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

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This is level 8; Mixed questions on solving quadratic equations. Use decimals rather than fractions in your answers. You can earn a trophy if you get at least 9 correct.

 1. Find the values of x for which x2 + 6x + 8 = 0. x = and 2. Solve the equation x2 + 2x − 3 = 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 2x2 − 13x + 15 = 0 x = and 5. Find the values of x for which 3x2 + 4x − 7 = 0. Give your answers to three significant figures. x = and 6. Solve 4x2 − 2x − 6 = 0. Give your answers to three significant figures. x = and 7. Find the roots of 4x2 − 3x = 7. Give your answers to three significant figures. x = and 8. Find the values of x for which 2x2 − 3x = 5. 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 8. You can also try:
Level 1 Level 2 Level 3 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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The Transum Newsletter for February 2023 has just been published. Click on the image above to read about the latest developments on this site and try to solve the puzzle of the month. You can read the newsletter online or listen to it by downloading the podcast.

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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.

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## Teachers

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Friday, April 22, 2022

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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 - 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.

## Curriculum Reference

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

## Help

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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