S2 Flashcards
What is a population?
A collection of items/individuals
What is a census?
When information is obtained from all members of a population.
Give three advantages of a census.
- Every member is used.
- Unbiased
- Gives accurate answer
Give three disadvantages of a census.
- Long time to do
- Expensive
- Difficult to ensure whole population surveyed
What is a sample?
The chosen members of a population
What is a sampling frame?
A list of all of the sampling units.
Give three advantages of sampling
- Cheaper than census
- Destruction of all sampling units not needed (lifespan)
- Data easier to collect
Give a disadvantage of sampling.
Bias can occur
What is a random sample?
A sample in which every item has an equal chance of being selected
What is a sampling distribution?
All of the potential outcomes and their probability
What is a statistic?
A quantity calculated from the observations of a sample.
What is a critical region?
The range of values which lead to H0 being rejected.
What is the parametric form of an ellipse?
𝑥 = a cos θ , 𝑦 = b sin θ
What is the parametric form of a hyperbola?
𝑥 = a cosh θ , 𝑦 = b sinh θ
What is a hyperbola/ellipse?
A hyperbola/ellipse can be defined as the locus of a
point P which moves so that PS = e PN
How is the locus of a point on an ellipse/hyperbola found?
- Find equation of tangent
- Find where tangent crosses axes.
- Find midpoint
- Solve for sinx/cosx
- sin^2+cos^2=1
What is ∫ sec x tan x dx
secx
What are the 4 methods for solving non-standard integrals?
- Multiply by 1
- Substitution
- Complete square
- Reverse chain rule
For ∫x^n/(a^2+x^2)^1/2 dx, what substitution is best?
- u=a^2+x^2 when n is odd
- Trig/hyp when n is even
How is a reduction formula for sin^nx found?
^n-1 x sin
How is a reduction formula for cos^nx or tan^nx found?
^n-2 x …
In = ∫ sinnx/
sin x dx solve?
sin[(n-2)x +2x]
Volume of parallelepiped?
|a . (b × c)|
Volume of a tetrahedron?
1/6|a . (b × c)|
Distance from the point P (α, β, γ) (or point on plane) to the plane
ax + by + cz – d = 0?
𝑠 = |aα + bβ + cγ − d|
| √a2 + b2 + c2 |
How is cartesian equation for plane found?
ax + by + cz – d = 0 is given by r. n = d (ie perpendicular vector)
Reflection in plane?
OA’ = OA + 2AP
Distance between skew lines.
d = (c − a) . b × d
|b × d|
Normalise vector
divide by magnitude
Diagonalise matrix
- Find eigenvalues
- Find eigenvectors
- Normalise eigenvectors
- Find orthogonal matrix
- Find diagonal matrix
