Maths Pure

Front 1

What is a mapping rule

Back 1

It is signed more than one output to each input

Front 2

What do you call a mapping rule where each input only has one output

Back 2

A function

Front 3

Why do you use the vertical line test?

Back 3

To see if a mapping is a function, if it is a function each line will only meet the graph once

Front 4

What is the horizontal line test?

Back 4

It determines what kind of functions it is

Front 5

What is a one-to-one function?

Back 5

Every why only has one x, each line only meets the graph once in the horizontal line test

Front 6

What is a many to one function?

Back 6

At least one y value corresponds to more than 1 X value , meets the graph more than once in the horizontal line test

Front 7

What is domain

Back 7

The set of input values, the X values

Front 8

What is range?

Back 8

All the possible outputs, y values

Front 9

Which function comes first in fg(X)?

Back 9

G into f

Front 10

What is another way of writing ff(X)?

Back 10

f^2(X)

Front 11

What must occur for FG (X) to occur?

Back 11

The range of g must lie within the domain of f

Front 12

What is a composite function?

Back 12

A function applied to a function

Front 13

How do you find an inverse function

Back 13

-make f(X) to y

-rearrange to get x by itself

-replace y's with x's and x with f(X)

Front 14

F(X) into F^-1(X)

Back 14

X

Front 15

In terms of f(X) , what is f^-1(X) range

Back 15

Domain of f(X)

Front 16

What order must you put transformations in if it is a horizontal transformation and a vertical transformation?

Back 16

The order doesn't matter

Front 17

Order for horizontal and horizontal transformation?

Back 17

Translate then stretch

Front 18

Order for vertical then vertical translation

Back 18

Stretch then translation

Front 19

What does the modulus absolute value do

Back 19

It is a function that reverses the sign of negative numbers

Front 20

|x-a|<b =

Back 20

a-b<x<a+b

Front 21

What must you do when solving a modulus function?

Back 21

Sketch the graph

Front 22

What can you do if the intersection of your two graphs is on the unreflected side in a modulus function graph?

Back 22

You can rewrite the equation without the modulus

Front 23

What can you do if the intersection of your two graphs on a modulus function graph is on the reflected side?

Back 23

Rewrite the equation with a minus sign instead of the modulus

Front 24

|a|=|b| ~

Back 24

b^2=a^2

Front 25

How would you find the limit of a convergent sequence?

Back 25

You would set Un+1=Un , and then replace all Un+1 and Un with L and solve for L

Front 26

What is a series?

Back 26

The sum of a sequence up to a certain point

Front 27

Do geometric or arithmetic sequences have a common difference?

Back 27

Arithmetic sequences

Front 28

What can you use to find the first term and the common difference in an arithmetic sequence?

Back 28

Simultaneous equations

Front 29

What must you do if asked to find the number of terms or a term number in a geometric series?

Back 29

Use logs after setting up an inequality

Front 30

What do the three trig graphs look like?

Back 30

Front 31

What is arcsin domain and range?

Back 31

Domain -1, 1

Range - pi / 2, pi/2

Front 32

What is arc cos domain and range?

Back 32

Domain - 1, 1

Range 0, pi

Front 33

What is arctan domain and range?

Back 33

Domain real numbers

Range - pi / 2, pi / 2

Front 34

What do you get if you take tan (arctanx)

Back 34

X

Front 35

What is the period of a graph?

Back 35

The horizontal distance until the graph

Front 36

How do you work out the period of a graph

Back 36

2 pi/|b|

Front 37

What is the length of an arc

Back 37

Rx theta

Front 38

What is the area of a segment?

Back 38

1/2r^2(theta-sin(theta))

Front 39

Small angle approximation of sin theta

Back 39

Theta

Front 40

What is the small angle approximation of cos theta

Back 40

1 - 1 / 2 theta^2

Front 41

What is the small angle approximation of tan theta

Back 41

Theta

Front 42

What is tan (A+B)

Back 42

tana + tanb/ 1 - tan a tan b

Front 43

Sin2A

Back 43

2sinAcosA

Front 44

Cos 2A

Back 44

2cos^2-1

1-2sin^2A

Cos^2-sin^A

Front 45

Tan2A

Back 45

2tan/1-tan^2A

Front 46

In form Rsin(X+&)

Back 46

-Expand using compound angle identities

-Equate r sin theta to sin and r cos theta to Cos

-find R using R=√a^2+b^2

-find & using tan^-1B/A

Front 47

Secx

Back 47

1 / cos x

Front 48

Cosec x

Back 48

1 / sin x

Front 49

Cotx

Back 49

1 / tanx

Front 50

Differentiate sin x

Back 50

Cos x

Front 51

Differentiate cos x

Back 51

-sinx

Front 52

Differentiate tan x

Back 52

Sec^2x

Front 53

The chain rule

Back 53

Split function so one section = u

Dy/du X du/dx

Front 54

Product rule y=uv

Back 54

Vu'+uv'

Front 55

Back 55

.

Front 56

.

Back 56

Front 57

Back 57

Front 58

Back 58

Front 59

A/X graph

Back 59

Front 60

A/x^2

Back 60