MASH Bath: Question Bank

Finding composite functions of a linear function and an exponential function.

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.

Calculating the amount of money in a savings account after a given amount of time, and calculating how long it will take for the amount of savings to exceed a given value. 

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 $n\log(a)\pm m\log(b)$ 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.

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

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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Independent events in probability. Choose whether given three given pairs of events are independent or not.