Use of Maths

Module- Algebra

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  • Created by: Emily
  • Created on: 13-12-11 09:42

Linear Functions

Linear model

M and C are constants.

The gradient = M The intercept on the y axis = C

Gradient = Ystep/ X step

Graph mode, Enter equation, Draw, G-Solve = Y intercept

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Linear Functions

Models of direct proportion 

Variables X and Y are in direct proportion if Y=kX

The graph of Y against X is a STRAIGHT LINE, with gradient k, which passes through the origin (0,0). 

k often gives a significant measure, e.g for a currency conversion graph k  gives the rate of exchange.  

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Quadratic Functions

Quadratic Functions

Y=ax²+ bx+c

a,b and c are constants.

You can make every possible quadratic function by changing the values of a,b and c.

 Completeing the square gives the form Y=m(x+n)²+ p

If m is positive,  the function has a minimum  value of p, when x=-n.

If m is negative, this function has a maximum value of p, when x= -n.


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Quadratic Functions

Quadratic equations

Quadratic equations can be solves by:

  • Using a graph
  • Completing the square
  • Factorising
  • Using the formula x= -b±√ b² - 4ac / 2a

Quadratic models can be used to model all or part of a set of data.


                                                 

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Quadratic Functions

Quadratic graphs

Quadratic graphs have either a single minimum  point or a single maximum point.

Y= ax²+ bx +c


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Quadratic Functions

Quadratic graphs

Graphs can be used to solve equations by finding the x co-ordinates of the points of intersection with the x axis or other lines.

 Graph mode, Enter equation, Draw, G-Solve, roots = points of intersection. 

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Quadratic Functions

Roots-  The solution when y=0, or the x-axis interception (cross)

Zeros- 

Vertex- 

Minimum- Lowest value

Maximum-  Highest value

Turning points-  Minimum/maximum

Line of symmetry- Line of which both sides are symmetrical 

Y intercept- Point of which the graph crosses the y axes.

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Quadratic Functions

Real life situation/s:

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Trig functions

Y=Asin(B(X+C))+D 

A= Amplitude

degrees/B = Period 

C= phase shift

D= vertical shift


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