# Quadratic Equations

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

##### FactorisingLevel 1Level 2Level 3Level 4Level 5Level 6Level 7Level 8ExamMenuHelp

This is level 7; Three terms and the roots are not necessarily integers. You can earn a trophy if you get at least 7 correct. For this exercise all answers should be rounded to three significant figures.

 $$x^2 + 2x + 1 = 0$$ x = and $$x^2 + 4x + 1 = 0$$ x = and $$x^2 + 6x + 1 = 0$$ x = and $$x^2 − 6x + 5 = 0$$ x = and $$3x^2 + 2x − 2 = 0$$ x = and $$3x^2 + 5x + 2 = 0$$ x = and $$6x^2 − 5x + 1 = 0$$ x = and $$6x^2 − 5x − 2 = 0$$ x = and $$7x^2 − 5x − 3 = 0$$ x = and $$4x^2 − 3x − 4 = 0$$ x = and $$6x^2 − 7x + 2 = 0$$ x = and $$2x^2 + 7x − 3 = 0$$ x = and
Check

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

## 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.

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#### Four Colour Theorem

This mathematical activity involves colouring in! That makes a change. Using the paint bucket tool can you flood fill the regions so that no two adjacent regions are the same colour?

## 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

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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

Here is the formula for solving the equation $$ax^2 + bx + c = 0$$.

$$x = \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}$$

Did you know that there is another formula for finding the roots of quadratic equations? It is called the 'citardauq' (the word quadratic backwards) formula and you can read more about it here but you will never need it for school Maths.

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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