Cheatography
https://cheatography.com
as level p1 of all topics
This is a draft cheat sheet. It is a work in progress and is not finished yet.
Miscellaneous
When money is involved (i.e - money of a company) round off the answer to its significant figure which is usually three. Also, add '.00' (ex - 29.00) if value is only two digits long. |
triangle theories |
area of a triangle |
1/2 absin(C) |
to find third side |
a2 = b2 + c2 - 2bc*cosA |
to find angle |
cosA = (b2 + c2 - a2)/2bc |
sin rule |
a/sinA = b/sinB = c/sinC |
Quadratics
General formula |
ax2 + bx + c = 0 |
Discriminant |
b2 - 4ac |
Sum and product of roots |
if roots are x1 and x2
x1 + x2 =-b/a
x1 * x2=c/a |
Vertex |
y = a(x-h)2 + k
coordinates of vertex:
h = -b/2a
Substitute h as x in the quadratic equation and find y |
Axis of symmetry |
x = -b/2a |
Circular measures
types of circles |
x2 + y2 = r2 |
(x-a)2 + (y-b)2 = r2 |
x2 + y2 + 2gx + 2fx + c= 0 |
radius = root of (g2 + f2 - c)
center = -g,-f |
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Functions
Types of functions |
One-to-many, many-to-one, one-to-one or many-to-many |
Sequence of transformations |
The order of vertical and horizontal transformations do not affect the graph. However the order of two vertical (or horizontal) transformations affects the final graph. |
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to do transformations, first convert f to a f (b(x + c)) + d
Do all the transformations from left to right |
Composition of functions |
Doman of composition function depends on domain of first function
Range of resultant function depends on range of second functions |
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Coordinate geometry
Angle between two lines when slopes are given. |
tan(θ) = Absolute value of (m2-m1)/(1+m2m1) |
gradient of y axis is undefined |
gradient of x axis is 0 |
If the question says 'at the same rate' it means that the lines are parallel |
when intersects x axis and y axis are given |
x/a + y/b = 1 |
considering general form of a line to be |
Ax + By + C = 0 |
Distance from a Point to a Line |
d = [|Ax0 + By0 + C| / √(A2 + B2)] |
The centroid of a Triangle |
x coordinates - (x1 + x2 + x3)/3 |
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y coordinates - (y1 + y2 + y3)/3 |
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