Free Diagnostic Maths Test For Primary And Secondary Schools And How To Create Your Own

A diagnostic maths test is designed to identify students’ misconceptions or knowledge gaps. They inform teachers’ decisions about the next stage of a lesson or programme of study.

Studies have shown these diagnostic tests to be one of the top three most effective techniques to improve student achievement (Wisniewski, Zierer, and Hattie). But their effectiveness is dependent on how and when the test is delivered and how the results are used.

This guide will help you understand how to use diagnostic maths tests to improve student learning and students’ understanding. If you want to jump straight to the free diagnostic maths tests for primary and secondary students, you can find them here: Free diagnostic maths tests.

What is a diagnostic maths test?

A diagnostic maths test provides teachers with a detailed understanding of the individual strengths and weaknesses of a student. Made popular by Craig Barton, diagnostic tests provide a precise analysis of the misconception through each student’s chosen answer.

For the most informative results, diagnostic maths tests are most useful when focused on one subject knowledge area, for example, fractions, decimals or percentages. However, they can be used more broadly to identify mathematical gaps and misconceptions in students’ knowledge.

Diagnostic maths tests are a type of formative assessment or assessment for learning. Unlike summative assessments, which measure learning and track progress, a diagnostic assessment allows teachers to understand where knowledge gaps lie among students before, during or after a lesson.

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The results of the diagnostic maths test can be used to inform any targeted support or personalised interventions for a student to improve academic achievement. For example, when students start their online maths tuition with Third Space Learning, they have to complete a short diagnostic maths assessment to ensure tutors know both what to teach and any specific shortcomings there may be within a topic.

Structure and format of a diagnostic maths test

Most often, maths diagnostic tests are multiple choice questions set at a level appropriate for the student’s age and ability. A test should take no more than ten seconds for a student to complete, which means it can be used regularly throughout every lesson, providing frequent and detailed feedback to the teacher from every single pupil. 

At Third Space Learning, all students complete a kick-off quiz – a diagnostic maths test – before they begin tutoring sessions with us. This is a carefully designed multiple choice test where each incorrect answer reveals a specific misconception. It’s designed so that it should not be possible for a student to answer the question correctly while still holding a misconception. This means the kick-off quiz diagnoses gaps in students’ learning and the specific misconceptions holding them back.

diagnostic maths solve and calculate
Third Space Learning’s diagnostic maths Kick Off Quiz

How do diagnostic maths tests improve learner outcomes?

Students’ understanding and attainment improve when teachers use the results of a diagnostic maths assessment effectively. Diagnostic assessments can help identify when an intervention is required and for which topics.

Diagnostic maths tests provide teachers with feedback about the effectiveness of their teaching methods and what learning has occurred. This helps teachers make informed decisions about how to proceed with learning.  

READ MORE: Adaptive teaching

However, to capitalise on the effectiveness of diagnostic assessments, these tests should make it clear to the teacher what each incorrect answer reveals about their students’ understanding.

Answer sheets should reveal details about:

  • Students’ misconceptions
  • Which students gave an incorrect answer
  • Why students made the mistake

This has a powerful impact on teachers’ ability to adjust the lesson and directly address students’ misconceptions to improve their learning and attainment.

Students can also benefit from these results as they receive feedback on their understanding, allowing them to become more reflective and aware of their learning.

Use of diagnostic maths tests to improve pupil progress in tutoring

1. Carefully designed diagnostic questions

Former teachers and pedagogy experts carefully design each diagnostic assessment. Every multiple choice question includes one correct answer and three distractors. Each distractor corresponds to a misconception a pupil may hold.

diagnostic maths quiz
Third Space Learning’s diagnostic assessment for GCSE

All pupils on our programmes, from KS2-KS4, sit this 30-minute initial diagnostic assessment before their first tutoring session. This helps inform their personalised programme of lessons.

2. One question per learning objective on the programme

Each question asked in the initial assessment relates to a single Learning Objective, mapped to each of the 500+ Learning Objectives in our online intervention curriculum.

3. Diagnostic maths test provides a benchmark

Initial diagnostic assessments help to measure the impact of tutoring throughout the term. We compare the answers students give with post-session questions and their end-of-term assessments to track their progress. Teachers have on-demand access to all student reports, including the initial diagnostic maths test. 

The progress of students during a term and their achievements on their end of term test are subject to many factors. For this reason, we encourage teachers to reflect on each student’s responses individually where possible.

4. Continuous assessment for learning within each lesson

Diagnostic maths assessment carries on beyond the initial assessment. ​​ Personalised learning allows tutors to guide students through each lesson at the appropriate pitch and pace.

Tutors are trained to ask questions throughout the session to assess student’s understanding and adapt teaching accordingly. This gives students the best opportunity to make progress.

How to create an effective diagnostic maths test for your own maths lessons

There are three important areas for consideration when creating effective diagnostic tests for maths lessons: 

  • Effective design
  • Classroom culture
  • Professional development

1. Effective design of a diagnostic maths test

The tests should be well-designed and tailored to the individual needs of the class. 

Multiple choice questions are the most effective form of diagnostic maths test with questions specifically designed to show any misconceptions. Each incorrect answer for the multiple choice question should relate to a different maths misconception. It should not be possible for a student to select the correct answer while holding a misconception.  

2. A low stakes environment with the freedom to make mistakes

Students will inevitably give incorrect answers. So there needs to be a classroom culture that allows students to feel comfortable making mistakes and a shared growth mindset that incorrect answers represent an opportunity to improve learning. 

Diagnostic questions will be counterproductive if they create anxiety as this adds to students’ cognitive load and makes it more difficult for them to learn new information. When teachers refer to incorrect answers as misconceptions, it can help lessen the anxiety or blame students feel.  

3. Professional development

The most experienced teachers will likely find it easier to identify the most common misconceptions associated with each topic. This knowledge makes it easier to set the questions for the assessment. This will develop naturally over time as a teacher’s experience grows but can be supported with resource sharing and professional development

Sharing best practices is one of the most effective forms of teacher professional development.  There are two ways in which sharing best practices can support colleagues improve students’ learning through the use of diagnostic assessments:

  • Sharing premade diagnostic questions
  • Sharing strategies and resources that challenge students’ misconceptions

Third Space Learning created diagnostic questions and free resources to support teachers’ intervention strategies that can be downloaded below. However, it is not enough to identify students’ misconceptions. Teachers need to develop the skills required to challenge and correct them.  

Alternative diagnostic tools for maths

If carefully created with the express purpose of diagnosing the error (not just providing a score or an ‘achieved/not achieved’ result) other tools can be used diagnostically such as:

Generally speaking, other formative assessment tools, such as open-ended questions, closed questions or standard worksheets, are not suitable for diagnosing misconceptions.

Free and premium diagnostic maths tests

Even the most experienced maths teachers can find it time-consuming to create effective diagnostic maths tests. That’s why Third Space Learning created a bank of free resources for teachers, including diagnostic maths tests, suitable for students from key stage 2 to key stage 4.  

To supplement these are detailed per-topic diagnostic assessments as part of our premium subscription.

Free detailed diagnostic maths tests for primary school and SATs

Misconceptions are a natural part of the learning process in mathematics. Identifying and challenging these misconceptions when they occur prevents them from becoming ingrained and detrimental to learning in secondary school.

The free diagnostic assessments from Third Space Learning are designed in pairs. Use one at the start and end of a unit of study. 

  • The pre-test is an effective baseline assessment to inform teachers about their students’ prior knowledge and misconceptions. This allows teachers to deliver the subsequent lessons at an appropriate level and without including any unnecessary previously learned content. 
  • The post-topic diagnostic test assesses whether the students successfully meet the learning outcomes, if any topics need to be retaught, or if students need further support.  

Each diagnostic maths assessment includes a detailed mark scheme that indicates the correct answer and explains the distractor answers and misconceptions.

Free general diagnostic maths tests per year group

If you’re looking for something more general for your class there are also multi-topic diagnostic maths tests for your year group. These can be used at the beginning or end of the year and come in two separate bundles to make this easier to manage.


Working with expert maths teachers we’ve created over 60 more detailed diagnostic maths assessments for all key national curriculum maths and numeracy topics. These are available with a premium subscription to the Third Space Learning Maths Hub. They come in pairs so you can do a pre and post lesson quiz with pupils. 30 minutes well spent to get a detailed insight into each pupils strengths and weaknesses on a topic.

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Free diagnostic maths tests for secondary school and GCSE 

You can download over 50 GCSE diagnostic maths tests from this collection of Diagnostic Questions.

Each diagnostic maths test contains twenty multiple-choice questions that directly relate to the key skills required to master the GCSE topics. Carefully selected incorrect answers highlight a specific misconception. Therefore, subsequent teaching can be target misconceptions to improve learning and understanding most efficiently. 


For a full selection of diagnostic maths tests available make sure you visit the totally free Secondary Resource Library. As well as diagnostic maths tests for all topics across Number, Probability, Geometry, Ratio and Proportion and Statistics, you’ll also find over 40 GCSE maths papers, hundreds of GCSE maths worksheets with exam questions and lots of GCSE maths revision resources.

Discover the FREE Secondary Resource Library

Diagnostic maths tests FAQs

What is a diagnostic maths test

A diagnostic maths test identifies students’ misconceptions to help adapt learning activities or instruction to meet students’ needs.

What are the key features of a multiple-choice diagnostic maths question?

A multiple-choice diagnostic maths question has one correct answer that can only be answered correctly if a student does not hold any misconceptions.  Each incorrect answer is designed to reveal a different misconception.

What is the difference between summative and formative assessment?

Formative assessments, such as diagnostic questions, are designed to improve learning. They provide teachers with the necessary information to adapt their teaching.  Summative assessments inform teachers about the learning students retain, such as an end-of-topic test.

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Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly maths intervention programmes designed to plug gaps and boost progress.


Since 2013 these personalised one to one lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.


Learn about the diagnostic assessment or request a personalised quote for your school to speak to us about your school’s needs and how we can help.


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