Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

Given some numbers in standard index form, convert to decimal form.

Nursing question. IV question. Given volume and flow rate what time will is take for the bag to run dry? Student have to round to the nearest quarter of an hour.

- David Sherwood didn't think this was a question that should be asked

Metal Anealling

Introduces the GCD and a simple form of the Euclidian Algorithm

Introduction to modular arithmetic using a multiplication table and lookup.

Full worked solution using the Extended Euclidian Algorithm

Introduction to modular arithmetic in $\mathbb Z_b$ using a multiplication table and lookup with coprime $b \in \mathbb N$.

Utilizza un grafico di una retta $y=mx+c$ incluso da Geogebra con coefficienti casuali impostati da NUMBAS. Il grafico contiene anche un punto $P$ di coordinate casuali impostate da NUMBAS. L'esercizio chiede di determinare l'equazione della retta e quelle delle rette parallela e perpendicolare per $P$.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

A sneak peek at a really clever integration of GeoGebra with Numbas.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Integration by susbtitution, no hint given

Integration by susbtitution, no hint given

Simple Indefinite Integrals

Simple Indefinite Integrals

Practice use of summation notation for regression question.

rebelmaths

Practice with adding, subtracting and dividing basic algebraic fractions

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.

A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

Introduction to using the product rule

A basic introduction to differentiation

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

This question contains a "choose several answers" part which has an "all-or-nothing" mark scheme: the student is only awarded marks if they tick all of the correct choices, and no incorrect choices.