Quadratic EquationsPractise solving quadratic equations algebraically with this selfmarking exercise. 
This is level 7; Three terms and the roots are not necessarily integers. You can earn a trophy if you get at least 9 correct. For this exercise all answers should be rounded to three significant figures.
InstructionsTry 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.orgThis 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. 
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 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College: "Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work" Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" 
Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page. 

AnswersThere 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. If you would like to enjoy adfree access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe 

Go MathsLearning 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 MapAre 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: 
Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes. 
It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B! 
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. 
Close
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.
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/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More Algebra including lesson Starters, visual aids, investigations and selfmarking 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.
See the National Curriculum page for links to related online activities and resources.
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.
Answers can be typed in as decimals or fractions but not mixed numbers. For example the answer of \(1.2\) can also be typed in as \( \frac{6}{5} \) but not as \( 1\frac{1}{5} \). This due to limitations of the software used to check your answers. Note that the mixed numbers option would be acceptable in examinations.
Use the forward slash / when typing in fractions.
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 doubleclick 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.
These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.
Close
Lisa, HPSC
Thursday, August 11, 2022
"Be great if we could enter fractions using the slash e.g. 1/2.
[Transum: Great idea Lisa. The fraction input capability has been activated, Use the forward slash / when typing in fractions. Mixed numbers however will not be recognised so please type those as improper fractions.]"