Some impossible-looking questions about quadratic equations which can be solved with a bit of thinking.

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.

Some students believe a decimal is larger if it is longer, some believe a decimal is larger if its first non-zero digit is larger.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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.

Differentiation question with customised feedback to catch some common errors and corresponding partial marks.

malrules

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

Simple ratio question with custom marking and partial credit possible

The marking checks for some common errors and awards partial credit and appropriate feedback. The errors that give different levels of partial credit include: forgetting to add one to the denominator, forgetting to change to a percentage.

Some questions which use JSXGraph to create interactive graphics.

A small sequence of questions on calculating percentage increases and decreases. Moving from percentages of 100, to percentages of some random whole number, and onto calculating percentage changes in applied financial situations.

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

Some questions to show off features of Numbas, linked from the Numbas homepage.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

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

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Enumerate the elements in some sets defined using set builder notation.

Inverse and division of complex numbers.  Four parts.

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

Some practice collecting like terms of algebraic expressions, with detailed advice.

Adapted from 'Collecting like terms' by Ben Brawn.

This quiz asks questions on basic techniques of differentation and some introductory applications.

This quiz asks questions on basic techniques of differentation and some introductory applications.

This question assesses the student's ability to use some given information involving two different units of measurement to rewrite the information as a compound measure.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Some questions of relevance to consumers.

Some questions of relevance to consumers.

This is the question for week 3 of the MA100 course at the LSE. It looks at material from chapters 5 and 6. The following describes how two polynomials were defined in the question. This may be helpful for anyone who needs to edit this question.

In part a we have a polynomial. We wanted it to have two stationary points. To create the polynomial we first created the two stationary points as variables, called StationaryPoint1 and StationaryPoint2 which we will simply write as s1 ans s2 here. s2 was defined to be larger than s1. This means that the derivative of our polynomial must be of the form a(x-s1)(x-s2) for some constant a. The constant "a" is a variable called PolynomialScalarMult, and it is defined to be a multiple of 6 so that when we integrate the derivative a(x-s1)(x-s2) we only have integer coefficients. Its possible values include positive and negative values, so that the first stationary point is not always a max (and the second always a min). Finally, we have a variable called ConstantTerm which is the constant term that we take when we integrate the derivative derivative a(x-s1)(x-s2). Hence, we can now create a randomised polynomial with integers coefficients, for which the stationary points are s1 and s2; namely (the integral of a(x-s1)(x-s2)) plus ConstantTerm.

In part e we created a more complicated polynomial. It is defined as -2x^3 + 3(s1 + s2)x^2 -(6*s1*s2) x + YIntercept on the domain [0,35]. One can easily calculate that the stationary points of this polynomials are s1 and s2. Furthermore, they are chosen so that both are in the domain and so that s1 is smaller than s2. This means that s1 is a min and s2 is a max. Hence, the maximum point of the function will occur either at 0 or s2 (The function is descreasing after s2). Furthermore, one can see that when we evaluate the function at s2 we get (s2)^2 (s2 -3*s1) + YIntercept. In particular, this is larger than YIntercept if s2 > 3 *s1, and smaller otherwise. Possible values of s2 include values which are larger than 3*s1 and values which are smaller than 3*s1. Hence, the max of the function maybe be at 0 or at s2, dependent on s2. This gives the question a good amount of randomisation.

Some questions that use the quantities extension to handle units.