FSMQ Formulas to Learn
Quadratic Equations
Coordinate Geometry
 b  b 2  4ac
x
2a
You have two points A (x1 , y1) and B (x2 , y2)


Midpoint of line joining two points
 x1  x2 y1  y 2 
,


2 
 2
Distance between two points
AB 

 y2  y1 2  x2  x1 2
Gradient given two points
m
y2 - y1
x2 - x1

Equation given a point and the gradient
y y1 = m(x x1 ) or y = mx + c

Equation of a circle centre (a , b)
x  a 2   y  b 2  r 2
Trigonometry


Right-angled triangle trigonometry
opp
adj
sin  
cos 
hyp
hyp
tan  
opp
adj
Non-right angled triangle trigonometry
o Cosine rule
b2  c2  a2
2bc
Use when you know two sides and the angle between them or
all three sides.
o Sine rule
sin A sin B sin C
a
b
c




OR
a
b
c
sin A sin B sin C
a 2  b 2  c 2  2bcCosA
OR
cos A 
Use when you know an angle and its opposite size and one
other side or angle.

Trig Identities
o sin 2   cos 2   1
sin 
o tan  
cos 
Polynomials


Remainder theorem
The remainder when a polynomial, f(x), is divided by (x - a) is equal
to the value of f(a).
Factor theorem
If (x – a) is a factor of f(x) then f(a) = 0.
If f(a) = 0 then (x – a) is a factor of f(x).
Binomials
(a + bx)n




Find the (n + 1)th row of Pascal’s triangle and write this out
Next to each of these numbers write an, then an-1, then an-2 all
the way down to a0.
Next to each of these write (bx)0, then (bx)1, then (bx)2 all the
way up to (bx)n.
Work each term out and make sure you write them in the order
you have been asked to in the question.
Binomial probability
X is an event and the probability that “X happens r times out of n” is:
P( X  r )  nCr ( p r ) (1  p) nr
Where
n = number of trials
r = number of successes you want out of n trials
p = probability of success for ONE trial
Differentiation
If y  x n then
dy
 nx n1
dx

Finding equation of tangent at a point A (x1 , y1)
dy
o Find gradient function,
and substitute the x-coordinate of A
dx
to find the gradient of the tangent.
o Then use y y1 = m(x x1 ) or y = mx + c to find the equation.

Find the equation of normal at a point A (x1 , y1)
dy
o Find gradient function,
and substitute the x-coordinate of A
dx
to find the gradient of the tangent, m.
1
n
o Then find the gradient of the normal, n, by calculating
m
o Then use y y1 = n(x x1 ) or y = nx + c to find the equation of the

normal.
Stationary Points
dy
 0 and solve to find the x-coordinates.
o Set
dx
o Use the original equation to find the y-coordinates.
o Set up a table like this:
x
An x-value
smaller
dy
dx
x-coordinate of
stationary point
0
An x-value
bigger
o Decide what type of stationary point it is by looking at the
pattern of the gradients:
Minimum
Maximum
Points of Inflection
Integration
x n1
 x dx  n  1
n

Integration with limits
b
 x n1   b n1   a n1 
  

x
dx


  
a
 n  1 a  n  1   n  1 
b
n

Area under a curve

Area between two curves
Find
b
 ( x  3)dx a
b
 (x
a
2
 1)dx
Kinematics/equations of motion
s = displacement
u = initial (starting) velocity
v = (final) velocity
a = acceleration
t = time
 Equations of motion – USE WITH CONSTANT ACCELERATION
ONLY!
v  u  at
uv
s
t
 2 
1
s  ut  at 2
2
2
2
v  u  2as

Finding velocity and acceleration from displacement
If s = f(t) then:
ds
v
dt
dv
a
dt

Finding velocity and displacement from acceleration
If a = f(t) then:
v   a dt
s   v dt

Key words for kinematics questions
o Initial means t  0
o At rest means v  0
o Constant velocity means a  0
o At greatest height v  0