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Here are the tutorial notes for each week
Tutorial Topic One Factorising quadratics ax2 + bx + c, difference of two squares a2 – b2,
sum / difference of two cubes a3 +/– b3 Common Factors
Tutorial Topic Two Logarithms Log base answer = Power and Powers base power = answer
Questions with growth/decay of form N(t) =N(0)e kt
Tutorial Topic Three Trigonometric equations Sin x = 0.5, 2 Sin 3x = 1 and equations e(2y-7) =7
Tutorial Topic Four Pythagorean Identities, Sin2 x + Cos 2 x = 1, 1 + Cot2 x = Cosec2 x,
1 + Tan2 x = Sec2 x and exact values of Sin 15 etc...
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 Eleven Differentials dy/dx = dy/dx and Linear Approximations f(x + dx ) = f ' (x) dx + f(x)
Tutorial Topic Twelve Differentiation Max, Min, Inc, Dec, Concavity etc
Tutorial Topic Thirteen Integration Basic x (power +1) / (power +1) and Substitution where u = then ∫ u’s du
a
Definite Integration ∫b x’s dx
Tutorial Topic Fourteen Area enclosed by curve and x-axis and area between two curves
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 Differential Equations ∫y ’s dy = ∫x’s dx
Tutorial Topic Eighteen Descriptive Statistics Mean Mode Median Stemplot Boxplot
Tutorial Topic Nineteen Normal Distribution P (x < 14), P(z > k), what is x value when you know the area
or probability
Tutorial Topic Twenty Binomial P (x < 14) = P (x ≤ 13) if less than and equals to tables
Tutorial Topic Twenty One Numerical Integration Trapezoidal and Simpson’s Rule
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