Formulas

Question 1

Modulus turning point

Answer 1

1. Separate ONLY MODULUS PART into >0 and <0
2. Solve for x, the answer on the other side

Question 2

Finding f^-1 of a function

Answer 2

1. MUST BE 1 TO 1 FUNCTION
2. Let y = f(x)
3. Solve for x
4. Re substitute x for y

Question 3

f(-x)

Answer 3

Reflection in y axis, so all negative x values became positive

Question 4

-f(x)

Answer 4

Reflection in the x axis, so all negative Y values become positive

Question 5

Order of transformations

Answer 5

REFLECTIONS FIRST e.g 2f(-x+5), REFLECT X VALUES FIRST
STRETCHES NEXT e.g 2f, so xY by 2 next
THEN TRANSLATIONS LAST y+7 or x+5 last ok

Question 6

Gf(x)

Answer 6

Means g of f(x) so substitute f(x) wherever there in an x in G

Question 7

Sec x

Answer 7

1/cosx

Question 8

Sec x asymptotes

Answer 8

Wherever cos x = 0, so +-90, 270 etc

Question 9

Cosec x

Answer 9

1/ sin x

Question 10

Cosec asymptotes

Answer 10

Wherever sin x is 0, so +- 180, 360 etc

Question 11

Cot x

Answer 11

1/tan x

Question 12

Cot asymptotes

Answer 12

Wherever tan x =0, so +-180, 360, lines go other way

Question 13

Sec ^2 x = ?

Answer 13

1 + tan^2 x = sec ^2 x

Question 14

Cosec^2 x = ?

Answer 14

1 + cot^2 x

Question 15

Arc sin arc cos and arc tan are what?

Answer 15

Sin^-1, cos^-1 and tan^-1

Question 16

Range and domain of arc sin

Answer 16

Range: -pi/2 to pi/2
Domain: -1 to 1

Question 17

Range and domain of arc cos

Answer 17

Range: 0 to pi
Domain -1 to 1

Question 18

Range and domain of arctan

Answer 18

Range: -pi/2 to pi/2
Domain: all real numbers

Question 19

Identity with arc sin and arc cos (hint: sum of them)

Answer 19

Arc sin + Arc cos = pi/2

Question 20

Sin (A+B)
Sin (A- B)

Answer 20

SinACosB + SinBCosA
SinACosB - SinBCosA

Question 21

Cos (A+B)
Cos (A - B)

Answer 21

CosACosB - SinASinB
CosACosB + SinASinB

Question 22

Tan (A+B)
Tan (A- B)

Answer 22

TanA + Tan B / 1- TanATanB
Tan - TanB / 1 + TanATanB

Question 23

Sin2A

Answer 23

2sinACosA

Question 24

Cos2A

Answer 24

Cos^2 A - Sin^2 A
1 - 2Sin^2 A
2Cos^2 A - 1

Question 25

Tan 2A

Answer 25

2TanA / 1- Tan^2 A

Question 26

aSinx + bCosx aCos x + bSin x

Answer 26

RSin(x+a) RCos(x+a)

Question 27

Getting into form RSin/Cos (x+a)

Answer 27

1. First expand Rsin/cos (x+a) with addition formula 2. Compare the formula and cancel out sinx and cosx so left with Rsina and Rcosa = … 3. Divide Rsina by Rcosa to get tanA and arctan to get A 4. Do Rsina^2 and Rcosa^2 equals wtv answer squared 5. Factorise R out and sin^2 + Cos^2 equals 1 6. Solve for R

Question 28

When f(x) is e^x find f’(x)

Answer 28

The same: e^x

Question 29

If f(x) is e^kx find f’(x)

Answer 29

K * e^kx

Question 30

For graphs y = ax^n and y= ab^x against log y, log x and x respectively

Answer 30

1. Take logs of both sides 2. Compare to Y=mx +c to figure which represents each letter

Question 31

Interpret the meaning of the constant … in the model

Answer 31

Y= the constant when the power is either 0 or 1, most likely 0 This is when the thing starts, so is the INITIAL value

Question 32

Differentiate sin x Differentiate sin kx

Answer 32

Cos x Kcos kx

Question 33

Differentiate cos x Differentiate cos kx

Answer 33

-sin x -Ksin kx DON’T FORGET THE MINUS !

Question 34

Y = ln x, differentiate

Answer 34

1/x

Question 35

For differentiating complex things like if contains e and sin/cos

Answer 35

Use product rule: 1. Let u = one part and v = the other 2. Differentiate u and v 3. U’V + V’U equals the expression differentiated

Question 36

Differentiate the function of a function y = f(g(x))

Answer 36

= f’(g(x))g’(x)

Question 37

If they give you x = ….. and ask to differentiate

Answer 37

1. Do dx/dy (basically just differentiate the y instead of x) 2. Do 1/ans as dy/dx is just that flipped

Question 38

Differentiate ln x

Answer 38

1/x

Question 39

Quotient rule

Answer 39

Y’ = vu’ - uv’ / v^2

Question 40

Product rule

Answer 40

Y’ = uv’ + vu’

Question 41

Chain rule

Answer 41

Y’ = dy/du x dy/dx

Question 42

Differentiate sin^2 x

Answer 42

2sinxcosx Use chain rule: Let u = sin x Let v = u^2 Differentiate each = 2u x cosx (sin differentiated) = 2sinxcosx