Julie Crowley

First- and second order recurrence equations, homogenous and nonhomogenous

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

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Graph Limits

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Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. The y-intercept is given.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

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Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

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Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. 

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Compute a table of values for a quadratic function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

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Compute a table of values for an exponential function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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Indices

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Splitting an algebraic fraction into partial fractions

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Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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Practice use of summation notation for regression question.

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$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Transposition of formulae. Changing the subject of an equation. 

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Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

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