Pure Maths 2

Question 1

Sin (A+B)

Answer 1

SinACosB + CosASinB

Question 2

Cos(A+B)

Answer 2

CosACosB - SinASinB

Question 3

Sin(A-B)

Answer 3

SinACosB - CosASinB

Question 4

Cos(A-B)

Answer 4

CosACosB + SinASinB

Question 5

Tan(A+B)

Answer 5

TanA + Tan B / 1-TanATanB

Question 6

Tan(A-B)

Answer 6

TanA-TanB / 1+TanATanB

Question 7

Sin(-x)

Answer 7

-Sin(x)

Question 8

Cos(-x)

Answer 8

Cos(x)

Question 9

Cos(A-B) 2.0

Answer 9

CosACos(-B) - Sin(A)Sin(-B)

Question 10

Sin2A

Answer 10

2SinACosA

Question 11

Cos 2A (for sin and cos)

Answer 11

Cos^2A - Sin^2A

Question 12

Cos2A (for sin only)

Answer 12

1-2Sin^2A

Question 13

Cos2A (for cos only)

Answer 13

2Cos^2A - 1

Question 14

Tan2A

Answer 14

2TanA / 1-Tan^2A

Question 15

How do you work out E(x)?

Answer 15

Sum of : r(P=X)

Question 16

E(x^2)

Answer 16

Sum of: r^2(P=X)

Question 17

Var(X)

Answer 17

E(X^2) - E(X)^2

Question 18

What is the product rule?

Answer 18

[UV]’ = UV’ + U’V

Question 19

What is the Quotient Rule?

Answer 19

[U/V]’ = U’V - UV’ / V^2

Question 20

What conditions are needed for binomial probabilities?

Answer 20

1. The number of trials are fixed
2. Only two possible outcomes (success and failure)
3. The trials are independent so the outcome of one trial does not affect that of the others
4. The probability of success is the same in each trials
5. The variable is the total number of successes in the n trials

Question 21

Probability of getting heads 0.6, I throw 7 times what is the probability of getting 2 heads?

Answer 21

7C2 x (0.6)^2 x (0.4)^5

Question 22

How do you differentiate 2sin5x

Answer 22

2 x 5 x cos5x

Question 23

How do you integrate cos3x + 2sin3x ?

Answer 23

1/3 sin3x - 2/3 cos3x + c

Question 24

What are conditions for normal distribution?

Answer 24

1. Data is continuous
2. Data is roughly symmetrical in the middle
3. Virtually all of data within 3 standard deviations of the mean