Pure Maths

Front 1

How do you find the maximum/minimum value of a function?

Back 1

Find the second derivative (d²y/dx²), and input the X-coordinate of the turning point into it.

>0 means it's a minimum

<0 means it's a maximum

Front 2

How do you check if a stationary point is a Point of Inflection?

Back 2

Check thesecond derivative (d²y/dx²), and if it equals zero then it could be a Point of Inflection.

Then check points either side of the stationary point (1 below and 1 above X), and if dy/dx doesn't change then it is a Point of Inflection.

Front 3

What does the discriminant tell you about a graph? And why does it mean that?

Back 3

If b²-4ac<0 there are no real roots

If b²-4ac=0 there is one rep. root

If b²-4ac>0 there are 2 real roots

Because b²-4ac is within a square root in the Quadratic Formula, so if it is positive then their are two answers, if it = 0 there is one answer (0), and negative means there is no answer so the Formula doesn't work.

Front 4

What are the trigonometric identities?

Back 4

tanX = sinX/cosX

sin²X + cos²X = 1

÷sin²X--> 1 + cot²X = cosec²X

÷cos²X--> tan²X + 1 = sec²X

Front 5

What are the double angle formulae?

Back 5

sin2θ = 2sinθcosθ

cos2θ = cos²θ-sin²θ

=2cos²θ-1

=1-2sin²θ

tan2θ = 2tanθ/1-tan²θ

Front 6

How do you find other values of tanX?

Back 6

Add 180⁰ to your previous answers

Front 7

How to convert degrees to radians?

Back 7

Multiply the given value by π/180

because π=180, therefore 180π/180=π

Front 8

Log Laws

Back 8

logx (a) + logx (b) = logx (ab)

logx (a) - logx (b) = logx (a/b)

loga (a) = 1

ln x = logex

ln e^x = x

e^x=2 ----> x=ln2

Front 9

Write logab = c in Exponential Form

Back 9

a^c = b

Front 10

What is the formula for the Surface Area of a Cylinder?

Back 10

2πr^2+πdh

Front 11

What is the formula for Arc Length?

Back 11

S (Arc Length) = rθ

Front 12

Formula for Sector Area

Back 12

1/2 x r² x θ

Front 13

What is the area of a triangle formula?

Back 13

1/2 a b sinC

Front 14

Cosine Rule

Back 14

Cos A = (b^2 + c^2 - a^2)/2bc

or

a^2 = b^2 + c^2 - 2bc cos A

Front 15

Geometric Sequence formula for nth term

Back 15

a= first term

r= common ratio

Formula= ar^(n-1)

Front 16

Arithmetic Sequence formula for nth term

Back 16

a=first term

d=common difference

Un = a + d(n-1)

Front 17

Index Laws

Back 17

a^m x a^n = a^m+n

a^m ÷ a^n = a^m-n

(a^m)^n=a^mn

Front 18

Differentiate the following:

A^kx

e^kx

sin(kx)

ln(kx)

Back 18

A^kx ---> k(lnA)A^kx

e^kx---> ke^kx

sin(kx)---> kcos(kx)

ln(kx)---> 1/x

Front 19

Integrate the following:

e^kx

1/x

Back 19

e^kx---> (1/k)e^kx+ c

1/x---> ln x + c

Front 20

What is the process for Integration by Substitution?

Back 20

Set u=.....

du/dx=.....

(If an area under graph question, don't forget to change limits)

Front 21

How would you write 1/(x+1)(x-1)² to do partial fractions?

Back 21

=A/(x+1) + B/(x-1) + C/(x-1)²

Front 22

What is the parametric differentiation rule (when t is included in the two equations)?

Back 22

dy/dx = dy/dt x dt/dx