Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Partial Fractions

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Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Given the pdf  $f(x)=\frac{a-bx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q | X \gt t)$.

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

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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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Tests the ability to match a quadratic function to a given parabola.

multiple choice testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

Using differentiation to find the tangent and normal to a line at a given point

This question asks a student to draw a straight line graph by dragging points.

Tests the ability to find the gradient and intercept of a straight line graph.

No description given

The test asseses the students ability to apply the Lagrange multiplier method to various calculus problems.

Given the original formula the student enters the transformed formula

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

Integration by susbtitution, no hint given

Find a regression equation given 12 months data on temperature and sales of a drink. 

Elementary Exercises in multiplying matrices. 

Basic solving of linear equations.

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

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This is a description I wrote when I created the SCORM package.

Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

Given constant demand for a product, calculate the economic order quantity, and the minimum cost per year.

Given constant demand for a product, calculate the economic order quantity, and the minimum cost per year.

Integration by Substitution

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9 questions: Expanding out expressions such  $(ax+b)(cx+d)$ etc.