Pure Maths Flashcards by Adele Schiff

What are the steps for a proof?

Specialise to understand eh problem
Make a generalisation
Calculate and simplify
Write a conclusion using wording of phrase

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What are the three types of sequence?

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

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

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

N is term
A is first term
D is difference between the terms

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

Position to term rule: tn = 6n + 5

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

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

Look at notes

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How do you find the gradient of a line?

Y-Y1 / X-X1 = gradient

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How do you fined the midpoint of the line?

(x1 + x2 ) / 2 = xm

(y1 + y2) / 2 = ym

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How do you find the length of a line?

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

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What is the trapezium rule?

Find area under a curve, split into equal length

- ((a+b) / 2)h

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What is the equation for arc length?

Theta x r

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What is the equation for area of a sector?

0.5 x r^2 x theta

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How do you convert from radians to degrees?

x 180/pi

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How do you convert from degrees to radians?

Divide by 180/ pi

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What is the equation of a circle?

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

-Where (a,b) is the centre

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What is the equation for a geometric sequence?

tn = a x r^n-1

a is the first term
r is the common ratio

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

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

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

Un + 1 and state U1 =

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What are the log addition rule?

logcA + logcB = logcAB

logcA + logcA = logcA^2

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What is the log subtraction rule?

logcA - logcB = logc (A/B)

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What is 2logcA also seen as?

logcA^2

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What is the power rule for logs?

nlogcA = logcA^n

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What are the steps for finding the stationary point?

Find dy/dx
Solve dy/dx = 0
Then plug these x values into the original equation to get y values
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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What are the trigometric value we need to know?

Study These Flashcards

sin^2theta + cos^2theta = 1

sin / cos = tan

What is secX ?

Study These Flashcards

secX = 1/cosX

What is cosecX?

cosecX = 1/sinX

What is cotX?

cotX = 1/tanX

What are the two conditions for a function?

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

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

f first

What do you do in differentiation?

1. Bring the old power down to the front | 2. Decrease the power by one

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

1. Increase power by one 2. Divide by new power 3. + c

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

e^x

What is dy/dx of y=lnx?

1/x

What is the rule for chain rule?

nstuff^n-1 x stuff’ - (x^2 + 3x )^4 - 4(x^2 + 3x)^3 x (2x + 3)

What is e^stuff differentiated?

e^stuff x stuff’

What is ln(stuff) differentiated?

stuff’ / stuff

What is the infinite sum?

Sn = a / 1-r

What is the cosine rule?

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

What is the sine rule?

aSinB = bSinA

What is the binomial expansion?

(1+x)^n = 1 + nx + n(n-1)/2! x^2 + n(n-1)(n-2)/3! x^3 ..... | USE BRACKETS!

When is the binomial valid?

mod (x/number) < 1 | mod(x) < 1

What does sinx differentiate to?

cosx

What does cosx differentiate to?

-sinx

What does tanx differentiate to?

sec^2x

How do you differentiate cos(stuff)?

-stuff' x sin(Stuff)

How do you differentiate sin(stuff)?

cos(Stuff) x stuff'

What are some trigonometric identities?

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

How do you work out R in harmonic form?

``` 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) ```

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

Max: R + 5 Min: -R + 5

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

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

What is an even function?

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

What is an odd function?

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

What does change of sign show?

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

What is Newton Raphson excel?

``` x f(x) f(x') x0 ```

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

0.5*A$2*(C4+C5)

How do you do integration by parts?

make v' be the e (you can do it) | Check by integrating!

How do you do integration by substitution?

Change limits!

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

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

Pure Maths Flashcards

(57 cards)