Core One - complete set of revision notes.

Set of notes i typed up for my core one maths exam, which helped incredibly on OCR

Sorry the notes are seperated, we had two different teachers so everything is a little all over the place, but everything is pretty much there, hope it can help anyone, took me long enough to do!

Good Luck!

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Page 1

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Core 1
Laws of indices
For indices with the same base:
When multiplying the bases , add together the powers e.g. a2X a3 = a5
When dividing the bases, subtract the powers e.g. a2÷ a3 = a-1

When there is power to a power, multiply the powers e.g. (an)m =…

Page 2

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25 = c c=5

Gradient of a line between two co-ordinates




Use these figures to figure out the gradient by dividing :
For example = m = 4 2 =2


Straight Lines
Equations of Straight Lines
To find the equations of a straight line the minimum you need is a…

Page 3

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equations (the equations of the lines that cross) are the values of the X
Y co-ordinates.


Differentiation
Differentiation is finding the gradient of curves. This can be asked in many ways and use in multiple
forms of questions,
All of these are ways of just asking you to differentiate the…

Page 4

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The nature of stationary points are whether or not they are a maximum or a minimum turning point,
to find this out, once you have found the stationary points you must take the second derivative and
sub in both X's to that second derivative, once you have done so the…

Page 5

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(x - 5)(x + 1) = 0 x = 5 x =- 1

-b±b2-4ac
Using the quadratic formulae 2a
A= number in front of the square
B = number in front of the X
C = number on its own
These numbers must be added into the formulae which can…

Page 6

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The discriminant is the part of the equation that determines what type of solutions you will get for
the formulae e.g. one/two/no answers.
Therefore the discriminant of the quadratic equation is b2 - 4ac :
If b2 - 4ac > 0 solving the equation will leave us with 2 distinct…

Page 7

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Solving a quadratic in x1 2
This disguised quadratic will be written with a square root of x in making it x1 2 . This therefore
makes the first power of x equal to two times the middle power of x.
To solve these equations you must let x =…

Page 8

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Linear inequalitites
as simple as rearranging equations, treat these as if there is an equal sign in the middle and solve
them in that way :
e.g.
10x - 3 5 - 6x
16x 8
x 1
2


Quadratic inequalities
To solve a quadratic inequality, one side must contain an…

Page 9

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If the question asks to sketch the graph of a curve such as y = (x + 2)(x - 1)2 the squaring of the last
bracket means that there is a repeated factor, this means that the curve touches the x axis at that
point, and therefore it is a…

Page 10

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Tangents to Circles

Normal

Tangent



If asked to find the equations of either Tangent or Normal's to a circle (given its equation) at one
particular point, first you must find the co-ordinates of the centre by either using the equation given
or by completing the square to get an appropriate…

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