F Maths Pure

Question 1

Series

Answer 1

1 = n

r = 0.5n(n+1)

Question 2

Roots of Polynomials

Answer 2

Sum of alpha = -b/a
Sum of alpha x beta = c/a
Sum of alpha x beta x gamma = 
-d/a
Sum of alpha x beta x gamma x delta = e/a

Question 3

Sums of Squares

Answer 3

Alpha^2 + Beta^2 etc = (Sum of alpha )^2 - 2 x Sum of alpha x beta

Question 4

Sum of Cubes

Answer 4

Alpha^2 + Beta^2 etc = (a + b) ^2 - 3 x (sum of alpha x beta) x sum of alpha + 3 x (sum of alpha x beta x gamma )

Question 5

Volumes of revolution

Answer 5

X axis : Etc y^2

Y axis : etc x^2

Parametric: (y^2 dx/dt )dt vice versa

Question 6

Cylinder

Answer 6

Pi r^2 h

Question 7

Cone

Answer 7

1/3 pi r^2 h

Question 8

Determinate of Matrix

Answer 8

ad - bc

Question 9

Angle between lines

Answer 9

Cos 0 = (a•b) / |a||b|

Question 10

Angles between planes and line

Answer 10

sin 0 = (a•b) / |a||b|

Question 11

Angles between plane and plane

Answer 11

Cos 0 = (n•n) / |n||n|

Question 12

Shortest Distance from point to plane

Answer 12

Point (alpha, beta, gamma)
Plane ( ax + by + cz = d)

|a x alpha + b x beta + c x gamma - d | / root (a^2 + b^2 + c^2)

Question 13

Inverse of 3x3 matrix

Answer 13

Find det
Do matrix of minors
Do matrix of cofactors
Transpose 
Multiply by 1/det

Question 14

Skew

Answer 14

Not parallel and does not intersect

Question 15

Un

Answer 15

Sn - Sn-1

Question 16

Differential equations (second order homogenous) (complementary function)

Answer 16

b^2 > 4ac

y=Ae^(ax) + Be^(bx)

b^2 = 4ac

y=(A + Bx)^(ax)

b^2 < 4ac

y=e^px(A(cosqx)+ B(sinqx))

Question 17

Differential equations (second order homogenous) (particular integral)

Answer 17

p to a
p + qx to (a + bx)
p + qx + rx^2 to (a + bx + cx^2)
pcos(wx) + qsin(wx) to acos(wx) + bsin(wx)
pe^(kx) to ae^(kx)

Question 18

Methods of Differences

Answer 18

f(n) - f(n+1)

Question 19

Hyperbolic Functions

Answer 19

sinhx = 0.5(e^x - e^-x)

coshx = 0.5(e^x + e^-x)

tanhx = (e^2x -1)/(e^2x + 1)

Question 20

Osborne’s Rule

Answer 20

Sinhx x sinhx = -

Question 21

Eulers Relation

Answer 21

z = re^(i0) = r(cos0 + isin0)

Question 22

De Moivres Theorem

Answer 22

(r(cos0 + isin0))^n = r^n(cos(n0) + isin(n0))

Question 23

Sin0 and cos0 in terms of z

Answer 23

Z + 1/z = 2c

Z- 1/z = 2s

Question 24

Sum of z series

Answer 24

W + wz + wz^2 … wz^(n-1)

= (w(z^n - 1))/(z-1)

Question 25

Mean of a function

Answer 25

1/b-a x integral between [b,a]

Question 26

Polar Coordinates

Answer 26

X = rcos0
Y = rsin0

Question 27

r = a(p+ qcos0)

Answer 27

P = q
Cardioid (bean with point into 0,0)

q< P < 2q
Dimple

P>=2q
Oval

Question 28

Area of polar curves

Answer 28

0.5x integral of r^2

Question 29

Parallel to initial line/ perpendicular to initial line

Answer 29

Y = rsin0 and y = 0

X = rsin0 and x = 0