Pure AS

Question 1

=>

Answer 1

It follows that

Question 2

<=>

Answer 2

If and only if

Question 3

N

Answer 3

Natural numbers

POSITIVE integers

Question 4

Z

Answer 4

Integer

Question 5

Q

Answer 5

quotients / rational numbers

Expressed as a FRACTION

Question 6

R

Answer 6

Real numbers

not IMAGINARY

Question 7

a ^ m/n

Answer 7

n rt(a^ m)

Question 8

b^2 - 4ac > 0

Answer 8

2 disctint roots

Question 9

b^2 - 4ac = 0

Answer 9

1 repeated root

Question 10

b^2 - 4ac < 0

Answer 10

No roots

Question 11

Turning point (a,b)

Answer 11

(x - a) + b

Question 12

x = (quadratic formula)

Answer 12

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

Question 13

=< when region drawing

Answer 13

SOLID line

Question 14

< when region drawing

Answer 14

DOTTED line

Question 15

=< on number line

Answer 15

FILLED dot

Question 16

< on number line

Answer 16

OPEN dot

Question 17

=< in interval notation

Answer 17

SQUARE bracket [

Question 18

< in interval notation

Answer 18

CURVED bracket (

Question 19

Interval bracket for infinity

Answer 19

CURVED ( as <

Question 20

define polynomial

Answer 20

Finite expression with N indices

Question 21

state factor theorem

Answer 21

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

Question 22

When to use identity symbol

Answer 22

Simplifying expressions

Question 23

y = k / x

Answer 23

top right, bottom left

Gets flatter when k increases

Question 24

fg(x) meaning

Answer 24

f of g(x)

Question 25

Inverse function notation

Answer 25

f ^-1 (x)

Question 26

Inverse function of e ^x

Answer 26

ln x

Question 27

midpoint

Answer 27

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

Question 28

Collinear definition

Answer 28

Of the SAME LINE

Question 29

tangent definition

Answer 29

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

Question 30

Normal defintion

Answer 30

Line 90 degrees to tangent at one point

Question 31

r^2 =

Answer 31

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

Question 32

Define circumcircle

Answer 32

unique circle around 3 vertices of a triangle

Question 33

Why is a = 1 not an exponential graph

Answer 33

Because 1^x is always 1

Question 34

a^x = b

Answer 34

loga b = x

Question 35

loga (a^x) =

Answer 35

x

Question 36

a ^ (loga x) =

Answer 36

x

Question 37

e =

Answer 37

2.71819

Question 38

differentiate e^kx

Answer 38

ke^kx

Question 39

Exponential decay

Answer 39

Ae^kx

Question 40

Exponential decay

Answer 40

Ae^-kx

Question 41

Differentiate e^-kx

Answer 41

-ke^kx

Question 42

loga 1 =

Answer 42

0

Question 43

log a (1/x) =

Answer 43

• loga x

Question 44

log (x + y) =

Answer 44

CAN’T BE SIMPLIFIED

Question 45

y = (exponential graph)

Answer 45

A (coefficient of e)

Question 46

Make linear graph with logs

Answer 46

Logs of both sides
Separate RHS
constant is gradient
Variables are axis

Question 47

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

Answer 47

y = loga y
x = loga b
gradient = k

Question 48

Derivation from first principles

Answer 48

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

Question 49

As h -> 0 …

Answer 49

nh -> 0 and nh^2 -> 0

Question 50

Find equation on normal at point (x,y)

Answer 50

dy/dx to find tangent
x -1/grad is gradient
Solve y=mx+c

Question 51

is interval () strict or not?

Answer 51

NOT

Question 52

Is interval[] strict or not

Answer 52

STRICT

Question 53

find if maximum or minimum

Answer 53

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)

Question 54

Define dV / dr

Answer 54

rate of change in volume WRT radius

Question 55

|a| =

Answer 55

sqrt( Δx^2 + Δy^2 + Δz^2)

Question 56

a hat = (unit vector)

Answer 56

a / |a|

Question 57

Find vector angle with y axis

Answer 57

cosθ = y / |a|

Question 58

Find vector angle with x axis

Answer 58

cosθ = x / |a|

Question 59

Find vector angle with z axis

Answer 59

cosθ = z / |a|