Finding composite functions of a linear function and a logarithmic function.

Finding composite functions of a linear function and a function of the form $x^n+a$.

Finding composite functions of 2 linear functions.

Given an equation of the form $m=m_0 e^{-kt}$ to model the mass of a radioactive material, calculate the decay constant $k$ and the time taken for the material to reach a certain percentage of its initial mass. 

Given an equation of the form $T=T_0 e^{kt}$ to model temperature, calculate the temperature after a given time, the time taken to reach a certain temperature, and the time taken for the temperature to double.

Rewriting expressions of the form $n \log(a)\pm m \log(b) \pm p \log(c)$ as a single logarithm.

Rewriting expressions of the form $\log(a)\pm \log(b)$ as a single logarithm.

Rewriting $\log_{10}\left(\frac{\sqrt{x}}{y}\right)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$, $x$ and $y$ are given.

Rewriting $\log_{10}(\sqrt{x})$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Rewriting $\log_{10}\left(\frac{x}{y}\right)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$, $x$ and $y$ are given.

Solving $\log(y)+\log(x)=\frac{1}{n}\log(ay^n)$ for $x$, where $a$ and $n$ are positive integers.

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_a\left(\frac{1}{x}\right) = b$, where $a$ is a positive integer and $b$ is a negative integer.

Finding $x$ from a logarithmic equation of the form $\log_x \left(\frac{1}{\sqrt(a)}\right) = \frac{1}{2}$, for a positive integer $a$.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ is a positive integer and $b$ is a positive fraction.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_xa = b$, where $a$ and $b$ are positive integers.

Solving $e^{\ln(x)}+\ln(e^x)=a$ for $x$.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

trial for inclusion in module assessment

Given the polar coordinates of a point $P$, calculate the equivalent cartesian coordinates

Give the cartesian coordinates of a point $P$, find the equivalent polar coordinates

Given a randomised log function select the possible ways of writing the domain of the function.

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Questions testing understanding of the index laws.

Questions testing rather basic understanding of the index laws.

Finding the value of a variable

Create a truth table with 3 logic variables to see if two logic expressions are equivalent.

Extra practice on some basic algebra skills, including solving linear equations. You can try as many times as you like and also generate new versions of the questions for extra practice.

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