Using a shuffled list variable to randomise the order of all options in a multiple choice part except the last one.

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

aij  notation and definition of the order of a matrix.

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

rebelmaths

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

rebelmaths

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

rebelmaths

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

rebelmaths

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

Solving 2nd order differential equation for pendulum, with and without damping.

A group (chosen randomly, the groups with 6 and those 8 elements are available) is given by its multiplication table. The task is to check whether the group is commutative, to identify all elements of order $\le 2$, and to find a subgroup which has half as many elements as the given group.

(In German.)

Aufgabe zum Chinesischen Wurzelziehen, inspiriert von: Katz, V. J. (2009). A history of mathematics: An introduction (3. ed.). Boston: Addison-Wesley (pp. 199/200).

Aufgabe zum Chinesischen Wurzelziehen, inspiriert von: Katz, V. J. (2009). A history of mathematics: An introduction (3. ed.). Boston: Addison-Wesley (pp. 199/200).

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.

https://numbas.mathcentre.ac.uk/question/22664/addition-and-subtraction-of-fractions/ by Lauren Richards

Translated to German and Part d) added.

Given an ODE solution: $y=  b x^n + cx$

Use a condition: $y(1)=a$ to find the particular solution and hence the value of $y(d)$.

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.

Separable 1st order ODE with exponentials

Questions which ask the student to intepret vector diagrams in order to write out the components in terms of base vectors. Also addition and subtraction of vectors and vector magnitude.

No description given

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Also two other questions on integrating by parts.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$. Find $g(x)$.