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Flashcards in S2 Deck (30)
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1

What is a population?

A collection of items/individuals

2

What is a census?

When information is obtained from all members of a population.

3

Give three advantages of a census.

- Every member is used.
- Unbiased
- Gives accurate answer

4

Give three disadvantages of a census.

- Long time to do
- Expensive
- Difficult to ensure whole population surveyed

5

What is a sample?

The chosen members of a population

6

What is a sampling frame?

A list of all of the sampling units.

7

Give three advantages of sampling

- Cheaper than census
- Destruction of all sampling units not needed (lifespan)
- Data easier to collect

8

Give a disadvantage of sampling.

Bias can occur

9

What is a random sample?

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

10

What is a sampling distribution?

All of the potential outcomes and their probability

11

What is a statistic?

A quantity calculated from the observations of a sample.

12

What is a critical region?

The range of values which lead to H0 being rejected.

13

What is the parametric form of an ellipse?

𝑥 = a cos θ , 𝑦 = b sin θ

14

What is the parametric form of a hyperbola?

𝑥 = a cosh θ , 𝑦 = b sinh θ

15

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

16

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

17

What is ∫ sec x tan x dx

secx

18

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

- Multiply by 1
- Substitution
- Complete square
- Reverse chain rule

19

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

20

How is a reduction formula for sin^nx found?

^n-1 x sin

21

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

^n-2 x ...

22

In = ∫ sinnx/
sin x dx solve?

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

23

Volume of parallelepiped?

|a . (b × c)|

24

Volume of a tetrahedron?

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