Transum Software

Quadratic Equations

Practise solving quadratic equations algebraically with this self-marking exercise.

Factorising Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Exam Desc Help More

This is level 6; Three terms and the roots are not necessarily integers. You can earn a trophy if you get at least 7 correct. For this exercise all answers should be rounded to three significant figures.

\( x^2 + 2x − 2 = 0 \)

x = and Correct Wrong

\( x^2 + 4x − 1 = 0 \)

x = and Correct Wrong

\( x^2 + 6x + 6 = 0 \)

x = and Correct Wrong

\( x^2 + 7x + 3 = 0 \)

x = and Correct Wrong

\( 7x^2 + 4x − 3 = 0 \)

x = and Correct Wrong

\( 6x^2 − 2x − 5 = 0 \)

x = and Correct Wrong

\( 6x^2 − 5x − 7 = 0 \)

x = and Correct Wrong

\( 3x^2 + 3x − 6 = 0 \)

x = and Correct Wrong

\( 2x^2 + 7x + 5 = 0 \)

x = and Correct Wrong

\( 4x^2 − 4x − 4 = 0 \)

x = and Correct Wrong

\( 7x^2 + 2x − 5 = 0 \)

x = and Correct Wrong

\( 5x^2 + x − 1 = 0 \)

x = and Correct Wrong


This is Quadratic Equations level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Featured Activity

Roman Numerals Quiz

Roman Numerals Quiz

You may understand our number system better by learning about another number system. A basic knowledge of Roman numerals will allow you to complete level one of this self marking quiz. Beyond level one will require a little more!


There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:


Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2019 WWW.TRANSUM.ORG

Description of Levels



Factorising - Factorise algebraic expressions in this structured online self marking exercise.

Level 1 - A quadratic equation presented in a factorised form.

Level 2 - Two terms where the unknown is a factor of both. The roots are integers.

Level 3 - Three terms where the squared term has a coefficient of one. The roots are integers.

Level 4 - Three terms where the squared term has a coefficient other than one and the expression factorises.

Level 5 - The difference between two squares.

Level 6 - Three terms and the roots are not necessarily integers.

Level 7 - Mixed questions on solving quadratic equations

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Algebra including lesson Starters, visual aids, investigations and self-marking exercises.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


The video above is from the wonderful Mr Hegarty.

Here is the formula for solving the equation \(ax^2 + bx + c = 0\).

$$ x = \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a} $$

Did you know that there is another formula for finding the roots of quadratic equations? It is called the 'citardauq' (the word quadratic backwards) formula and you can read more about it here but you will never need it for school Maths.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up