11 Plus Maths Exam Preparation Guide: Papers, Questions and Tips

Introduction to 11+ Maths Preparation

The Maths section of the 11+ exam tests skills that your child will have covered at school following the national curriculum. At Study Mind we are experts in guiding students through the daunting 11 plus maths exam, providing proven strategies & resources from our expert tutors to help you through the process to ensure you & your child can find success. 

Understanding the 11 Plus Maths exam is a critical component of the selective school admission process in the UK. Achieving a high score can open doors to some of the best grammar & independent schools, making preparation essential. But beyond just getting into a good school, the skills you develop while preparing—such as problem-solving, critical thinking & time management—are invaluable life skills.

Our approach to preparation combines tried and tested methods like 11 plus maths worksheets, 11 club maths worksheets, 11 plus maths books with modern, interactive tools like 11 plus maths games to keep learning engaging & effective. We’ll cover everything from creating a study schedule to using the best resources available, ensuring you or your child is fully equipped to excel.

Understanding the 11+ Maths Exam

The structure for the 11+ exam can vary depending on the school & exam board involved. As a tutor, I would recommend checking with the school to determine which board they use, as there are multiple 11+ exam boards.  When it comes to the 11+ maths exam, its structure depends on the school & the exam supplier. Some schools may create their own bespoke papers through their maths department while others opt for premade tests by exam boards. Generally, 11+ maths exams are non-calculator.

Exams are either adaptive or non adaptive, answered on paper or online. Most vary from around 45-60 mins. Adaptive refers to the questions becoming more challenging based on your child’s performance. 

Atom Assessments

Atom Assessments is an adaptive online exam used by many independent schools, with questions adjusting in difficulty based on the student’s performance.  All questions are multiple-choice. 

CEM Select

CEM Select is another online, non-adaptive test used by some independent schools. It includes six sections, with the general maths section comprising 30 questions in drag-&-drop or multiple-choice formats.

GL Assessment

Used by most UK grammar schools & some independent schools, GL Assessment 11 Plus exams are paper-based & non-adaptive. They consist of multiple-choice questions, with students marking answers in an answer booklet that is electronically scanned for grading.

ISEB Common Pre-Test

This online adaptive test is used by some independent schools & includes four sections. The ISEB maths section is 40 minutes long & consists of multiple-choice questions. Students can use a pen & paper for calculations, though this is not marked.

11 Plus Maths Pre-Test

Pre-tests for the 11 Plus, which can occur before entry into Year 7. They are primarily computerised & multiple-choice.

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Key Topics in the 11+ Maths Exam

Let’s explore the 11+ maths syllabus. As a tutor, I know first-hand how daunting it may seem to try and cover all parts of the 11+ maths curriculum, but with careful planning and understanding, it’s manageable. 

Data

• Representing Data: Use pictograms, tables, bar charts, line graphs, Venn diagrams & pie charts to organise & interpret data. Read & interpret data from these formats, including calculating averages (mean, median, mode) & solving problems using data.

Number

• Place Value: Understand & work with numbers up to 1,000,000; round whole numbers & decimals; recognise the value of digits, including in decimal numbers up to three decimal places.
• Four Operations: Perform mental & written addition, subtraction, multiplication, & division; use column methods for large numbers. Work with square & cube numbers, estimate, find multiples, factors, & prime numbers, & solve word problems.
• Using Negative Numbers: Understand & use negative numbers in calculations.
• Sequences: Identify & continue simple numerical sequences.
• Properties of Numbers: Work with factors, multiples, primes, squares, & cubes; find missing numbers in sequences & calculations.

Fractions, Decimals, & Percentages

• Fractions: Understand fractions, equivalent fractions, mixed & improper fractions; compare, order, & perform operations such as adding, subtracting, & multiplying fractions.
• Decimals: Learn about decimals, convert between decimals & fractions, compare, order, add, subtract, multiply, & divide decimals.
• Percentages: Understand & calculate percentages, including finding percentage increases & expressing percentages as fractions. Compare & order percentages.

Ratio

• Simplifying Ratios: Simplify ratios & solve problems involving ratios.
• Sharing & Unequal Shares: Share quantities & represent unequal shares as fractions.
• Measurement
• Conversion of Measurements: Convert between metric measurements & understand imperial measurements, including the miles to kilometres ratio.
• Perimeter & Area: Calculate the perimeter & area of quadrilaterals, triangles, & estimate the area of irregular shapes.
• Volume: Calculate the volume of cuboids.
• Other Measurements: Measure time & temperature.

Geometry

• Properties of Shapes: Identify & describe properties of 2D & 3D shapes, including angles in triangles, straight lines, parallel lines, & quadrilaterals.
• Transformations: Understand & apply transformations such as reflection, rotation, & translation.
• Coordinates & Nets: Use coordinates on a grid; draw & understand nets of cubes & cuboids.

Algebra

• Expressions & Equations: Form, simplify, & solve algebraic expressions & simple equations. Use visual puzzles, trial & improvement, & solve simultaneous equations.

Probability

• Basic Probability: Express basic probabilities as fractions & on a probability line.

Statistics

• Data Representation: Read & interpret data from line graphs, conversion graphs, time & distance tables, tally & frequency tables.
• Averages: Calculate & interpret averages (mean, median, mode, range).

Drawing Bar Charts: Create & interpret bar charts.

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Hard 11+ Maths Questions

As students progress through their 11+ preparation, they often encounter more challenging maths problems that test their critical thinking and problem-solving skills. These questions are designed to push students beyond basic calculations, requiring them to apply their knowledge in more complex ways. Below are some of the most common types of difficult questions students may face on the 11+ Maths exam:

Types of Difficult Questions

• Word Problems: Complex scenarios requiring multi-step solutions & logical reasoning. These may contain a lot of different topics which may not be obvious when you first read the question
• Advanced Fractions & Decimals: Problems involving multiple operations with fractions & decimals.
• Algebraic Expressions: Questions involving the manipulation & solving of algebraic expressions & equations. This is a topic that is tested regularly in year 7, so a basic knowledge is useful 
• Geometry Problems: Challenges with complex shapes and angles
• Ratio & Proportion: Often involving more than one step or concept.
• Data Interpretation: Complex questions based on interpreting multiple types of data, such as pie charts with angles 
• Sequences & Patterns: Advanced problems requiring the identification of complex number sequences or patterns.

As an academic coach, ensuring that students have a solid grasp of the skills to be tested is key before tackling more advanced and difficult 11+ Maths questions. Without a strong foundation, students may struggle with the complexities these questions present. Once that foundation is in place, they can approach challenging problems with greater confidence. Let’s explore some effective strategies for handling these tougher questions:

Strategies for Tackling Challenging Problems

• Understand the Question: Carefully read & break down the problem into smaller parts. Identify what is being asked & what information is given.
• Identify Key Information: Highlight or note down important numbers, relationships, & conditions.
• Choose the Right Approach: Determine the most suitable method (e.g., drawing diagrams for geometry problems, setting up equations for algebra).
• Work Step-by-Step: Approach the problem methodically. Solve one part at a time & keep track of your working.
• Check Your Work: Revisit your solution to ensure that it makes sense & check for any mistakes.

Practice Regularly: Regular practice with a variety of difficult problems helps build problem-solving skills & familiarity with complex questions.

Effective Study Strategies for the 11+ Maths Exam

Preparing for the 11+ Maths exam is a major milestone for students, and from my experience as a tutor, I’ve learned that with the right strategies, the process can become both manageable and rewarding. Over the years, I’ve developed a number of effective study tips to help students not only succeed but also enjoy the learning journey.

Tip 1

Creating a Study Schedule is essential and is a tip I always emphasise. A well-organised plan helps students (and parents!) navigate the vast syllabus, setting clear goals & allocating time effectively. By setting specific, achievable goals, we can ensure that every topic is covered thoroughly without overwhelming the student. This approach also allows us to track progress and make adjustments as needed.

Tip 2

Practising with 11 Plus Maths Papers & Worksheets enables students to prepare effectively for exams by getting used to the test format and timing requirements. Consistent practise is key. In my sessions,  I encourage students to practice regularly with timed papers to get familiar with the test format. This not only highlights areas that need improvement but also builds their confidence and helps them manage their time effectively under exam conditions.

Tip 3

I often recommend engaging in maths games and online learning activities, which can make studying more enjoyable by adding a fun element to the process of preparation for tasks related to mathematics. These interactive games are designed to reinforce concepts in an interesting manner that makes learning feel less like a burdensome duty. Young learners particularly benefit from these games as they help sustain their curiosity and drive to learn. When education is infused with elements of play and enjoyment together with learning materials, students tend to remember information and cultivate a favourable outlook towards mathematics. 

Tip 4

Practising maths using flashcards and online quizzes are fantastic to improve speed and accuracy which is essential for exam success! Flashcards and quizzes offer practice opportunities to work specifically in areas that need improvement while being convenient for quick study sessions anytime. 

Tip 5

Turning Learning into a Game by applying mathematical concepts to real-life situations, like calculating costs while shopping, can make learning more relevant & enjoyable. This approach not only reinforces what has been learned but also shows students how maths is used in everyday life. By making learning practical, students can develop a deeper grasp of mathematical concepts.

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Tip 6

Forming a Study Group. Group discussions allow students to share ideas & problem-solving strategies, especially when trying to find students who are applying for the same school as your child. This can make the preparation process less isolating & more enjoyable.

Tip 7

Making a Timetable helps ensure consistent & organised study sessions. A well-structured timetable should include a mix of activities—such as practice papers, interactive games, & group study sessions—to keep the learning process varied & engaging. Consistency in study habits is key to long-term success, & a timetable provides the structure needed to maintain this consistency.

Tip 8

Using Past & Sample Papers is crucial for mastery of the types of questions that may appear on the exam. These papers provide insight into the exam’s format & level of difficulty, allowing students to develop effective strategies for tackling different types of questions. Familiarity with past papers can greatly reduce anxiety on the day of the exam, as students will know what to expect. Simply look up your target school as sometimes they provide sample papers online, or there are paid versions available

Tip 9

Taking Mock Exams simulates the conditions of the actual test, providing valuable practice in managing time & handling exam pressure. Mock exams also help students assess their progress & identify areas that need further attention. By taking multiple mock exams, students can build their confidence & ensure they are fully prepared for the real exam.

Tip 10

Using Solved Papers for review allows students to interpret & learn from their mistakes. Reviewing solved papers helps students see where they went wrong & realise the correct approach to solving problems. This reflective practice is crucial for continuous improvement & mastery of the material.

Tip 11

Finally, Rewarding Yourself for achieving study goals is important for maintaining motivation. Small rewards, such as a favourite treat or a break to do something enjoyable, can make the hard work feel more worthwhile. By setting up a system of rewards, students can stay motivated & maintain a positive attitude towards their studies.

Resources for 11+ Maths Preparation

Books are a traditional & reliable resource for exam preparation. Available at most supermarkets or stationery stores.  Key resources include 11+ Maths Practice Papers by CGP, which offers a range of practice questions that closely mimic the style & difficulty of the actual exam. Bond 11+ Maths by Bond is another excellent resource, providing comprehensive coverage of the syllabus with detailed explanations & tips. 

Worksheets provide additional practice & can be tailored to focus on specific topics or skills. Websites like Education.com & Math-Aids.com offer free printable worksheets, while platforms like Twinkl & MathsBot provide customisable worksheets that can target individual needs. These worksheets are a valuable tool for reinforcing learning in a more hands-on, interactive way. You can use them to test your knowledge on each subject. Some more websites worth checking out are Mathsgenie and TES. Some may require you to sign up, and beware – they may ask you to pay for some resources.

Online platforms offer many interactive resources accessible anywhere and at any time. Khan Academy offers video tutorials in which learners can learn at their own pace on a wide range of topics. MathsWatch offers interactive exercises to test the knowledge. Atom Learning delivers adaptive practice questions personalised to a student’s ability. These provide instantaneous feedback and opportunities for self-reflection, which is important for learning from one’s mistakes and thereby improving skills rapidly.

Pros & Cons of Online Learning

Some of the key advantages of online learning include accessibility, engaging interaction tools, and immense resource availability. Resources can be accessed at any time, making it easier to fit study sessions into tight schedules. This is how online platforms render learning interactive and fun; feedback provided instantly lets students learn from mistakes immediately. There has been an increase in the number of resources available online, so a platform to suit your child’s needs will, no doubt, be available.

However, online learning also has its drawbacks. Among the disadvantages is that it might be very distracting at certain times. The internet is full of non-educational content, which can easily divert students away from studying. Moreover, in online learning, a student misses out on personal interaction, sometimes becoming a big disadvantage to students who require more guidance or problem discussion with a teacher or peers. Finally, online learning depends on technology, which sometimes fails and may disrupt study sessions.

In spite of all the challenges, online learning can be effective if combined with all other ways of studying. So, if a student combines online resources with traditional books, worksheets and, if possible, personal tutoring or group study sessions, he will be able to create a well-rounded & effective preparation plan.

Pros & Cons of Different 11+ Maths Preparation Methods

How one prepares for the 11+ Maths may be all-important in determining the result of the performance of a student. Each method-private tutoring, group tuition, or individual study-presents its own advantages and disadvantages. Being aware of these advantages and disadvantages will go a long way in enabling parents and students to choose an appropriate method.

11+ Maths Private Tuition

Private Tuition provides personalised attention and tailored study plans to meet the individual needs of the student. This personalised tutoring will be, without a doubt, much more effective in helping students, particularly those with certain weaknesses. 11 Plus tutors may also adapt lessons according to the learning pace and style that matches the student best, ensuring that they truly comprehend what is being delivered. The schedule can be made flexible enough to accommodate the most convenient times. Another great motive is finding a tutor that your child gets along with, which can also provide peace of mind for the parents-especially knowledgeable tutors who have previous experience with your target school.

However, private tutorials are expensive, & finding a good tutor is somewhat demanding. There is also the danger of the student getting too dependent on their tutor, which can prevent the learning skills of independent studying. The student should, therefore, be taught how to study effectively on their own since this is an important skill that will help them in their academic careers.

11+ Maths Group Classes

Group classes encourage peer learning and provide a structured environment with a systematic curriculum. Interaction with the other students can allow an exchange of ideas and strategies that may help with some trickier questions. Generally speaking, group classes are more cost-effective than private tutoring, making them accessible to more families.

The disadvantage of group classes is the reduced amount of individual attention. A teacher’s attention must be divided if in a group, which may not enable them to attend to the needs of each student. Skill levels would also differ for each student, probably affecting the effectiveness of the lessons. Thirdly, the scheduling of group classes is often less flexible and may not suit every family.

11+ Maths Self-Study

With Self-Study, the option for flexibility and cost-effectiveness is a given, as students can study at a pace that they are comfortable with. This style nurtures autonomy and self-discipline since students handle their learning. Such a system can be well achieved if highly motivated students are aware of how to budget time. All resources will be available to complement this: books, worksheets, and online programs. The student may freely work out their customised study plan to suit their personal requirements.

However, self-study depends vastly upon self-motivation and discipline. Left without the framework provided by a tutor or teacher, it is so easy for students to get sidetracked or lowly focused. There is also a possibility of losing important content or failing to follow through on some topics as there is no teacher available to give immediate feedback. This can also be isolating for students, especially for those who may struggle with a particular topic or concept or for those who are more used to the classroom setting.

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