An introduction to using the quotient rule

Using the chain rule with polynomials

Using Mohr's Circle to calculate principal stresses in plane stress 2D case.

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

This question asks students to decrypt a message using a simple Caesar cipher, without giving them the key.

This question models an experiment: the student must collect some data and enter it at the start of the question, and the expected answers to subsequent parts are marked based on that data.

The student's values of the variables width, depth and height are stored once they move on from the first part.

This question models an experiment: the student must collect some data and enter it at the start of the question, and the expected answers to subsequent parts are marked based on that data.

A downside of working this way is that you have to set up the variable replacements on each part of the question. You could avoid this by using explore mode.

An economic dispatch problem with three generators. The steps help the students to solve this using lagrangian multipliers. This question is designed to allow students studying economic dispatch to practice solving the problem.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

A two part question. Students are first given the formula for the time for a ball to come to rest after being dropped on a block. Part a) asks the students to rearrange the formula to make e, the coefficient of restitution, the subject of the formula. Part b) gives students realistic values for variables in the formula and asks them to calculate the coefficient of restitution using the formula derived in part a). 

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

rebelmaths

The subtraction algortihm using the borrow and pay back method with integers.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

HELM Book 1.5.1: using formulae and substitution: task 1

Shows how to switch to the 3D graphics view of a geogebra applet using an extension function.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

The student must write code to compute the standard deviation of an unknown list of measurements.

The suggested answer uses numpy.std.

rebelmaths

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Practice question solving linear homogeneous second order differentials using the auxiliary equation method.

Practice question simplifying fractions for integration by using partial fractions.