Given a linear programming problem in standard form, write down the dual problem.

Demo question: do some sneaky symbolic differentiation to check that the student's answer is the integral of the expression they're given.

Needs an advice section before it can be used.

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

Using differentiation to find the tangent and normal to a line at a given point

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

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 $y(d)$.

Deduce some properties of elements of $\mathbb F_4$, given its multiplication table. (E.g., which element is the zero, the one element, ...)

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. NC = Non Calculator strand. Students are shown a table of lunch options, given a child's food preferences and asked how many combinations are possible. There are seven possible questions.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. SP = Statistics & Probability strand. Students are given the experimental probability in ratio form in a sentence, and asked to write it as a decimal. There are 7 different versions of this question.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the gifted proportion as a decimal, and the proportion of those who receive support as a decimal, and are required to find the proportion of the whole school who are gifted but do not receive support (as a decimal). There are 9 versions of this question.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given two probabilities in ratio form, and are required to select the higher probability. There are 7 different versions of this question.

Three lines given with different information provided. Equation of the line is asked for.

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

Original: https://numbas.mathcentre.ac.uk/question/11698/equation-of-a-straight-line/ by Newcastle University Mathematics and Statistics,

translated to German, added Parts b), c), d), e)

Given a quantity per day, how many per week

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).