Formulas (Pure)

Question 1

What is the formula for the nth term of an arithmetic series?

Answer 1

a + (n-1)d

Question 2

What is the formula for the nth term of a geometric series?

Answer 2

ar^(n-1)

Question 3

What does secx become? (relationship)

Answer 3

1
cosx

Question 4

What does cosecx become? (relationship)

Answer 4

1
sinx

Question 5

What does cotx become? (relationship)

Answer 5

1
tanx

or

cosx
sinx

Question 6

What does tanx become? (relationship)

Answer 6

sinx
cosx

Question 7

What does sin2A become? (double angle)

Answer 7

2sinAcosA

Question 8

What does tan2A become? (double angle)

Answer 8

2tanA
1-tan^2A

Question 9

What are the 3 double angle formulas for cos2A?

Answer 9

cos^2A-sin^2A
1-2sin^2A
2cos^2A-1

Question 10

What are the 3 trigonometric identities?

Answer 10

sin^2x + cos^2x = 1
1 + tan^2x = sec^2x
1 + cot^2x = cosec^2x

Question 11

What does logM + logN become?

Answer 11

logMN

Question 12

What does logM - logN become?

Answer 12

log(M/N)

Question 13

what does KlogM become?

Answer 13

logM^K

Question 14

For y=Ax^n what is the log version and using this what is the gradient and the y-intercept?

Answer 14

logy=nlogx + logA

Where n is the gradient and logA is the y intercept.

Question 15

For y=Ab^x what is the log version and using this what is the gradient and the y-intercept?

Answer 15

logy = xlogb + logA

Where logb is the gradient and logA is the y-intercept.

Question 16

What does e^x differentiate to?

Answer 16

e^x

Question 17

What does e^(2x) differentiate to?

Answer 17

2e^x

Question 18

what does lnx differentiate to?

Answer 18

1
x

Question 19

What does ln(3x+2) differentiate to?

Answer 19

3
(3x+2)
where 3 is the differential of the bracket

Question 20

What does (3x+2)^3 differentiate to?

Answer 20

3x3(3x+2)^2
= 9(3x+2)^2

(Times the power by the differential of the bracket)

Question 21

What is the product rule in differentiation?

Answer 21

y=uv

uv’ + vu’

Question 22

What is the quotient rule in differentiation?

Answer 22

y=u/v

(vu’ - uv’) / v^2

Question 23

What is sinx differentiated?

Answer 23

cosx

Question 24

What is cosx differentiated?

Answer 24

-sinx

Question 25

When do the points of inflection occur?

Answer 25

When f ''(x) = 0

Question 26

How do you find the magnitude of the vector a = 3i + 4j

Answer 26

|a| = 3^2 + 4^2 (all square rooted)

Question 27

How is arc length calculated in radians?

Answer 27

rθ

Question 28

How is the area of a sector calculated in radians?

Answer 28

1/2r^(2)θ

Question 29

What does -sinx integrate to?

Answer 29

cosx

Question 30

What does cosx integrate to?

Answer 30

sinx

Question 31

What is cos(3x+7) integrated?

Answer 31

1/3 sin(3x+7) + c

Question 32

What is e^(4x+1) integrated?

Answer 32

1/4 e^(4x+1) + c

Question 33

What is sec^(2)3x integrated?

Answer 33

1/3tan3x + c

Question 34

What is 1/(3x+2) integrated?

Answer 34

1/3 ln(3x+2) + c

Question 35

What is 1/(3x+2)^2 integrated?

Answer 35

(3x+2)^-2 = -1/3 (3x+2)^-1 + c