help!!!

[mari khan]

hey i need math notes for olevelss...
specially cordinate geometryyy notes
can someone post it ??/

 

[student8]

https://www.xtremepapers.com/community/threads/o-level-mathematics-notes-formulas.16401/
hope it help but i would say dont rely on notes but practice pastpapers, they make will u ready for exams, cus for math practice is necessary,note does not help

 

[unitika]

If lines L1 and L2 are parallel, they have the same angle of inclination to the x-axis. This means that, parallel lines have equal gradients.

Perpendicular lines
Perpendicular lines are lines that cross at right angles to each other.
To find if two lines are perpendicular you simply have to follow these simple steps:

1. Calculate the gradient of the first line.
2. Calculate the gradient of the second line.
3. Multiply your answers together.

If the answer is -1, then you know that the lines are perpendicular. (If the answer is anything else, then the lines are not perpendicular.)
The mathematical way of describing these steps is to say that the product of the gradients of lines equals minus 1.

 

[unitika]

The equation for a straight line can always be described by an equation of the form:
y = mx + c
where m is the gradient of the line, and c is where the line intercepts the y-axis. (This is because the graph crosses the y-axis when x = 0, and if x = 0, y = c.)
See the diagram below:
So if we know the values for m and c, we can instantly write the equation of the line!
For example:
A line with gradient 3 that crosses the y-axis at (0, 4) has equation, y = 3x + 4.
Finding the equation of a line if we know one point and the gradient
If we know the gradient and the position of one point on the line, we can easily find the equation of the line by inserting the values we know into the equation y = mx + c.
For example:
If we know a point on the line is (4, 2) and that the gradient is 3, then:
2 = 3 x 4 + c.
Therefore, c = 2 - 12 = -10.
Now, we know c and m, so the equation of the line is y = 3x - 10.
An alternative method is to use the formula:
(y - y1) = m(x - x1)
where m = gradient, and (x1, y1) is the known point.
Explanation:
This works because the gradient between any two points on the line is always the same. Therefore the gradient between a general point (x, y) and a known point (x1, y1) is constant.
This gives:

or more usefully,
(y - y1) = m(x - x1)
where m = gradient, and (x1, y1) is the known point.
Using our earlier example:

Finding the equation of a line if we know two points on the line
If we know the position of two points on the line, we can easily find the gradient (m), using:

Once you have calculated the gradient, you can use either of the known points to then find the equation of the line.
For example:
Find the equation of the line joining (2, 7) to (5, -2).

Therefore, using the point (2, 7) we get that the equation of the line is:

 

[unitika]

The curves of y = kxn (where n is a positive integer)
You must be able to recognize the various graphs of y = kxn, so here they are for you to learn...

 

[unitika]

There are three features that are of interest when sketching a quadratic graph

1. Where the graph crosses the y-axis.
2. Where the graph crosses the x-axis.
3. Where the graph turns.

The graph crosses the y-axis when x = 0. For instance, at the value of the constant in the equation.
The graph crosses the x-axis when y = 0. For instance, solve the quadratic = 0. The turning point is found by either completing the square or using differentiation.

 

[unitika]

If we don't already know what a graph will look like we need to find its main features. These are:

1. Where the graph crosses the y-axis, which is when x = 0. (i.e. at the constant).
2. Where the graph crosses the x-axis. To find the roots (where the graph crosses the x-axis), we solve the equation y = 0.
3. Where the stationary points are. The stationary points occur when the gradient is 0 (i.e. differentiate.) Whether there are any discontinuities.
4. Are there any discontinuities? A discontinuity occurs when the graph is undefined for a certain value of x. This occurs when x appears in the denominator of a fraction (you can't divide by zero).
5. What happens as x approaches ± ∞? When x becomes a large positive or a large negative number the graph will tend towards a certain value or pattern.