Circular Measure, Representation Of Data, Trigonometry

Question 1

Write 360° in radians

Answer 1

2pi

Question 2

To convert from ° to rad?

Answer 2

× pi/180

Question 3

To covert from rad to °

Answer 3

× 180/pi

Question 4

Number of radians is in a complete revolution is:

Answer 4

No of times radius divides into the circumference

Question 5

What is 1rad or 1c

Answer 5

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

Question 6

Length of an arc in radians

Answer 6

r theta

Question 7

Area of a sector in rad

Answer 7

0.5× r^2 × theta

Question 8

What is the basic trigonometric identity

Answer 8

sin2x + cos2x =1

*Ie sinx whole squared

Question 9

Tan2 theta =

Answer 9

sin2 theta / cos2 theta

Question 10

What are the 4 quadrants. State and explain

Answer 10

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

Question 11

What to do to make negative angle to positive?

Answer 11

Add 360

Question 12

State properties of each of the 3 functions graphs

Answer 12

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)

Question 13

What is sin cos tan 0?

Answer 13

0
1
0

Question 14

What is sin cos tan 30

Answer 14

1/2
√3/2
1/√3

Question 15

What is sin cos tan 45

Answer 15

1/√2
1/√2
1

Question 16

What is sin cos tan 60

Answer 16

√3/2
1/2
√3

Question 17

What is sin cos tan 90

Answer 17

1
0
Infinity

Question 18

Each piece of info is called

Answer 18

Datum

Question 19

Stats is the branch of maths which deals with

Answer 19

Collection, organisation and analysis of data

Question 20

What are qualitative and quantitative data

Answer 20

Qualitative data consists of description using words

Quantitative data can take numerical value

Question 21

What are discrete and continuous data

Answer 21

Discrete are those that can take only exact values

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

Question 22

Raw data is

Answer 22

Just collected from an experiment

Question 23

2 things that must be in a stem and leaf plot

Answer 23

Key

Numbers in brackets stating the leaves belonging to each stem

Question 24

Why is histogram often used instead of stem and leaf?

Answer 24

When data is large

Histogram can divide data into classes

Question 25

Why is stem and leaf better than box and whisker plot

Answer 25

All data items can be shown

Question 26

Important conditions that differ a histogram to bar chart

Answer 26

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

Question 27

Why is mean calculated from a frequency table not accurate?

Answer 27

Mid values of intervals are used as x

Question 28

Formula of frequency density:

Answer 28

Frequency/class width

Question 29

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

Answer 29

The boundaries are 26.5<= length<=31.5

Question 30

Cumulative frequency is plotted again _ as x axis

Answer 30

Upper class boundary eg 54->54.5

Question 31

Box plot illustrates ... Using...

Answer 31

Spread/dispersion of distribution | Highest and lowest values, median, Q1(lower), Q3(higher), median Q2

Question 32

What is measure of location | Aka - - ?

Answer 32

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

Question 33

Median is the :

Answer 33

n+1/2 th observation (odd) c+d/2 th (even, where c and d are 2 middle values)

Question 34

mean (x bar) =

Answer 34

Sigma x f / f If data is grouped x is miss class value

Question 35

Which are measures of spread

Answer 35

Range, interquartike range, variance, standard deviation

Question 36

Advantages and disadvantages of range?

Answer 36

Ad- simple and easy to calculate | Disad- only 2 values considered, affected by extremes, ignores patten of spread

Question 37

Outliers are

Answer 37

Unusual values that differ greatly in magnitude from majority of dafa

Question 38

Outliers formulae (fences)

Answer 38

Upper fence: Q3 +1.5(Q3-Q1) Lower fence: Q1 -1.5(Q3-Q1)

Question 39

Standard deviation is

Answer 39

Square root of variance

Question 40

Formula of variance (normal)

Answer 40

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

Question 41

Formula of variance (frequency table)

Answer 41

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

Question 42

Formula of variance (coded data)

Answer 42

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