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AS Mathematics > Circular Measure, Representation Of Data, Trigonometry > Flashcards

Circular Measure, Representation Of Data, Trigonometry Flashcards

1
Q

Write 360° in radians

A

2pi

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2
Q

To convert from ° to rad?

A

× pi/180

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3
Q

To covert from rad to °

A

× 180/pi

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4
Q

Number of radians is in a complete revolution is:

A

No of times radius divides into the circumference

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5
Q

What is 1rad or 1c

A

An arc equal in length to radius, subtended at an angle of 1 radian at the centre.

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6
Q

Length of an arc in radians

A

r theta

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7
Q

Area of a sector in rad

A

0.5× r^2 × theta

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8
Q

What is the basic trigonometric identity

A

sin2x + cos2x =1

*Ie sinx whole squared

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9
Q

Tan2 theta =

A

sin2 theta / cos2 theta

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10
Q

What are the 4 quadrants. State and explain

A

1st- A 0-90, all are positive
2st - S 90-180, only sin is postive
3rd- 180-270, only tan is positive
4th- C 270-360, only cos is positive

And vice versa for negative angles

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11
Q

What to do to make negative angle to positive?

A

Add 360

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12
Q

State properties of each of the 3 functions graphs

A

Sin- continuous curve, -1<=sin0<=1, period is 2pi(repeated)

Cos- continuous curve, -1<=cos0<=1, period is 2pi(repeated)

Tan- not continuous has breaks, range values of tan theta is unlimited, period is pi(repeated)

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13
Q

What is sin cos tan 0?

A

0
1
0

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14
Q

What is sin cos tan 30

A

1/2
√3/2
1/√3

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15
Q

What is sin cos tan 45

A

1/√2
1/√2
1

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16
Q

What is sin cos tan 60

A

√3/2
1/2
√3

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17
Q

What is sin cos tan 90

A

1
0
Infinity

18
Q

Each piece of info is called

A

Datum

19
Q

Stats is the branch of maths which deals with

A

Collection, organisation and analysis of data

20
Q

What are qualitative and quantitative data

A

Qualitative data consists of description using words

Quantitative data can take numerical value

21
Q

What are discrete and continuous data

A

Discrete are those that can take only exact values

Continuous can take values within a specific range or measured Yo a degree of accuracy

22
Q

Raw data is

A

Just collected from an experiment

23
Q

2 things that must be in a stem and leaf plot

A

Key

Numbers in brackets stating the leaves belonging to each stem

24
Q

Why is histogram often used instead of stem and leaf?

A

When data is large

Histogram can divide data into classes

25
Q

Why is stem and leaf better than box and whisker plot

A

All data items can be shown

26
Q

Important conditions that differ a histogram to bar chart

A

H bars have no spaces between them
H area is proportional to frequency
In H frequency density is y axis
H bars represent distribution of continuous, quantitative, non discrete variables (grouped ranges), where as in bar charts discrete, categorical variables are compared

27
Q

Why is mean calculated from a frequency table not accurate?

A

Mid values of intervals are used as x

28
Q

Formula of frequency density:

A

Frequency/class width

29
Q

In frequency table intervals, what does 27-31 actually mean?

A

The boundaries are 26.5<= length<=31.5

30
Q

Cumulative frequency is plotted again _ as x axis

A

Upper class boundary eg 54->54.5

31
Q

Box plot illustrates … Using…

A

Spread/dispersion of distribution

Highest and lowest values, median, Q1(lower), Q3(higher), median Q2

32
Q

What is measure of location

Aka - - ?

A

Single value that woukd condense the info contained in data set
Aka central tendency or average

33
Q

Median is the :

A

n+1/2 th observation (odd)

c+d/2 th (even, where c and d are 2 middle values)

34
Q

mean (x bar) =

A

Sigma x f / f

If data is grouped x is miss class value

35
Q

Which are measures of spread

A

Range, interquartike range, variance, standard deviation

36
Q

Advantages and disadvantages of range?

A

Ad- simple and easy to calculate

Disad- only 2 values considered, affected by extremes, ignores patten of spread

37
Q

Outliers are

A

Unusual values that differ greatly in magnitude from majority of dafa

38
Q

Outliers formulae (fences)

A

Upper fence: Q3 +1.5(Q3-Q1)

Lower fence: Q1 -1.5(Q3-Q1)

39
Q

Standard deviation is

A

Square root of variance

40
Q

Formula of variance (normal)

A

(Sigma x^2/n)- (x bar^2)

41
Q

Formula of variance (frequency table)

A

(Sigma x^2/f) - (sigma xf/f)^2

42
Q

Formula of variance (coded data)

A

Sigma (x-a)^2/n - (sigma(x-a) /n)^2

AS Mathematics (3 decks)

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