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A2 Maths > C3 > Flashcards

C3 Flashcards

(69 cards)

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1
Q

When do you use long division in partial fractions

A

When the biggest power on the top is greater than or equal to the biggest power on the bottom

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2
Q

How do you do “valid for” in binomial

A

|ax| < 1

|x| < 1/a

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3
Q

When do you use the chain rule for differentiation

A

When you have a function with a power

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4
Q

Describe the steps when using the chain rule

A
  1. Multiply the number in front by the power
  2. Differentiate the bracket
  3. Write the function again but take one away from the power
  4. Simplify
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5
Q

When do you use the product rule

A

Differentiate y = uv

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6
Q

What is the product rule

A

dy/dx = v du/dx + u dv/dx

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7
Q

When do you use the quotient rule

A

Differentiate y = u/v

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8
Q

Write the quotient rule

A

v du/dx - u dv/dx
—————————
V^2

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9
Q

When do you use implicit differentiation

A

When differentiating an equation which has terms with both x and y

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10
Q

What are the steps for implicit differentiation

A
  1. Differentiate each term with respect to x (treat y’s as numbers)
  2. Differentiate each term with respect to y and write dy/dx after it (treat x’s as numbers)
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11
Q

What is a parametric equation

A

An equation which has an extra letter as well as x and y

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12
Q

What is a Cartesian equation

A

An equation with only x’s and y’s in it

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13
Q

How would you change a parametric equation into a Cartesian equation

A
  • Rearrange the easier equation to get the other letter on its own
  • sub it into the other equation
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14
Q

Write the equation for parametric “magic equation”

A

dy/dx = dy/dt X dt/dx

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15
Q

What are the steps for parametric differentiation

A
  • Find dx/dt and dt/dx (to find dt/dx just use 1 over dx/dt)

- Use magic equation

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16
Q

What does the range represent in terms of functions

A

The range is the values that y can take

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17
Q

How do you solve modulus equations

A

Solve normally and then solve with a - in front of the bracket
(Will get two answers)

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18
Q

How do you solve a modulus equation with a modulus on both sides

A

Square both sides and solve

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19
Q

How do you solve a modulus equation graphically

A
  • Draw the graph as normal

- reflect the part below the x axis in the x axis

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20
Q

How to solve modulus inequalities

A
  • solve the equation

- draw graph

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21
Q

How do you draw the modulus graph of y = |f(x)|

A

Reflect anything under the x axis in the x axis

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22
Q

How do you draw the modulus graph of y = f (|x|)

A
  • ignore anything to the left of the y axis
  • reflect the right hand side in the y axis
  • keep both sides
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23
Q

How would you deal with a composite function

A
  • Sub the number into the function - nearest to the bracket first
  • take answer and sub it into the function
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24
Q

What is the inverse function

A

f^-1 (x)

It is f(x) reflected in the line y = x

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25
How do you find the inverse function
1. Put y = f(x) 2. Rearrange to get x on its own 3. Switch the letters x and y
26
How is the range of a function related to the inverse
The range of the function is the same as the domain of the inverse And vice versa
27
Draw the graph of y = sin Ø
See notes | Starts at 0 and goes through 180° and 360°
28
Draw the graph of y = cos Ø
See notes Starts at 1 Goes through 90 and 270
29
Draw the graph of y = tanØ
see notes S shape Goes through 0 and 180 Asymptote at 90 and 270
30
Draw the graph of y = cosec Ø
See notes | Y= sin Ø but flipped
31
Draw the graph of y=secØ
See notes | y=cosØ flipped
32
Draw the graph of y=cotØ
See notes Y=tanØ reversed and now goes through 90 and 270 Asymptotes at 180 and 360
33
What is the order of graph transformations
1. Left/right (inside bracket and opposite) 2. Multiply / divide 3. Reflection - -f(x) = x axis and f(-x) = y axis 4. Up/down - outside and is what you expect
34
How do you find range and domain
- draw graph - range = y values - domain = x values
35
What does cosecØ equal
1/sinØ
36
What does sec equal
1/cos
37
What does cot equal
1/tan
38
What do you do if it’s 2Ø in cast questions
Change the range eg double range
39
What does sin/cos equal
Tan
40
What does sin^2 + cos^2 Equal
1
41
What does sec^2 equal
1 + tan^2
42
What does cosec^2 equal
1 + cot^2
43
What does cot equal in terms of cos and sin
Cos/sin
44
What does sin(A+/-B) equal
sinAcosB +/- cosAsinB
45
What does cos(A+/-B)
cosAcosB -/+ sinAsinB
46
What does tan(A+/-B) equal
TanA +/- tanB ———————- 1 -/+ tanAtanB
47
What does cos x equal in relation to sin
Sin(90-x)
48
What does sin2A equal
2sinAcosA
49
What does cos2A equal
cos^2A - sin^2A 1 - 2sin^2A 2cos^2A-1
50
What does tan 2A equal
2tanA ———- 1 - tan^2A
51
How do you do Rcos(Ø + &) questions
See notes
52
How do you differentiate sin x and sin(f(x))
Cos x | F’(x)cos(f(x))
53
What does differential of cos x equal and also cos (f(x))
- sin x | - f’(x) sin(f(x))
54
What does the differential of tan x equal
Sec^2 x
55
What does the differential of cot x equal
-cosec^2 x
56
What does the differential of cosec x equal
-cosec x cot x
57
What does the differential of sec x equal
Sec x tan x
58
How do you differentiate e^x and e^f(x)
e^x f’(x) e^f(x) (Power always stays the same)
59
How do you integrate when one part is a multiple of the differential
See notes (end of book- “harder integrals”)
60
How do you integrate sin^2 x / cos^2 x
- Use the cos2x rule - rearrange so that sin^ 2x / cos^2 x is on its own - integrate
61
What is the differential of lnx
1/x
62
What is the differential of ln f(x)
Differential of function ——————————— Function
63
What are the four methods for integrating a fraction
1️⃣ if only one thing on bottom then divide each term and integrate separately 2️⃣ use partial fractions 3️⃣ If top related to multiple of differential of bottom then it must have been an ln function 4️⃣ if number on top and binomial on bottom then bring bottom up and use chain rule
64
What is the graph of y = e^x
See notes (start of second book)
65
What do you do when transforming the graph of y = e^x
Transform asymptote first
66
Draw the graph of y = lnx
See notes (start of second book)
67
How do strips relate to ordinates in the Simpson’s rule
Number of Strips is one less than the number of ordinates
68
What is a root in relation to the newton-raphson method
A riot is a solution of an equation equal to zero
69
What does a sign change in the newton-raphson method indicate
Change of sign indicates root

A2 Maths (1 decks)

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