Manipulation of an exponential function

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)

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.

poles of a transfer function

Gain & Phase of a transfer function

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

5 indefinite integrals containing exponential functions

rebelmaths

Composite functions.

Manipulation of an exponential function

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.

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.

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 $f(x,y)$.

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

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Simple examples combining functions

Composite functions.

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.

An introduction to terminology about the surjective property of a function.

This question asks the student to find the inversed composite function finding the inverses of two functions then 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.

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

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

rebelmaths

Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$. Calculate $f(p,q)$.

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

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Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

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)