving, exam technique and time management as well as knowing all of the topics on the course. There simply isn’t much room for error! Students aiming for an 8/9 should practise harder extension questions (there are books/resources dedicated to questions like this such as the CGP practice book).

2.7 What to do – September to December (Before Mocks)

Before mock exams begin in January, pupils should dedicate the majority of their revision timetable to re-familiarising themselves with topics from Year 9 and Year 10, and focus on the discipline of mathematical problem solving – i.e. the practice of finding a solution to a question. As mentioned above, problem solving questions should be repeated to ensure they’re understood.

Pupils should identify a target grade and structure their revision timetable using the advice provided above, relative to the grade they wish to achieve. Teachers can help with finalising a timetable, and offer advice on how much time should be dedicated to each topic.

Past papers

Before taking their mocks, pupils should start completing past papers – an essential tool in achieving a good grade, both in mock exams and the actual GCSE. Pupils should set aside time in their study guide to sit timed past papers for the tier they are enrolled on. These past papers should be tackled in timed condition and then marked using the mark scheme.

2.8 January/February (After Mocks)

From January to February, after the mock exams have been completed and marked, pupils should focus solely on the topics that they are weakest at, relative to the grade they want to achieve.

At this stage, it is vitally important to re-draft study plans, adhere to marking schemes when completing revision tasks and not waste valuable revision time on topics that the pupil is not experiencing any difficulty with.

If a pupil has performed well in their mock exam and is comfortable with all the topics required to achieve their targeted grade, they should move onto more difficult topics (ideally the easiest topics from the next grade up from their targeted grade).

Students should do a practice paper every few weeks in exam condition to keep exam technique fresh. 

Additional resources

For the final push towards the exam, parents and pupils should make use of every study resource available, from a variety of sources (especially those who are targeting Grade 8 and Grade 9.

These include:

  • Corbett maths
  • Hegarty maths
  • MyMaths
  • CGP exam practice workbooks

2.9 March/April

In the run-up to May, pupils should split their time equally between topic-based revision around areas they are struggling with, and problem solving.

At this stage, students should be continually mindful of not just their recall ability, but how their questions are going to be marked on the exam. As such, revision should be checked using a marking scheme and things that aren’t understood should be covered with a teacher/tutor.

Problem solving

Problem solving worksheets are available from a variety of different sources, and are an essential tool in developing the skills and methods that are required to properly answer a Maths question:

Sources include:

  • CGP exam-style workbooks
  • Corbett Maths worksheets
  • Just Maths
  • Paro Tuition worksheets and free resources

Past papers

In the last week of April, pupils should focus their attention on past papers, as they did prior to their mocks, but with a slightly different approach.

Firstly, pupils do not need to complete sections of the paper that are higher than their targeted grade – i.e a pupil aiming for a Grade 6 doesn’t need to complete the last 4 or 5 questions on the Higher paper. It’s counter productive to be spending much time on these questions that will be completely inaccessible to students targeting a 6.

Secondly, these papers should be completed in as close to exam conditions as is possible – adhering to the calculator rule, closed books and no external assistance – in order to provide learners with an understanding of how well they react to exam scenarios, and what exam techniques they may need to brush up on.

These papers need to be properly marked and analysed to identify precisely where a pupil needs additional help. Once marked, students should note (the relevant areas) in which they’ve lost marks. These will likely be a combination of silly errors and struggling with some problem-solving questions. Students should also try to reattempt these papers a couple of weeks later to see if they can improve their mark.

2.10 May/June

This period is quite often where most marks are won and lost.

As with the previous few months, the focus should be on completing past papers relevant to their targeted grade. Papers should be properly marked and annotated to highlight simple mistakes and identify areas for further revision.

Pupils should aim to complete at least 2 sets of exams (6 papers), in exam conditions. Papers should be redone until the required grade is comfortably achieved each time.

Past paper strategy (based on targeted grade)

Students can use the following strategy to help focus their past paper use. It should be noted that it’s NOT written in stone!

For example, if a student targeting a Grade 4 feels there is a question at the end of the Foundation paper that they can tackle then they should have a go at it and not just skip it because it may be a Grade 5 question. 

Note – recommended targets are not the same as average grade boundaries

2.11 Consider Private Tuition

Learning how to pass exams is a science in itself, and there is no other GCSE subject more formulaic and precise in nature than Mathematics. Quite often, learning how to solve a maths problem is the difference between a smile or a frown on results day, regardless of any other exam result.

Even if a pupil is comfortably achieving their targeted grade in mock exams and past papers, there is always room for additional help that complements classroom learning and independent study.

Private tuition, whilst an additional expense, pays dividends in the form of above average grades and a less stressful revision period. Private tuition has been shown to add anywhere between 1 to 3 grades on to students’ final grades.

Studies have shown that classroom size and teaching expertise are the two most important variables (excluding underlying ability) in a pedagogical environment. Private one-to-one tuition, or group tuition with an attentive set of learners, provides an opportunity for pupils to receive targeted support based on their individual academic needs that is unobtainable in a classroom environment.