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