Maths Pure 2

Question 1

30, 40, 60

Answer 1

P/6 , p/4, p/3

Question 2

Sin p/6, p/4, p/3

Answer 2

1/2 , 1/root 2, root 3/2

Question 3

Cos p/6, p/4, p/3

Answer 3

Root 3/2, 1/ root 2, 1/2

Question 4

Tan p/6, p/4, p/3

Answer 4

1/root 3, 1, root 3

Question 5

Arc

Answer 5

Radius x angle

Question 6

Sector

Answer 6

0.5 x radius^2 x angle

Question 7

Segment

Answer 7

0.5 x radius^2(angle-sin angle)

Question 8

Small angle approximations

Answer 8

Sin angle to angle

Cos angle to 1-0.5angle^2

Tan angle to angle

Question 9

Identities for reciprocal angle

Answer 9

Tan^2x + 1 = sec^2x

Cot^2x + 1 = cosec^2x

Question 10

Arithmetic Sequences

Answer 10

Un = 1st term + (n-1) d

Sn = n/2 (2a + (n-1)d)

Question 11

Geometric Sequence

Answer 11

Un = ar^(n-1)

Sn = a(1-r^n)/1-r

Question 12

Double Angle Formulae

Answer 12

Sin 2ø to 2sinøcosø

Cos2ø to :

cos^2ø - sin^2ø
2cos^2ø - 1
1 - 2sin^2ø

Tan2ø to (2tanø)/(1-tan^2ø)

Question 13

Diff: sinx

Answer 13

Cos x

Question 14

Diff: cos x

Answer 14

-sinx

Question 15

Diff: e^kx

Answer 15

ke^kx

Question 16

Diff: a^kx

Answer 16

a^x k lna

Question 17

Diff: lnx

Answer 17

1/x

Question 18

Chain rule

Answer 18

Dy/dx = dy/du x du/dx

Question 19

Product rule

Answer 19

y = uv

Dy/dx = u dv/dx + v du/dx

Question 20

Quotient rule

Answer 20

y= uv

Dy/dx = (v du/dx - u dv/dx) / v^2

Question 21

Diff: tankx

Answer 21

K sec^2 kx

Question 22

Diff: coseckx

Answer 22

-k coseckx cotkx

Question 23

Diff: seckx

Answer 23

K secks tankx

Question 24

Diff: cotkx

Answer 24

-k cosec^2kx

Question 25

Diff: arcsinx

Answer 25

1/root(1-x^2)

Question 26

Diff: arc cosx

Answer 26

-1/root(1-x^2)

Question 27

Diff: arctanx

Answer 27

1/(1+x^2)

Question 28

Implicit Differentiation

Answer 28

D(f(y))/dx = f’(y) dy/dx

Question 29

Second Derivative

Answer 29

F’’(x) <= 0 Concave/max = 0 Concave, point of inflection, convex >= 0 Convex/min

Question 30

Newton Raphson Method

Answer 30

X n+1 = X n - (f(x n)/f’(x n))

Question 31

Order of transformation

Answer 31

Inside bracket then outside bracket Inside: translation, then stretch Outside: stretch, then translation