Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

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

Is this number divisible by 5? Half the time the number is, half the time it isn't. Steps give the divisibility test and a way to determine the number of fives.

This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

15 questions based on module so far. 

Rounding practice to given decimal places and significant figures.

Counting the number of significant figures and rounding integers and decimals.

Round numbers to a given number of significant figures.

Solving inequalities that involve a quadratic and where the right-hand side is 0.

Solving inequalities that involve a quadratic and where the right-hand side is not 0. 

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Several quadratics are given and students are asked to complete the square.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

A basic introduction to differentiation

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

A static block of given mass is sits on a flat plane with defined static and kinetic friction values. It is pushed with enough force to start it moving - calculate the speed of the block after a given distance.

Find roots and the area under a parabola

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. 

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. 

A particle is projected up a rough plane at a given speed. Given the angle of the slope and the coefficient friction, find the distance the particle travels before it comes to instantaneous rest.

Calculate the efficiency and heat from the hot reservoir in a Carnot Cycle (with carnot diagram)

Calculate the efficiency and heat from the hot reservoir in a Carnot Cycle (with carnot diagram)

A random heating question, that randomly picks a material, and then heats it through one phase change, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

A random heating question, that randomly picks a material, and then heats it through one phase change, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

A simple ideal gas law question, using number of molecules, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp. As such the boltzmann constant is in either J/K or L atm/K.

pV = 1/3 Nm<v2>

A simple ideal gas law question, using number of molecules, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp. As such the boltzmann constant is in either J/K or L atm/K.

A simple ideal gas law question, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp.

A simple ideal gas law question, using number of molecules, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp. As such the boltzmann constant is in either J/K or L atm/K.

pV = 1/3 Nm<v2>