Year 2

Question 1

Double angle formula: sin2A

Answer 1

2sin(A)cos(A)

Question 2

Double angle formula: cos2A

Answer 2

• ; cos^2(A) - sin^2(A)
• ; 2cos^2(A) - 1
• ; 1 - 2sin^2(A)

Question 3

Double angle formula: tan2A

Answer 3

2tan(A) / 1-tan^2(A)

Question 4

Name the two trig identities involving sec^2 and cosec^2:

Answer 4

1 + tan^2(x) = sec^2(x)

1 + cot^2(x) = cosec^2(x)

Question 5

Name the trig identity involving tan:

Answer 5

Sinx / cosx = tanx

Question 6

Name the trig identity involving sin^2 and cos^2:

Answer 6

sin^2(x) + cos^2(x) = 1

Question 7

Differentiate cos(5x):

Answer 7

-5sin(5x)

Question 8

Differentiate 3sin(5x^2):

Answer 8

30xcos(5x^2)

Question 9

What is the product rule?

Answer 9

udv/dx + vdu/dx

Question 10

Differentiate 6lnx:

Answer 10

6 / x

Question 11

What is the quotient rule?

Answer 11

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

Question 12

Differentiate y = a^kx:

Answer 12

a^kx k lna

Question 13

Integrate 1/x:

Answer 13

lnx + c

Question 14

Integrate sin5x:

Answer 14

-1/5 cos5x + c

Question 15

What is the arithmetic sequence formula?

Answer 15

u = a + (n-1)d

Question 16

What is the geometric sequence formula?

Answer 16

u = ar^n-1

Question 17

How to work out arc length?

Answer 17

r x theta

Question 18

How to work out sector area?

Answer 18

1/2 x r^2 x theta

Question 19

How to work out segment area?

Answer 19

1/2r^2 x ( theta - sin theta )

Question 20

What is the general mnemonic to choose u in integration by parts?

Answer 20

Logs
Algebra
Trigonometry
Exponentials

Question 21

Given a 3D vector how do you calculate the angle between the vector and x,y,z axes?

Answer 21

Cos(theta) = axes(x,y or z) / magnitude of vector

Question 22

What is the volume of a sphere?

Answer 22

4/3 x pi x r^3