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

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

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.

The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.

Some quadratics are to be solved by factorising

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Q1 is true/false question covering some core facts, notation and basic examples.  Q2 has two functions for which second derivative needs to be determined.

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.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Multiplication and addition of complex numbers. Four parts.

Given a graph of some line or curve - the student is asked about the nature of the map and whether it constitutes a function.

Some questions to practice your fundamental skills in vectors.

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

This quiz is designed to help you practise your integration techniques.

Improvements needed:

• Add some definite integrals to Q2
• Use different variables

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

Given a graph of some line or curve - the student is asked about the nature of the map and whether it constitutes a function.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Implicit differentiation question with customised feedback to catch some common errors.

Implicit differentiation question with customised feedback to catch some common errors.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Given results from a survey about what people eat for breakfast, where some people eat one or both of cereal and toast. Student is asked to pick the probability of eating either one or the other from a list. Distractors pick out common errors.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.