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. 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.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Some simple questions around injectivity, surjectivity, bijectivity (and the inverse function) of linear functions $\mathbb R\to \mathbb R$ (i.e., $x\mapsto mx+b$ for some real numbers $m$, $b$).

More work on differentiation with trigonometric functions

Introductory function notions

This assessment reviews some of the material covered in the first lecture session. 

What is the function of the given graph?

Gives students an introduction to the injective property of functions

Introduces students to the floor and ceiling functions

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Determine the largest possible domain of a rational function.

Determine if a function is odd, even or neither. 

Small demo using the JME implementation of JSXGraph inline in a multiple choice question. This version uses a JME variable to store the expressions and then calls a function wherever a plot is required.

This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

Differentiate $ (a+bx) ^ {m} \sin(nx)$

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

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 $\arcsin$.