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Z A Level Maths > Pure Maths > Flashcards

Pure Maths Flashcards

1
Q

What are the steps for a proof?

A
  1. Specialise to understand eh problem
  2. Make a generalisation
  3. Calculate and simplify
  4. Write a conclusion using wording of phrase
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2
Q

What are the three types of sequence?

A

Convergent (to a limit)
Oscillating (Period is number of different numbers)
Divergent (to infinity)

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3
Q

What is the equation for the sum of the first n terms of an arithmetic progression?

A

Sn = n/2(2a + (n-1)d)

  • N is term
  • A is first term
  • D is difference between the terms
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4
Q

What is an example of a position to term rule and a term to term rule?

A
  1. Position to term rule: tn = 6n + 5

2. Term to term rule: tn + 1 = tn + 6

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5
Q

For completing the square, how do you interpret it graphically?

A

Look at notes

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6
Q

How do you find the gradient of a line?

A

Y-Y1 / X-X1 = gradient

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7
Q

How do you fined the midpoint of the line?

A

(x1 + x2 ) / 2 = xm

(y1 + y2) / 2 = ym

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8
Q

How do you find the length of a line?

A

(deltay)^2 + (deltax)^2 = c^2

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9
Q

What is the trapezium rule?

A
  • Find area under a curve, split into equal length

- ((a+b) / 2)h

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10
Q

What is the equation for arc length?

A

Theta x r

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11
Q

What is the equation for area of a sector?

A

0.5 x r^2 x theta

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12
Q

How do you convert from radians to degrees?

A

x 180/pi

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13
Q

How do you convert from degrees to radians?

A

Divide by 180/ pi

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14
Q

What is the equation of a circle?

A

(x-a) ^ 2 + (y-b)^2 = r^2

-Where (a,b) is the centre

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15
Q

What is the equation for a geometric sequence?

A

tn = a x r^n-1

  • a is the first term
  • r is the common ratio
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16
Q

What is the sum of the first n terms of a geometric progression?

A

Sn = a x (1-r^n) / (1-r)

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17
Q

What is the term to term rule of a geometric progression?

A

Un + 1 and state U1 =

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18
Q

What are the log addition rule?

A

logcA + logcB = logcAB

logcA + logcA = logcA^2

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19
Q

What is the log subtraction rule?

A

logcA - logcB = logc (A/B)

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20
Q

What is 2logcA also seen as?

A

logcA^2

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21
Q

What is the power rule for logs?

A

nlogcA = logcA^n

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22
Q

What are the steps for finding the stationary point?

A
  1. Find dy/dx
  2. Solve dy/dx = 0
  3. Then plug these x values into the original equation to get y values
  4. Then find the second derivative and plug in your x values to find out if the point is a maximum or minimum - (<0 it is a maximum) (>0 it is a minimum)
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23
Q

What are the trigometric value we need to know?

A

sin^2theta + cos^2theta = 1

sin / cos = tan

24
Q

What is secX ?

A

secX = 1/cosX

25
Q

What is cosecX?

A

cosecX = 1/sinX

26
Q

What is cotX?

A

cotX = 1/tanX

27
Q

What are the two conditions for a function?

A
  1. Completeness Criteria: Every object in the domain has an image in the codomain
  2. Uniqueness Criteria: each object in the domain has a unique image
28
Q

Do you do g or f first in gf(x)?

A

f first

29
Q

What do you do in differentiation?

A
  1. Bring the old power down to the front

2. Decrease the power by one

30
Q

What do you do in integration? What do you always need to remember?

A
  1. Increase power by one
  2. Divide by new power
    • c
31
Q

What is dy/dx of y=e^x?

A

e^x

32
Q

What is dy/dx of y=lnx?

A

1/x

33
Q

What is the rule for chain rule?

A

nstuff^n-1 x stuff’

  • (x^2 + 3x )^4
  • 4(x^2 + 3x)^3 x (2x + 3)
34
Q

What is e^stuff differentiated?

A

e^stuff x stuff’

35
Q

What is ln(stuff) differentiated?

A

stuff’ / stuff

36
Q

What is the infinite sum?

A

Sn = a / 1-r

37
Q

What is the cosine rule?

A
  • a squared = b squared + c squared - 2bcCosA

- CosA = b squared + c squared - a squared / 2bc

38
Q

What is the sine rule?

A

aSinB = bSinA

39
Q

What is the binomial expansion?

A

(1+x)^n = 1 + nx + n(n-1)/2! x^2 + n(n-1)(n-2)/3! x^3 …..

USE BRACKETS!

40
Q

When is the binomial valid?

A

mod (x/number) < 1

mod(x) < 1

41
Q

What does sinx differentiate to?

A

cosx

42
Q

What does cosx differentiate to?

A

-sinx

43
Q

What does tanx differentiate to?

A

sec^2x

44
Q

How do you differentiate cos(stuff)?

A

-stuff’ x sin(Stuff)

45
Q

How do you differentiate sin(stuff)?

A

cos(Stuff) x stuff’

46
Q

What are some trigonometric identities?

A

sin^2x + cos^2x = 1
tan2^x + 1 = sec^2x
1 + cot^2x = cosec^2x

47
Q

How do you work out R in harmonic form?

A 
y1 = R^2sin^2alpha = 4
y2=R^2cos^2alpha = 9 
y1 + y2 = 13
R^2 (sin^2alpha + cos^2alpha) = 13
R^2 (1) = 13
R = sqrt(13)
48
Q

What is the maximum and minimum value of Rsin(3x+alpha)+5?

A

Max: R + 5
Min: -R + 5

49
Q

What is the maximum and minimum value of 1/Rsin(3x+alpha)+5

A

max: 1/5-R
min: 1/5+R

50
Q

What is an even function?

A

f(-x) = f(x) e.g. cos

51
Q

What is an odd function?

A

f(-x)=-f(x) e.g. y=x or tanx

52
Q

What does change of sign show?

A 
A root (always do it to one more dp to check around but draw swell)
!
53
Q

What is Newton Raphson excel?

A 
x f(x) f(x')
x0
54
Q

What is C4+C5/2 x a2 in excel?

A

0.5A$2(C4+C5)

55
Q

How do you do integration by parts?

A

make v’ be the e (you can do it)

Check by integrating!

56
Q

How do you do integration by substitution?

A

Change limits!

57
Q

What is implicit differentiation? What does y^2 = 3x^2y + x^2 differentiate to?

A

2y dy/dx = 6xy = 3x^2 dy/dx +2x

Z A Level Maths (4 decks)

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