Math Flashcards
What happens when circle touches both axis
centre = -g;-g & radius = g & c=g^2=f^2
Do cosine and sine rule work in radians
no without conversion
How to find non right-angles in right-angle triangles
If you have at least 2 sides
Use cos or sin
|AO| = 90
|DO| = 60
Cos(<DOA) = 60/90
<DOA = cos-1(60/90)
Equation of circle when given 3 points
Make 3 equations by subbing in points to eq. of circle from logbook
CosA = x/y
What is SinA
SinA = {y^2 - x^2}/y
Think of right angled triangles
R angled Triangle has angle A
Tan(A) is 96/37
What are two of the sides of the traingle
Opposite side is 96 and adjacent side is 37
How many cm^3 in a ml
1
Completing the square
x^2 + bc + c
Becomes
(x + b/2)^2 + c - (b/2)^2
What does completing the square tell us
a(x+b)^2 + c
The vertex(point where quadratic has min/max)
Vertex = (-b, c)
Stationary point
when derivative = 0
Height/radius which minimizes surface area
ds/dr = 0
Displacement + speed + acceleration
Derivative of an objects position/displacement is speed/velocity
Derivative of speed/velocity is acceleration
How to find value of c in integral
Generally there is a value that you can equate the integral too
Or sometimes the sum is 0 when the variable is 0 so that should allow you to figure out c value
How to find percentage reduction / increase
1 - [Changed / Original]
Multiply by 100 to get percentage
-If negative then it is an increase
1- [120/200] = 0.4 X100 = 40% reduction
1 - [500/200]= |-1.5 X 100|= 150% increase
Percentage error
|Expected-Actual|/ Actual
X 100
Derivative of irregular cos-1
E.g.
4/x, 3x^2
Must use chain rule. Use the whole value as the x value. I.e. sub 3x^2 in as x the formula and a as 1. Multiply that by derivative of x value
1. Sub 3x^2 in as x
2. Find derivative of 3x^2 = 6x
3. Multiply cos-1 formula by derivative(6x)
Cos-1 questions with basic x fractions ( x/3 , x/4, x/7 ) can just be subbed normally into formula with denominator as a. No need to multiply by derivative
Writing trigonemtric function steps
- a = (max + min) / 2
- b = | (max - min) / 2 |
- c = 2pi / period
- Pick one of:
•sin [starts on mid and goes up]
•cos [starts on max]
•-sin [starts on mid and goes down]
•-cos [starts on min]
Period
2pi / c
Find pth percentile
- p/100 X n(number of values) = c
- If c = whole number, get c and c+1 numbers and divide by 2
- If c = decimal round, round up and go to that position in dataset
What is the percentile ranking of x
- Order data
- Find position(c) of x in dataset
- (c-1)/n[number of items] = pth percentile
