AM and EM Assessment Book (GCE O format)

To assist students in their revision and preparation for GCE 'O' Level, the Mathematics Department has made arrangement with the bookshop to order the following 2 books for the students.

The information is as follows:

• Additional Mathematics by topic $7.00
• Mathematics by topic $5.50

Both will include solution booklet

Please make arrangement with your Math teacher on the procedures for purchases.

Performance Task1

updated on April 2013

updated for clarity

Introduction:

For a quadratic equation \( a{x}^2+bx+c=0 \):

Discriminant \( {b}^2-4ac \)	Nature of roots	Characteristics of curve
> 0	2 real and distinct roots	The curve cuts the x-axis (\(y=0\)) at 2 different points
Perfect square	2 real and rational roots
Not a perfect square	2 real and irrational roots
= 0	2 real and equal roots	The curve touches the x-axis at \(x=-\frac { b }{ 2a }  \).  The x-axis is a tangent to the curve.
< 0	No real roots	The curve does not cut or touch the x-axis. It lies entirely above (a > 0) or below (a < 0) the x-axis.

From the first 2 points, we conclude that

                                      \({ b }^{ 2 }-4ac\ge 0\Longleftrightarrow \) the roots are real

Some questions on Logarithm

Link to PDF file

Surds: Question Creating

Find the value, in simplest form, of


\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)

Answer:\(\sqrt{8}=2\sqrt{2} \)

Surds: Question Creating :D

Find the value, in simplest form, of

\(\sqrt{8+3\sqrt{7}}-\sqrt{8-3\sqrt{7}}\)

Answer = \(\sqrt{14}\)
Ming Yi Tay (06)

Find the value, in simplest form, of
\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\) .


Answer=4.
Dean Ang(00)