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M137  Students

M133/M135
(Algebra) Students

M135  Students

M103 Students

M136  Students

M121 Students

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Please be aware the notes are my personal notes and solutions and are here to aid your learning Questions are from Washington

Here are examples from M136 tutorials

Tutorial Topic One            Revision, Indices, solving square root problems ie Ö126,
                                             
rationalisingopposite sign one’

Tutorial Topic Two            Algebra, powers (m2 n-2 /z n-4 m7 )4, Equations of Straight lines,
                                              using two points, and point/intercept and gradient,
                                              perpendicular and parallel lines 

Tutorial Topic Three         Solving logarithms, log8 64 and powers 3 x = 81   Log Rules,
                                              Questions with
growth/decay of form N(t) =N(0)e kt

Tutorial Topic Four           Functions: Graph changes when you add/subtract etc...
                                              Domain and Range value problems,

                                              Composite fog, gof ...and finding the Inverse  -1 (x)        

Tutorial Topic Five            Limits: ways to solve limits to infinity
                                             
and when zero is on bottom of fraction
                                              or it looks  like it does not exist

Tutorial Topic Six              Continuity of a function and piece-wise functions
                                              the ones where the equation changes for different values of x

Tutorial Topic Seven         Differentiation from First Principles,
                                              Basic differentiation in Product/Quotient
                                              Rules Displacement, Velocity and Acceleration

Tutorial Topic Eight          Differentiation: Rules for (bracket) power (Chain) ,
                                              Sin, Cos, Tan etc....(Trigonometric)
                                             
Ln (bracket) (Logarithm) and   e(bracket)  (Exponential )

Tutorial Topic Nine           Implicit Differentiation differentiating with respect to another letter
                                              when you have two or  more letters i.e. dy/dt  du/dx

Tutorial Topic Ten             Related rates, differentiating with respect to time


Tutorial Topic Ten plus    Differentials dy/dx = dy/dx  and
                                              Linear Approximations f(x + dx ) = f ' (x) dx  + f(x)


Tutorial Topic Eleven       Differentiation Max, Min, Inc, Dec, Concavity etc 

Tutorial Topic Twelve       Integration Basic  x (power+1) / (power +1)
                                              Substitution where u = something  
                                                                                                             a
                                              then ∫ u’s du Definite Integration b     x’s  dx

Tutorial Topic Thirteen    Area enclosed by curve and x-axis and area between two curves                                   

Tutorial Topic Fourteen   Vectors  resultant vectors, adding vectors, angles between vectors

Tutorial Topic Fifteen       Ships Colliding or not

Tutorial Topic Sixteen       Application of Integration given the rate a population is changing,
                                              find a formula for the population number,
                                              Volumes of Revolution around the x-axis.

Tutorial Topic Seventeen Matrices adding/subtracting, multiplication, Inverse of 2 x 2, Row elimination,
                                              solving equations x -3y+ z =9 2x -3y+ 4z =19 2x -3z=2