Uses an extension to embed SageMath cells into content areas.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Basic properties of atoms

This question aims to test understanding and ability to use the laws of indices involving an unkown parameter. 

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

multiple choice question on this week's content

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