c1 exam questions

This is the sum of '3r' for values of 'r' from r = 1 to r = 4.

This is the general case. For the sequence U_r, this means the sum of the terms obtained by substituting in 1, 2, 3, ... n in turn for r in U_r.

The recurrence relationship in an arithmetic sequence is:

Un= 

The sum of the arithmetic sequence is:

When they give you the sum of the series and the recurrence relationship formula, and ask you to find the amount on day x:

1. Use simultaneous equations and solve for x.

When they tell you to find f(x) from a differentiated expression:

1. Integrate the expression

2. Substitute the numbers of the given point to find C.

3. Add the value of C to your integrated equation.

When they say find the normal to C at a given point:

1. Differentiate the expression.

2. Substitute the numers in to find M

3. As the gradient of the normal is -1/M, do this and use the equation

        y-y1=m(x-x1) along with the coordinates given.

If they ask you to prove this sum of the series:

Add these two:

Since L is the last term, we know it equals , where n is the number of terms of the series in the sum.

 , divide this by 2 and the formula is proved.

Translations and transformations:

f(x-a)= move a to left

f(x+a)= move a to right

f(x)+a= move a upwards.

f(ax)= multiply x coordinates by 1/a

af(x)= multiply y coordinates by a

f(-x)= the graph reflect on the Y AXIS

-f(x)= the graph reflects on the X AXIS

m= y2-y1/x2-x1

y2-y1/y-y1= x2-x1/x-x1

y-y1=m(x-x1)

the gradient of a perpendicular line is -1/m

the normal to a line is perpendicular to the tangent

Use pythagoras to find the distance between two points.

When you get a fractional indice REMEMBER to first do the square/cubed/etc. root and then multiply it by the power given.

Anything to the power of 0= 1

Integrate the following expression x^n --->>>  x^n+1/n+1

Differentiate the following expression: ax^n --->>> n(ax)^n-1

Completing the square: 

Even if you have extra numbers that aren't part of B just add them to the general equation!

When using inequality signs, you need to know which part of the graph they're looking for.

1. If 2x+3y+1<0, they're looking for the inside region- the part of the curve under the x-axis.

2. If 2x+3y+1>0, they're looking for the outside region- the part of the curve which is above the x-axis.