Pure Flashcards

1
Q

How to transform logarithmic graphs?

A

Write as a familiar function y=f(x) and then use normal transformation rules.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Relationship between lines of lnx and e^x

A

Reflection of each other in the line y=x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What does y=e^x look like?

A

Acceleration, crosses y-axis at (0,1), asymptotes of y=x and x-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What does y=lnx look like?

A

Deceleration, crossing x-axis at (1,0), asymptotes of y=x and y-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

How to convert a circle’s equation?

A

Complete the square

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Which formula to use when r>1?

A

r^n - 1, r-1 instead of the other one (on formula sheet)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

sin2A

A

2sinAcosA

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

cos2A

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

tan2A

A

2tanA/1-tan^2A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

sec^2A

A

1+tan^2A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

cosec^2A

A

1+cot^2A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

How to write parametric equations as a function?

A

x = p(t), y = q(t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is the domain of f(x)?

A

range of x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the range of f(x)?

A

range of y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

How to draw functions as graphs?

A

Work out domain and range.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

domain of secx?

A

R except even multiples of pi/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

range of secx?

A

-1≤ or ≥1

18
Q

domain of cotx?

A

R, except multiples of π

19
Q

range of cotx?

20
Q

range of cosec?

A

-1≤ or ≥1

21
Q

domain of cosec?

A

R, except multiples of π

22
Q

domain of arcsinx

A

-1 ≤ x ≤ 1

23
Q

range of arcsinx

A

[-π/2, π/2]

24
Q

domain of arccosx?

A

-1 ≤ x ≤ 1

25
range of arccosx?
[0, π]
26
how to draw arcfunctionx?
restrict domain of 'normal' function, then reflect in y=x
27
domain of arctanx?
all real numbers
28
range of arctanx?
[-π/2, π/2]
29
cos(-A) is the same as
cos(A)
30
sin(-A) is the same as
-sin(A)
31
sin30
1/2
32
cos30
√3/2
33
tan30
√3/3
34
sin45
√2/2
35
cos45
√2/2
36
tan45
1
37
sin60
√3/2
38
cos60
1/2
39
tan60
√3
40
cosine rule
a² = b² + c² - 2bccosA
41
How can we use the discriminant?
It's value tells us the number of times two lines intersect.
42
when modelling parametric, what is the value of dy/dt at max/min?
0, like dy/dx is 0