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quadratic equations

What Are Roots of a Quadratic Equation?

Do you know that roots of a quadratic equation can also mean the solutions, the x intercepts or simply put it the answers to the equation?

It is something we have learnt since lower secondary.

In 2019, GCE O Level Additional Maths Paper 2 Q10 tested candidates on their basic understanding of roots.

11 marks! Wow!

If you have been simply surface learning, you won't get past part (i) of the question.

See the video to see how I approach this question: https://www.youtube.com/watch?v=CPtbpO4At9w

Filed Under: A-Maths, Video Learning Tagged With: quadratic equations, sum and product of roots

A-Maths: Find Equation of Circle Given Tangent & Circle + More

Equation of Circle Qn

 

 

 

 

 

Many students after reading the question take a long time to begin as they don't know how to start. The trick is to draw! Drawing helps us to see and understand the question better.

Drawing is one of the keys to answer this question. To answer part (a), we need to notice the property of radius is perpendicular to tangent. Also, in part (b) of the question, we need to apply discriminant from the topic of Quadratic.

I have shared my thinking process and step-by-step solutions in the following videos.

How did you find the videos? Did they help you to understand better? Leave me your feedback in the comment section.

Part (a) URL: Click here to watch part (a)  7 minutes

Part (b) & (c) URL: Click here to watch part (b) & (c)  5 minutes.

Filed Under: A-Maths, Video Learning, Weekly Question Tagged With: angle properties of circle, discriminant, quadratic equations, standard equation of circle, tangent

A-Maths: Quadratic Equation - Sum & Product of Roots [video]

Quadratic Equation is an important topic in O-Level Elementary & Additional Maths.

Different areas are covered for each Math. For example in Additional Maths, we learnt:

  • Discriminant
  • Sum & product of roots
  • Relationship between line and curve

I would like to share with you a question sent to me by a Secondary 3 student on sum & product of roots.

This topic is taught in the beginning for Secondary 3 Additional Maths.

Youtube video link: http://www.youtube.com/watch?v=_Aw6ad7I_fc

Length of video:6 minutes

Filed Under: Video Learning Tagged With: quadratic equations, sum and product of roots

Quadratic Equations Song by St Margaret's Girls

Recently in my Secondary 3 Additional Maths Weekly Tuition Class, I was checking with my students if they have learnt the Quadratic Formula. One boy 'excitedly' pointed out the YouTube video done by three St Margaret Girls! It was shown to his class by his Maths teacher. I came across this video many years ago but could connect with what he was referring to.

Though it's a very simple song, it's useful especially if you're an auditory and kinesthetic learner.

I applaud the effort by the girls!

Direct link: http://www.youtube.com/watch?v=VS56N94Sllc

A Maths Tutor

 

Filed Under: E-Maths, Video Learning Tagged With: quadratic equations, quadratic formula

E-Maths: Completing Square Step-by-Step Video (Part 1)

I was talking to my Secondary 3 students in my O-Level E Maths weekly tuition class on Quadratic when they expressed disgust for the technique of Completing Square.

A similar thing happened when Completing Square was an alternative method offered to Equation of Circle concept. There was a collective yucks from the class.

I hope my video will ease the yuckness many students find with completing square technique and give you some hope to conquer it!

Test out your understanding by leaving your answer for the bonus question in the comments below!

Direct link to video: http://www.youtube.com/watch?v=bf8PfyP2h74

Filed Under: E-Maths, Video Learning Tagged With: completing square, quadratic equations

E-Math: Quadratic Checklist

checklist-emAs I'm writing this post, we are only 89 days away from GCE 'O' Level Elementary Maths Paper 1.

Personally I think in this last phase of preparation, students must feel confident by reflecting on the things they've understand all these while.

I'm going to start this checklist for both E-Math & A-Math in this countdown towards 'O' Level 2010 and I hope you find it useful & beneficial in boosting your confidence and motivating yourself to do better.

For the topic of Quadratic, do you know

  • How to find the intercepts ( x & y), the turning point (minimum or maximum), given a quadratic graph?
  • How to sketch a quadratic graph given any type of quadratic equation?
  • How to complete square for a quadratic equation?
  • How to state the minimum or maximum from a completed square equation?
  • The various methods to solve a quadratic equation?
  • How to handle a problem solving question in Paper 2 involving quadratic concepts?

Above are the main concepts you need to know for Quadratic, feel free to add on any more in the comment section so that more readers can benefit from your sharing.

Study smart & stay cool!

Filed Under: E-Maths Tagged With: checklist, quad, quadratic equations

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