Core 3 - Essentail points to remember

Question 1

Which of
- One-to-many
- Many-to-one
- One-to-one
Are functions

Answer 1

Many-To-One

One-To-One

Question 2

Define function

Answer 2

A special “mapping” such that every element of the domain is mapped to exactly one element in the range

Question 3

How does one make f(x) = sqrt(x) a function

Answer 3

Changing the domain to x >= 0

Question 4

Inverse functions are reflections of f(x) in what line

Answer 4

The line of y=x

Question 5

What is the inverse function of e^x

Answer 5

ln(x)

Question 6

State the growth and decay equations

Answer 6

N = Ae^(kt) and N=Ae^(-kt)

Where A and k are positive numbers

Question 7

State the consequence of f(x+a)

Answer 7

Horizontal translation of -a

Question 8

State the consequence of f(x)+a

Answer 8

Vertical translation of a

Question 9

State the consequence of f(ax)

Answer 9

Horizontal stretch of 1/a

Question 10

State the consequence of af(x)

Answer 10

Vertical stretch of scale factor a

Question 11

State the process to sketch a graph for y=|f(x)|

Answer 11

• Sketch the graph f(x)

- Reflect in the x-axis any parts where f(x)

Question 12

State the process to sketch graph for y=f(|x|)

Answer 12

• Sketch the graph y = f(x) for x >= 0

- reflect this in the y-axis

Question 13

sec(theta)

Answer 13

1/cos(theta)

Question 14

cosec(theta)

Answer 14

1/sin(theta)

Question 15

cot(theta)

Answer 15

1/tan(theta)

Question 16

sketch sec(theta)

Answer 16

see google lol

Question 17

Sketch cosec(theta)

Answer 17

see google lol

Question 18

Sketch cot(theta)

Answer 18

see google lol

Question 19

State 2 key identities derived from sin^2(x) + cos^2(x) = 1

Answer 19

• 1 + tan^2(x) = sec^2(x)

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

Question 20

State the inverse function of sin and its domain and range

Answer 20

arcsin

domain: -1

Question 21

State the inverse function of cos and its domain and range

Answer 21

arccos

domain: -1

Question 22

State the inverse function of tan and its domain and its range

Answer 22

arctan

domain: all real number
range: -pi/2

Question 23

Give the double angle formula for sin

Answer 23

sin2A = 2sinAcosA

Question 24

Give the double angle formulae for cos

Answer 24

cos2A = cos^2A - sin^2A = 2cos^2A - 1 = 1 - 2sin^2A

Question 25

Give the double angle formula for tan

Answer 25

tan2A = (2tanA)/(1 - tan^2A)

Question 26

How does one write asinx +- bcosx in terms of only sin or cos

Answer 26

Rsin(x +- alpha)

Question 27

How does one write acosx -+ bsinx in terms of only sin or cos

Answer 27

Rcos(x -+ alpha)

Question 28

How does one find “R” in context of trig

Answer 28

sqrt(a^2 + b^2)

Question 29

How does one find alpha in context of trig

Answer 29

a = tan^-1(b/a)

Question 30

State the quotient rule

Answer 30

dy/dx = (vdu/dx - udv/dx) / (v^2)

Question 31

State the product rule

Answer 31

dy/dx = udv/dx + vdu/dx

Question 32

What is the differentiated form of y = e^f(x)

Answer 32

dy/dx = f1(x)*e^f(x)

Question 33

What is the differentiated form of y = ln(f(x))

Answer 33

dy/dx = f1(x)/f(x)

Question 34

State the order in which the trig functions are differentiated

Answer 34

sin(x)
cos(x)
-sin(x)
-cos(x)
sin(x)
so fourth