Embedded Files
Section overview:
Section overview:
The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
Prior knowledge: GCSE Solving quadratic equations, GCSE Curve sketching (only quadratic graphs required in this section)
P1-Chp2-Quadratics.pptx
Notes:
Notes:
Section 1 Notes - Quadratic graphs and equations
Section 2 Notes - Discriminant and problem-solving
Remote learning:
Remote learning:
Use the following resources when directed in order to build up the fundamental skills to make the most of your classroom learning. Prior knowledge for the topic is highlighted at the top of the page.
1) Quadratic methods
1) Quadratic methods
This topic recaps and builds on the work from GCSE. Each section of the video recalls the core algebraic methods and their applications to graph sketching.
Watch the video for explanations and examples (times are shown below for the different sections, in case you feel confident to move on):
Quadratic methods.mp4Notes:
Notes:
You can find annotated notes from the video here (please check through these carefully if you have skipped any parts of the video):
Quadratics 1 SW (independent) - annotated.pdf(Click the icon in the top-right corner to open in a new window for increased readability.)
Additional exploration (just for fun):
Additional exploration (just for fun):
Use this GeoGebra applet to further explore the relations between geometric and algebraic aspects of quadratic equations.
Practice:
Practice:
Try a selection of problems from these worksheets before completing the Google Form review question. Remember to check your solutions at the end of the documents to assess your understanding.
See Google Classroom assignment post for Google Form review question
If you are unsure about any of this work, please use the rest of the resources on this page or contact your teacher to fully develop your understanding on the topic before your next lesson.
2) Using the discriminant
2) Using the discriminant
This remote learning section explores a new and important property of quadratic equations.
Watch the video for explanations and examples:
Quadratics - using the discriminant.mp4Visualise the discriminant with this applet or create your own problems here.
Notes:
Notes:
You can find annotated notes from the video here:
Quadratics 2 SW (independent) - annotated.pdf(Click the icon in the top-right corner to open in a new window for increased readability.)
Practice:
Practice:
Try a selection of problems the worksheet before completing the Google Form review question. Remember to check your solutions at the end of the document to assess your understanding.
See Google Classroom assignment post for Google Form review question
If you are unsure about any of this work, please use the rest of the resources on this page or contact your teacher to fully develop your understanding on the topic before your next lesson.
Extra resources:
Extra resources:
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
Playlist 1 - Quadratic methods
Playlist 2 - Quadratic modelling [Watch the video example before attempting the practice questions. There are hints available for each problem if you get stuck.]
Extra fun!
Interactive simulation:
Interactive simulation:
See quadratics in action!
You will need to be familiar with the algebra and geometry of the first three pages ('Explore', 'Standard Form' and 'Vertex Form'). Use this simulation to explore how one affects the other, as well as why the different forms of quadratics are useful.
Extension: The final page ('Focus & Directrix') is an extension beyond the A-level Maths specification. Can you see how these properties relate to the parabola (or, rather, how the parabola relates to these properties)? You can find out more about the focus and directrix here.
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