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Here are examples from M136 tutorials
Tutorial Topic One Revision, Indices, solving square root problems ie Ö126,
rationalising ‘opposite 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 f -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
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