Introduces students to the floor and ceiling functions

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.

This question shows how to load a GeoGebra applet in JavaScript, avoiding the JME functions. This allows you to do some more complicated manipulation of the worksheet than simply redefining objects.

Sketch a function graph by using fist and second derivatives.

Differentiate $f(x)=x^{m}\sin(ax+b) e^{nx}$.

The answer is of the form:
$\displaystyle \frac{df}{dx}= x^{m-1}e^{nx}g(x)$ for a function $g(x)$.

Find $g(x)$.

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Given sample data find mean, standard deviation, median, interquartile range.

Note that there are different versions of the upper and lower quartiles, so you may want to include your own versions - see the user defined functions in the question.

Find a regression equation.

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$. Solution involves inverse trigonometric functions.

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$. Solution involves the inverse trigonometric function $\arcsin$.

Solve for $x$: $a\cosh(x)+b\sinh(x)=c$. There are two solutions for this example.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Differentiate the function $(a + b x)^m  e ^ {n x}$ using the product rule.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

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

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

Spearman rank correlation calculated. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

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