Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

Introductory exercise about power sets.

Translation to Dutch of 

"Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop."

Cofactors Determinant and inverse of a 3x3 matrix.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Multiplication of  matrices of different sizes.

Simplifying indices.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Simplifying indices.

Solve a quadratic equation by completing the square. The roots are not pretty!

Rearrange equations to make $x$ the subject. 

Provided via mathcentre.ac.uk

rearranging the Michelas-Menten equation to make the substrate the subject.

rebelmaths

Decimal Places and Significant Figures

rebelmaths

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

From mathcentre.ac.uk

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Calculating particular harmonic components of a Fourier series expansion.

Several quadratics are given and students are asked to factorise them.

Introductory exercise about subsets using custom grading code.

No description given

Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Use the quotient rule to differentiate various functions.