We have below bronze, silver and gold tutorials for Determing the Nature of Roots in the Relationships unit of National 5 Mathematics. Bronze tutorials are typically unit assessment standard with the silver tutorials providing typical "exam type" questions as examples. If you can manage these you should try our more advanced gold tutorials containing the more unpleasant "exam type" questions. Typically as you work through the modules, the difficulty of the skills increase by one step ensuring smooth progression. Simply click on the video to play it and pause it at the relevant points for you to attempt the questions. Each tutorial has a corresponding worksheet for you to download if additional practice is required. Make sure you have a pen and paper handy! Once you've mastered the skills, why not try the Pastpaper questions at the bottom of the page?

These are the skills that you should already have mastered with BEFORE you begin studying this National 5 module. If you are unsure, watch the videos and try some questions.

• Solving multi-step equations (MTH 315a)       Bronze       Silver       Gold
• Solving linear inequalities (REL 1.1c)             Bronze       Silver       Gold
• Using the quadratic formula (REL 1.3a)          Bronze       Silver       Gold

Working with the dicriminant is a skill dropped down from the old higher. This bronze module teaches you how to calculate the discriminant and to use it to determine the nature of the roots, classic unit assessment stuff!

VIDEO 117: Outcome 1 - Determining the nature of the roots. Grab a pen and your Rigour jotter. Make sure you try all the questions! 

If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons (or use the worksheet) for any questions you answered incorrectly. Once you have completed the quiz, record the score in your profile and move onto silver level!

In our silver module we move on to the "a/b stuff" where we look at solving quadratic equations for equal roots.

Video 118: Outcome 1 - Solving for equal roots. Remember to copy down the worked examples and take notes. These will help you revise and remember!

If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons (or use the worksheet) for any questions you answered incorrectly. Once you have completed the quiz, record the score in your profile, go for gold and/or try the past paper questions!

Gold level takes it another step further yet again. In this module we solve for real or no real roots. Remember the rule for solving negative inequalities!

Video 119: Outcome 1 - Solving for real or no real roots. The final video in this module. After this, remember to think about your next steps!

If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons (or use the worksheet) for any questions you answered incorrectly. Once you have completed the quiz; record the score in your profile and try the past paper questions!

Once you have mastered the skills, why not try the pastpaper questions? Click on each question to play the video. Pause it when prompted to do so and have a go yourself first. When you've finished check the solution. You should aim to complete these questions more than once at various stages throughout the year. If you feel that you need more practice at that particular question go to the practice area suggested in the video...good luck!

You have completed this module - well done! Remember to go back and redo any areas of weakness, that's how we improve. If you are happy with all areas, go back to the main menu and pick another topic to practice!