Formulae

Question 1

The remainder theorem

Answer 1

Given the polynomial f(x), the remainder when f(x) is divided by (x – a) is f(a).

Question 2

The factor theorem

Answer 2

If (x – a) is a factor of a polynomial f(x), then x = a is a root (solution) of the equation f(x) = 0.

Question 3

Quadratic equation

Answer 3

(-b±√b²-4ac) / 2a

Question 4

Parallel lines gradient

Answer 4

m¹=m²

Question 5

Perpendicular line gradient

Answer 5

m¹xm²=-1

Question 6

Straight line equation

Answer 6

y=mx+c

Question 7

Distance between two points

Answer 7

(x¹,y¹),(x²,y²)= √(x¹-x²)²+(y¹-y²)

Question 8

Midpoint of a line

Answer 8

(x¹,y¹),(x²,y²)= {(x¹+x²)/2,(y¹+y²)/2}

Question 9

Circle on a graph

Answer 9

The circle (x-a)²+(y-b)²=r² has centre (a,b) and radius r .

Question 10

Sine rule

Answer 10

a/sinA=b/sinB=c/sinC or sinA/a=sinB/b=sinC/c

Question 11

Cosine rule

Answer 11

a²=b²+c²-2bccosA

Question 12

Area rule

Answer 12

Area=½absinC

Question 13

Identity with tan, cos and sin

Answer 13

tanϴ=sinϴ/cosϴ

Question 14

Identity with sin and cos

Answer 14

sin²ϴ+cos²ϴ=1

Question 15

Stationary points

Answer 15

Stationary points occur when dy/dx=0

Question 16

Differentiation

Answer 16

y=axⁿ —> dy/dx=naxⁿ-¹ (thats n-1)

Question 17

Integration

Answer 17

if y=axⁿ then ⌠ydx=(a/n+1)xⁿ+¹

Question 18

Area under a curve

Answer 18

Area under curve between x=a and x=b is
b⌠y dx
a⌡

Question 19

Kinematic, constant acceleration with v,u,a and t

Answer 19

v=u+at

Question 20

Kinematic, constant acceleration with s,u,v and t

Answer 20

s=½(u+v)t

Question 21

Kinematic, constant acceleration with s,u,t and a

Answer 21

s=ut+½at²

Question 22

Kinematic, constant acceleration with s,v,t and a

Answer 22

s=vt-½at²

Question 23

Kinematic, constant acceleration with v,u,a and s

Answer 23

v²=u²+2as

Question 24

kinematics non constant acceleration find v

if x = displacement, v = velocity, a = acceleration, t = time

Answer 24

v=ds/dt (differentiate displacement) or v=⌠a dt (integrate acceleration)

Question 25

kinematics non constant acceleration find s

if s = displacement, v = velocity, a = acceleration, t = time

Answer 25

s=⌠v dt (integrate velocity)

Question 26

kinematics non constant acceleration find a

if s = displacement, v = velocity, a = acceleration, t = time

Answer 26

v=dv/dt (differentiate velocity)