Pure AS Flashcards

(59 cards)

1
Q

=>

A

It follows that

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2
Q

<=>

A

If and only if

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3
Q

N

A

Natural numbers

POSITIVE integers

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4
Q

Z

A

Integer

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5
Q

Q

A

quotients / rational numbers

Expressed as a FRACTION

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6
Q

R

A

Real numbers

not IMAGINARY

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7
Q

a ^ m/n

A

n rt(a^ m)

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8
Q

b^2 - 4ac > 0

A

2 disctint roots

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9
Q

b^2 - 4ac = 0

A

1 repeated root

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10
Q

b^2 - 4ac < 0

A

No roots

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11
Q

Turning point (a,b)

A

(x - a) + b

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12
Q

x = (quadratic formula)

A

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

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13
Q

=< when region drawing

A

SOLID line

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14
Q

< when region drawing

A

DOTTED line

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15
Q

=< on number line

A

FILLED dot

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16
Q

< on number line

A

OPEN dot

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17
Q

=< in interval notation

A

SQUARE bracket [

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18
Q

< in interval notation

A

CURVED bracket (

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19
Q

Interval bracket for infinity

A

CURVED ( as <

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20
Q

define polynomial

A

Finite expression with N indices

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21
Q

state factor theorem

A

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

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22
Q

When to use identity symbol

A

Simplifying expressions

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23
Q

y = k / x

A

top right, bottom left

Gets flatter when k increases

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24
Q

fg(x) meaning

25
Inverse function notation
f ^-1 (x)
26
Inverse function of e ^x
ln x
27
midpoint
( x1 + x2 / 2 , y1 + y2 / 2)
28
Collinear definition
Of the SAME LINE
29
tangent definition
Gradient at one point on a curve When b^2 - 4ac = 0 Point which only touches at one point
30
Normal defintion
Line 90 degrees to tangent at one point
31
r^2 =
(x-a) + (y-b) with centre (a,b)
32
Define circumcircle
unique circle around 3 vertices of a triangle
33
Why is a = 1 not an exponential graph
Because 1^x is always 1
34
a^x = b
loga b = x
35
loga (a^x) =
x
36
a ^ (loga x) =
x
37
e =
2.71819
38
differentiate e^kx
ke^kx
39
Exponential decay
Ae^kx
40
Exponential decay
Ae^-kx
41
Differentiate e^-kx
-ke^kx
42
loga 1 =
0
43
log a (1/x) =
- loga x
44
log (x + y) =
CAN’T BE SIMPLIFIED
45
y = (exponential graph)
A (coefficient of e)
46
Make linear graph with logs
Logs of both sides Separate RHS constant is gradient Variables are axis
47
loga y = kx + loga b (what on axis)
y = loga y x = loga b gradient = k
48
Derivation from first principles
lim h-> 0 f(x + h) - f(x) / h
49
As h -> 0 …
nh -> 0 and nh^2 -> 0
50
Find equation on normal at point (x,y)
dy/dx to find tangent x -1/grad is gradient Solve y=mx+c
51
is interval () strict or not?
NOT
52
Is interval[] strict or not
STRICT
53
find if maximum or minimum
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
Define dV / dr
rate of change in volume WRT radius
55
|a| =
sqrt( Δx^2 + Δy^2 + Δz^2)
56
a hat = (unit vector)
a / |a|
57
Find vector angle with y axis
cosθ = y / |a|
58
Find vector angle with x axis
cosθ = x / |a|
59
Find vector angle with z axis
cosθ = z / |a|