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 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 $m$, $b$).

Questions around the notion of map, with underlying topic the statement of Goldbach's conjecture. The student has to write the conjecture (by filling in some gaps) as a surjectivity statement for a map, and compute some preimages of elements.

(In German)

Some simple abstract questions on injectivity, surjectivity, bijectivity.

Introductory function notions

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

Hello! This test an extra opportunity to complete some practice questions on the material we have covered so far. Your results will NOT count towards your final grade, and there is no time limit to complete the test. You can check your answers as you go along, and even try new examples of the same type. Full solutions are also available for most questions. If there are any questions you don't understand, take a photo and we can discuss it in class or at a one-to-one appointment. 

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Translated to German, made some minor changes to Advice section.

Original: https://numbas.mathcentre.ac.uk/question/22555/rationalising-the-denominator-surds/ by Lauren Richards

Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

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

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

Try to solve some simultaneous equations using matrix inverses.

A demo of some custom part types.

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.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

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

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

Some questions which demonstrate the adaptive marking feature.

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

Some questions demonstrating new features in Numbas v4.0: pattern-matching, inference of variable types in mathematical expression parts, and marking equations.