S2 Flashcards

1
Q

What is a population?

A

A collection of items/individuals

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2
Q

What is a census?

A

When information is obtained from all members of a population.

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3
Q

Give three advantages of a census.

A
  • Every member is used.
  • Unbiased
  • Gives accurate answer
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4
Q

Give three disadvantages of a census.

A
  • Long time to do
  • Expensive
  • Difficult to ensure whole population surveyed
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5
Q

What is a sample?

A

The chosen members of a population

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6
Q

What is a sampling frame?

A

A list of all of the sampling units.

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7
Q

Give three advantages of sampling

A
  • Cheaper than census
  • Destruction of all sampling units not needed (lifespan)
  • Data easier to collect
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8
Q

Give a disadvantage of sampling.

A

Bias can occur

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9
Q

What is a random sample?

A

A sample in which every item has an equal chance of being selected

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10
Q

What is a sampling distribution?

A

All of the potential outcomes and their probability

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11
Q

What is a statistic?

A

A quantity calculated from the observations of a sample.

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12
Q

What is a critical region?

A

The range of values which lead to H0 being rejected.

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13
Q

What is the parametric form of an ellipse?

A

𝑥 = a cos θ , 𝑦 = b sin θ

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14
Q

What is the parametric form of a hyperbola?

A

𝑥 = a cosh θ , 𝑦 = b sinh θ

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15
Q

What is a hyperbola/ellipse?

A

A hyperbola/ellipse can be defined as the locus of a

point P which moves so that PS = e PN

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16
Q

How is the locus of a point on an ellipse/hyperbola found?

A
  • Find equation of tangent
  • Find where tangent crosses axes.
  • Find midpoint
  • Solve for sinx/cosx
  • sin^2+cos^2=1
17
Q

What is ∫ sec x tan x dx

18
Q

What are the 4 methods for solving non-standard integrals?

A
  • Multiply by 1
  • Substitution
  • Complete square
  • Reverse chain rule
19
Q

For ∫x^n/(a^2+x^2)^1/2 dx, what substitution is best?

A
  • u=a^2+x^2 when n is odd

- Trig/hyp when n is even

20
Q

How is a reduction formula for sin^nx found?

A

^n-1 x sin

21
Q

How is a reduction formula for cos^nx or tan^nx found?

A

^n-2 x …

22
Q

In = ∫ sinnx/

sin x dx solve?

A

sin[(n-2)x +2x]

23
Q

Volume of parallelepiped?

A

|a . (b × c)|

24
Q

Volume of a tetrahedron?

A

1/6|a . (b × c)|

25
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 |
26
How is cartesian equation for plane found?
ax + by + cz – d = 0 is given by r. n = d (ie perpendicular vector)
27
Reflection in plane?
OA' = OA + 2AP
28
Distance between skew lines.
d = (c − a) . b × d | |b × d|
29
Normalise vector
divide by magnitude
30
Diagonalise matrix
- Find eigenvalues - Find eigenvectors - Normalise eigenvectors - Find orthogonal matrix - Find diagonal matrix