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

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7DescriptionHelpMore

This is level 7; Mixed questions on solving quadratic equations You can earn a trophy if you get at least 7 correct.

 1. Find the values of x for which x2 + 5x + 6 = 0. x = and 2. Solve the equation x2 − 12x + 32 = 0. x = and 3. Find the x values where the graph of y = 5x2 − 23x + 12 crosses the x-axis. x = and 4. Solve the equation 4x2 − x − 3 = 0 x = and 5. Find the values of x for which 2x2 + x − 6 = 0. Give your answers to three significant figures. x = and 6. Solve 5x2 − 5x − 1 = 0. Give your answers to three significant figures. x = and 7. Find the roots of 2x2 − 4x = 7. Give your answers to three significant figures. x = and 8. Find the values of x for which 2x2 − 7x = 4. Give your answers to three significant figures. x = and 9. Solve 25x2 = 16. x = and 10. A number is squared and added to seven times that same number to give a sum of one hundred and seventy. Let that number be x. Find the two possible values of x. x = and 11. One side of a rectangular garden is x metres long. An adjacent side differs in length by five metres. The area of the garden is 176 square metres. Form equations and solve them to find two possible values of x. x = and 12. Solve (x − 5)(x + 2) = 18 x = and
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This is Quadratic Equations level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

## 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.

## Transum.org

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.

## More Activities:

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 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait:

"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

#### Remainder Race

A brilliant game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number. There are one and two player versions and the rules are inspired by the Royal Game of Ur.

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.

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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

The video above is from the wonderful Mr Hegarty.

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 donâ€™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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