A method of randomly choosing variable names - use the expression() JME function to create a variable name from a randomly chosen string.

(This question also uses a custom marking script to check that the student has simplified the expression)

Use integration to find the volume of revolution of a function to estimate the volume of a mountain.

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=1-\sin(y)$, 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 $f(x,y)$.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x)-\sin(y)$, 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 $f(x,y)$.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x-y)$, 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 $f(x,y)$.

Newton-Raphson numerical method question to solve $g(x)=0$

Includes a graph of the function $g(x)$ in Advice using Jsxgraph.

Ask for the square of each number from 0 to 15, in random order.

The shuffle function puts a list in random order.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^3-y^3$, 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 $f(x,y)$.

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 $f(x,y)$.

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 $P(X \gt E)$.

Determine if the following describes a probability mass function.

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

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

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.

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

rebelmaths

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

Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.

Manipulation of an exponential function

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Given a graph, the student is asked to determine the quadratic function.

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

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5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$.

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

rebelmaths

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

This quiz contains questions on functions, limits, logs, exponential functions, simultaneous equations and quadratic equations.

Basic Derivatives, Product Rule, Quotient Rule, Chain Rule, Implicit Differentiation, Differentiating trigonometric and logarithmic functions, tangents 

rebel

rebelmaths

Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.