# Pure AS Flashcards Preview

## Edexcel A Level Maths Equations and Definitions > Pure AS > Flashcards

Flashcards in Pure AS Deck (59)
1
Q

=>

A

It follows that

2
Q

<=>

A

If and only if

3
Q

N

A

Natural numbers

POSITIVE integers

4
Q

Z

A

Integer

5
Q

Q

A

quotients / rational numbers

Expressed as a FRACTION

6
Q

R

A

Real numbers

not IMAGINARY

7
Q

a ^ m/n

A

n rt(a^ m)

8
Q

b^2 - 4ac > 0

A

2 disctint roots

9
Q

b^2 - 4ac = 0

A

1 repeated root

10
Q

b^2 - 4ac < 0

A

No roots

11
Q

Turning point (a,b)

A

(x - a) + b

12
Q

A

-b +- sqrt(b^2 -4ac) / 2a

13
Q

=< when region drawing

A

SOLID line

14
Q

< when region drawing

A

DOTTED line

15
Q

=< on number line

A

FILLED dot

16
Q

< on number line

A

OPEN dot

17
Q

=< in interval notation

A

SQUARE bracket [

18
Q

< in interval notation

A

CURVED bracket (

19
Q

Interval bracket for infinity

A

CURVED ( as <

20
Q

define polynomial

A

Finite expression with N indices

21
Q

state factor theorem

A

If f(a) = 0 then (x-a) is a factor

22
Q

When to use identity symbol

A

Simplifying expressions

23
Q

y = k / x

A

top right, bottom left

Gets flatter when k increases

24
Q

fg(x) meaning

A

f of g(x)

25
Q

Inverse function notation

A

f ^-1 (x)

26
Q

Inverse function of e ^x

A

ln x

27
Q

midpoint

A

( x1 + x2 / 2 , y1 + y2 / 2)

28
Q

Collinear definition

A

Of the SAME LINE

29
Q

tangent definition

A

Gradient at one point on a curve
When b^2 - 4ac = 0
Point which only touches at one point

30
Q

Normal defintion

A

Line 90 degrees to tangent at one point

31
Q

r^2 =

A

(x-a) + (y-b) with centre (a,b)

32
Q

Define circumcircle

A

unique circle around 3 vertices of a triangle

33
Q

Why is a = 1 not an exponential graph

A

Because 1^x is always 1

34
Q

a^x = b

A

loga b = x

35
Q

loga (a^x) =

A

x

36
Q

a ^ (loga x) =

A

x

37
Q

e =

A

2.71819

38
Q

differentiate e^kx

A

ke^kx

39
Q

Exponential decay

A

Ae^kx

40
Q

Exponential decay

A

Ae^-kx

41
Q

Differentiate e^-kx

A

-ke^kx

42
Q

loga 1 =

A

0

43
Q

log a (1/x) =

A
• loga x
44
Q

log (x + y) =

A

CAN’T BE SIMPLIFIED

45
Q

y = (exponential graph)

A

A (coefficient of e)

46
Q

Make linear graph with logs

A

Logs of both sides
Separate RHS
Variables are axis

47
Q

loga y = kx + loga b (what on axis)

A

y = loga y
x = loga b

48
Q

Derivation from first principles

A

lim h-> 0 f(x + h) - f(x) / h

49
Q

As h -> 0 …

A

nh -> 0 and nh^2 -> 0

50
Q

Find equation on normal at point (x,y)

A

dy/dx to find tangent
Solve y=mx+c

51
Q

is interval () strict or not?

A

NOT

52
Q

Is interval[] strict or not

A

STRICT

53
Q

find if maximum or minimum

A

d2y / dx2 using value for x
If n > 0 then MINIMUM
If n < 0 then MAXIMUM
If n = 0 then point of INFLECTION/ MAX/ MIN (use table)

54
Q

Define dV / dr

A

rate of change in volume WRT radius

55
Q

|a| =

A

sqrt( Δx^2 + Δy^2 + Δz^2)

56
Q

a hat = (unit vector)

A

a / |a|

57
Q

Find vector angle with y axis

A

cosθ = y / |a|

58
Q

Find vector angle with x axis

A

cosθ = x / |a|

59
Q

Find vector angle with z axis

A

cosθ = z / |a|