Sunday, 21 April 2013

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.

Saturday, 20 April 2013

Coordinate Geometry - about a SLOPE

Labels: Coordinate Geometry

The Slope of A Line source: http://math.about.com

Identify a few concepts on (i) gradient properties (ii) equation of a line (iii) trigonometry and gradient and (iv) collinearity from the article below. Post as comment.
When the slope of the line is 0, you know that the line is horizontal and you know it's a vertical line when the slope of a line is undefined. In the Figures below, the subscripts on point A, B and C indicate the fact that there are three points on the line. The change in y whether up or down is divided by the change in x going to the right, this is the 'rise over run' concept. y = mx + b is the equation that represents the line and the slope of the line with respect to the x-axis which is given by tan q = m. This is the slope-intercept form of the equation of a line. (m for slope? Seems to be the standard!) When the slope passes through a point A(x₁, y₁) then y₁ = mx₁ + b or with subtraction y - y₁ = m (x - x₁) You now have the slope-point form of the equation of a line. You can also express the slope of a line with the coordinates of points on the line. For instance, in the above figure, A(x, y) and B(s, y) are on the line y= mx + b : m = tan q = therefore, you can use the following for the equation of the line AB: The equations of lines with slope 2 through the points would be: For (-2,1) the equation would be: 2x - y + 5 = 0. For (-1, -1) the equation would be: 2x - y + 1 = 0

Coordinate Geometry - Line - Point - Ray

Labels: Coordinate Geometry

GCE O Elementary Mathematics syllabus for COORDINATE GEOMETRY

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LINE - POINT - RAY
source: http://www.mathsisfun.com

In geometry a line:

is straight (no curves),
has no thickness, and
extends in both directions without end (infinitely).
A line has no ends

What is the main difference(s) between (a) a line, (b) a segment and (c) a ray ?

Point, Line, Plane and Solid

A point has no dimensions, only location
A line is one-dimensional
A plane is two dimensional
A solid is three-dimensional

Coordinate Geometry - Cartesian Plane (review lower secondary work)

Labels: Coordinate Geometry

By Mr Johari

Watch the following video and answer the questions that follow:

Questions: (post your responses as comments)

.1 What is the significant of Cartesian plane?
.2 Give an example of an ordered pairs and explain all the terms used.
.3 What is the significant of the 4 quadrants in the Cartesian plane?
.4 Give an example of the application of Cartesian plane. (some examples are shown below)

Tuesday, 16 April 2013

16/4 MATH SCRIBE POST – Justin

~(•O•)~ E Math: Trigonometry Revision

CONTENT:
1. Trigonometric Functions
2. Trigonometric Rules
3. Special Angles!

*Do note that most, if not all, of these rules apply to only right angled triangles unless stated otherwise.

1. Trigonometric Functions
REVISION: Big Legged Lady
Toa (Big) – T for tangent, and O is before A.
Therefore: tan(x) = O/A
Cah (Leg) – C for cosine, and A is before H
Therefore: cos(x) = A/H
Soh (Lady/Auntie) – S for sine, and O is before H.
Therefore: sin(x) = O/H

sin^2(x) = (sin(x))^2 <–– THIS RULE applies to all trigonometric functions

2. Trigonometric Rules

1. tan(x) = sin(x) ÷ cos(x)

2. sin(90 - x) = cos(x)

cos(90 - x) = sin(x)

tan(90 - x) = 1/(tan(x))

3. sin^2(x) + cos^2(x) = 1

4. sin(180 - x) = sin(x)

cos(180 - x) = -cos(x)

tan(180 - x) = -tan(x)

5. PYTHAGORAS THEOREM

a^2 + b^2 = c^2

6. Using the Z-rule

angle of depression = angle of elevation