Transum Software

Quadratic Equations

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

Menu Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Exam Help

This is level 2; Two terms where the unknown is a factor of both. You can earn a trophy if you get at least 9 correct.

\( x^2 − 4x = 0 \)

x = and Correct Wrong

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

x = and Correct Wrong

\( x^2 − 7x = 0 \)

x = and Correct Wrong

\( x^2 − 5x = 0 \)

x = and Correct Wrong

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

x = and Correct Wrong

\( x^2 − 8x = 0 \)

x = and Correct Wrong

\( 2x^2 − 6x = 0 \)

x = and Correct Wrong

\( 3x^2 + 6x = 0 \)

x = and Correct Wrong

\( 4x^2 − 12x = 0 \)

x = and Correct Wrong

\( 10x^2 + 2x = 0 \)

x = and Correct Wrong

\( 4x^2 − 3x = 0 \)

x = and Correct Wrong

\( 10x^2 = −3x \)

x = and Correct Wrong


This is Quadratic Equations level 2. You can also try:
Level 1 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8


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.

Why am I learning this?

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 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

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Snooker Investigation

Snooker Investigation

Given the width and height of a snooker table can you predict which pocket the ball will end up in and how many times will it bounce off one of the sides?


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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:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if should go offline for whatever reason, there is a mirror site at that contains most of the resources that are available here on

When planning to use technology in your lesson always have a plan B!

Lisa, HPSC

Thursday, August 11, 2022

"Be great if we could enter fractions using the slash e.g. 1/2.

[Transum: Great idea Lisa. The fraction input capability has been activated, Use the forward slash / when typing in fractions. Mixed numbers however will not be recognised so please type those as improper fractions.]"

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.


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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.

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 - Quadratic equations that factorise after being rearranged.

Level 6 - The difference between two squares.

Level 7 - Three terms and the roots are not necessarily integers.

Level 8 - 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.

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.

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Curriculum Reference

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


Example Level 2

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

The expression on the left of this equation can be factorised as each of the two terms contains a factor of \(x\).

\(x(x + 7) = 0\)

Here there are two terms which multiply together to give zero. It is therefore true that at least one of the terms must be zero.

So either \(x=0 \)

Or \(x+7=0\) which means \(x=-7 \)

So the two answers are 0 and -7

Answers can be typed in as decimals or fractions but not mixed numbers. For example the answer of \(1.2\) can also be typed in as \( \frac{6}{5} \) but not as \( 1\frac{1}{5} \). This due to limitations of the software used to check your answers. Note that the mixed numbers option would be acceptable in examinations.

Use the forward slash / when typing in fractions.

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

Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

MathQuill Animation