Flashcards in Pure Maths Deck (38):

1

## What are the steps for a proof?

###
1. Specialise to understand eh problem

2. Make a generalisation

3. Calculate and simplify

4. Write a conclusion using wording of phrase

2

## What are the three types of sequence?

###
Convergent (to a limit)

Oscillating (Period is number of different numbers)

Divergent (to infinity)

3

## What is the equation for the sum of the first n terms of an arithmetic progression?

###
Sn = n/2(2a + (n-1)d)

-N is term

-A is first term

-D is difference between the terms

4

## What is an example of a position to term rule and a term to term rule?

###
1. Position to term rule: tn = 6n + 5

2. Term to term rule: tn + 1 = tn + 6

5

## For completing the square, how do you interpret it graphically?

### Look at notes

6

## How do you find the gradient of a line?

### Y-Y1 / X-X1 = gradient

7

## How do you fined the midpoint of the line?

###
(x1 + x2 ) / 2 = xm

(y1 + y2) / 2 = ym

8

## How do you find the length of a line?

### (deltay)^2 + (deltax)^2 = c^2

9

## What is the trapezium rule?

###
-Find area under a curve, split into equal length

-((a+b) / 2)h

10

## What is the equation for arc length?

### Theta x r

11

## What is the equation for area of a sector?

### 0.5 x r^2 x theta

12

## How do you convert from radians to degrees?

### x 180/pi

13

## How do you convert from degrees to radians?

### Divide by 180/ pi

14

## What is the equation of a circle?

###
(x-a) ^ 2 + (y-b)^2 = r^2

-Where (a,b) is the centre

15

## What is the equation for a geometric sequence?

###
tn = a x r^n-1

-a is the first term

-r is the common ratio

16

## What is the sum of the first n terms of a geometric progression?

### Sn = a x (1-r^n) / (1-r)

17

## What is the term to term rule of a geometric progression?

### Un + 1 and state U1 =

18

## What are the log addition rule?

###
logcA + logcB = logcAB

logcA + logcA = logcA^2

19

## What is the log subtraction rule?

### logcA - logcB = logc (A/B)

20

## What is 2logcA also seen as?

###
logcA^2

21

## What is the power rule for logs?

### nlogcA = logcA^n

22

## What are the steps for finding the stationary point?

###
1. Find dy/dx

2. Solve dy/dx = 0

3. Then plug these x values into the original equation to get y values

4. Then find the second derivative and plug in your x values to find out if the point is a maximum or minimum - (<0 it is a maximum) (>0 it is a minimum)

23

## What are the trigometric value we need to know?

###
sin^2theta + cos^2theta = 1

sin / cos = tan

24

## What is secX ?

### secX = 1/cosX

25

## What is cosecX?

### cosecX = 1/sinX

26

## What is cotX?

### cotX = 1/tanX

27

## What are the two conditions for a function?

###
1. Completeness Criteria: Every object in the domain has an image in the codomain

2. Uniqueness Criteria: each object in the domain has a unique image

28

## Do you do g or f first in gf(x)?

### f first

29

## What do you do in differentiation?

###
1. Bring the old power down to the front

2. Decrease the power by one

30

## What do you do in integration? What do you always need to remember?

###
1. Increase power by one

2. Divide by new power

3. + c

31

## What is dy/dx of y=e^x?

### e^x

32

## What is dy/dx of y=lnx?

### 1/x

33

## What is the rule for chain rule?

###
nstuff^n-1 x stuff’

- (x^2 + 3x )^4

- 4(x^2 + 3x)^3 x (2x + 3)

34

## What is e^stuff differentiated?

###
e^stuff x stuff’

35

## What is ln(stuff) differentiated?

### stuff’ / stuff

36

## What is the infinite sum?

### Sn = a / 1-r

37

## What is the cosine rule?

###
-a squared = b squared + c squared - 2bcCosA

-CosA = b squared + c squared - a squared / 2bc

38