• Skip to primary navigation
  • Skip to main content
singaporeolevelmaths

singaporeolevelmaths

Simple Tips for Better Maths Results!

  • Pass With Distinction A-Maths Programme
  • About
  • Books
    • O-Level Maths Ten Years Series Books
    • O-Level Pocket Summary
  • Videos
  • What They Say
  • Contact

proving

What You Need To Know To Do Well In Plane Geometry - Part 1

Plane Geometry is the new topic added in the new syllabus. There are hardly any calculations but lots of proving to be done.
We know students dislike proving, be it in Plane Geometry, Trigonometry, Quadratic Equations, Differentiation . . .

To score As in your exam, you must be good in proving.

Plane Geometry has proven to be a challenging topic for many students due to the nature of the diagrams, questions. Many a times, students do not know when to begin, not to mention which theorems to apply. I am going to share with you in this post on the key concepts you need to know at your fingertips for Plane Geometry.

There are 2 basic shapes in Plane Geometry: Triangle & Circle

In Triangle,

  1. You must know the different Congruency Tests & Similarity Tests. These are extremely important in proving plane geometry questions. Teachers did not emphasize on this as students are expected to know these concepts well from E-Math. But I realize many many students did not like Congruency & Similarity as it involves proving (which is a very systematic approach of thinking) and hence many did not understand these 2 concepts well.
  2. Mid point theorem (This is not exactly your mid point formulae in Co-ordinate Geometry)
  3. midpointtheorem.jpg

    D and E are the midpoints of AC and AB respectively.

  4. Intercept theorem
  5. intercepttheorem.gif

    When DE//CB, AD/DC = AE/EB

I will be adding on specific properties for circle in my next post. If you like to be updated, subscribe to my feed by clicking HERE

Filed Under: A-Maths Tuition Tagged With: plane geometry, properties of circles, proving, similar triangles

Quadratic Equation Discriminant Proving Question

I realize many students have a challenge with presenting the solution of proving question. I am going to illustrate the correct way using the following question.

Show that is always positive for all real values of x.

=> what is always +ve? the values of y not x ( x can be of any values)

=> The graph will not touch x-axis; it is "hanging" above the x-axis

=> No roots, hence discriminant is less than 0

TIPS FOR SHOWING/PROVING QUESTION

  • Have an end in your mind. Be clear of the underlying concepts that the question is asking you to prove. Work towards that. For example, in the question, we want to prove that the discriminant is less than 0. <== this is the end.
  • Sketch to have a clearer idea.

quadraticprovingqn.jpgquadraticprovingqn.jpg

Filed Under: A-Maths Tuition Tagged With: discriminant, proving, quadratic equations, showing

Copyright © 2023 · singaporeolevelmaths.com · Talk to us at 88290998