Core 1 Notes Edexcel

Notes for Core 1 Edexcel maths. I made these for my resit having, and having done C2 and C3 i didnt bother with differentiation/integration notes, but the rest of the spec is there.

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  • Created by: tom
  • Created on: 08-06-11 16:17
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Algebra and Functions
Indices
Indices are numbers that are raised to a power (eg. 251/2). The laws of indices are as follows:
ya × yb = ya+b
ya ÷ yb= ya-b
y -b = 1/yb
ym/n = (ny)m
(yn)m = ynm
y0 = 1
Surds
Surds are numbers left in root form to give exact answers when they equal numbers with
lots of decimal places (eg. 23 ). Rationalising Surds is a way of modifying surd expressions
so that the square root is in the numerator of a fraction and not in the denominator.
The method is to multiply the top and bottom of the fraction by the square root. If there is
an expression such as 1 + 2 in the denominator, you can use the difference of two squares
to rationalise it. In this case is would be achieved by multiplying the top and bottom of the
fraction by 1 - 2

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In general
Fractions in the form multiply top and bottom by
Fractions in the form multiply the top and bottom by
Fractions in the form multiply the top and bottom by
Quadratic Functions
A quadratic equation is an equation where the highest power of x is x2, so it is
an equation of the form ax2 + bx + c = 0. There are various methods of solving
quadratic equations, as shown below.…read more

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If b2 - 4ac = 0 then the quadratic formula says that x = - b/2a, so there is only
one solution. The graph will only touch the x-axis at one point, therefore.
However, if b2 - 4ac > 0, there will be 2 solutions to the equation and so the
curve will cross the x-axis at 2 points.
Completing the Square
To write a quadratic equation in form of a squared bracket, we divide the co-efficient of the x
term by 2.…read more

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Example
Suppose we wish to fi
nd the minimum value of the quadratic function f(x) = x2-6x -12.
We know that because f(x) = x2-6x-12 has a positive x2 term the graph will have a minimum
value.
This will occur when (x -3)2 is zero. The minimum value will be when y =-21 and x = 3.
NOTE: Completing the square can be used to find max/min points on a graph pr solve a
function.…read more

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Example: Solve the simultaneous equations y - 2x = 1 and 2y - 3x = 5
Rearranging Equation 1, we get y = 1 + 2x. We can replace the `y' in equation 2 by
substituting it with 1 + 2x. Equation 2 becomes: 2(1 + 2x) - 3x = 5, so 2 + 4x - 3x = 5
2+x=5 x = 3.…read more

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Graphs and their Fuctions
Graphs are used to plot two variables (x and y) against each other. Simple graphs include
linear, quadratic, cubic and inverse.
Linear graphs are given in the form y=mx+c, where 'm' is
the gradient of the graph and 'c' is the intercept.
Quadratic graphs have x2
as the highest power in the function.…read more

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Graphs can be translated left and right by adding or subtracting quantities, and
stretched or squashed by multiplying or dividing by quantities.…read more

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Co-ordinate Geometry
Distance Between Two Points:
The length of the line joining the points (x1, y1) and (x2, y2) is:
Example
Find the distance between the points (5, 3) and (1, 4).
(So in this case, x2 = 1, x1 = 5, y2 = 4 and y1 = 3).…read more

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Parallel and Perpendicular Lines:
If two lines are parallel, then they have the same gradient.
If two lines are perpendicular, then the gradients of the two lines are reciprocals of each other.
Example
a) y = 2x + 1
b) y = -½ x + 2
c) ½y = x - 3
The gradients of the lines are 2, -½ and 2 respectively. Therefore (a) and (b) and perpendicular, (b)
and (c) are perpendicular and (a) and (c) are parallel.…read more

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Recurrence Relationships:
This is where the next term of a sequence is defined using the previous term(s). To define a
recurrence relation, you have to give the first term. Then you give a formula to tell you how to work
out the next term from the previous ones.
For example, consider the sequence: 2, 4, 8, 16, 32, ... . Each term in the sequence is got by doubling
the previous term.…read more

Comments

C Clarke

Very clear and helpful.  

katie

thank you ever so much :) this is really helpful

leah

no intergration or differentiation?

AruntujhaPonniah

Useful website

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