Transum Software

Quadratic Equations

Practise solving quadratic equations with this self marking exercise.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Description More Algebra

This is level 7; Mixed You can earn a trophy if you get at least 7 correct.

1. Find the values of x for which x2 + 6x + 8 = 0.

x = and Correct Wrong

2. Solve the equation x2 − 8x + 15 = 0.

x = and Correct Wrong

3. Find the x values where the graph of y = 5x2 − 11x + 2 crosses the x-axis.

x = and Correct Wrong

4. Solve the equation 5x2 − 35x + 30 = 0

x = and Correct Wrong

5. Find the values of x for which 2x2 + x − 3 = 0. Give your answers to three significant figures.

x = and Correct Wrong

6. Solve 4x2 + 7x + 1 = 0. Give your answers to three significant figures.

x = and Correct Wrong

7. Find the roots of 7x2 + 6x = -1. Give your answers to three significant figures.

x = and Correct Wrong

8. Find the values of x for which 5x2x = 2. Give your answers to three significant figures.

x = and Correct Wrong

9. Solve 25x2 = 16.

x = and Correct Wrong

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 Correct Wrong

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 Correct Wrong

12. Solve (x − 5)(x + 2) = 18

x = and Correct Wrong


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


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.

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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:

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



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


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.