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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 3; Three terms where the squared term has a coefficient of one. The roots are integers. You can earn a trophy if you get at least 7 correct.

\( x^2 + 6x + 8 = 0 \)

x = and Correct Wrong

\( x^2 + 7x + 12 = 0 \)

x = and Correct Wrong

\( x^2 − 2x − 3 = 0 \)

x = and Correct Wrong

\( x^2 − x − 2 = 0 \)

x = and Correct Wrong

\( x^2 + 2x − 3 = 0 \)

x = and Correct Wrong

\( x^2 + 5x + 6 = 0 \)

x = and Correct Wrong

\( x^2 − 8x + 12 = 0 \)

x = and Correct Wrong

\( x^2 + 7x + 12 = 0 \)

x = and Correct Wrong

\( x^2 − 10x + 21 = 0 \)

x = and Correct Wrong

\( x^2 + 7x + 10 = 0 \)

x = and Correct Wrong

\( x^2 + 6x + 5 = 0 \)

x = and Correct Wrong

\( x^2 − 5x − 6 = 0 \)

x = and Correct Wrong

Check

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

Instructions

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.

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Featured Activity

Nine Digits

Nine Digits

Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

Answers

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.

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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.

Teachers

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.

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Description of Levels

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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.

Help

Example Level 3

\( x^2 - 6x + 8 = 0 \)

The expression on the left of this equation can be factorised.

\((x − 2)(x − 4) = 0\)

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

So either \(x-2=0\) which means \(x=2 \)

Or \(x-4=0\) which means \(x=4 \)

So the two answers are 2 and 4

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.

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