Ben McGovern

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 $x$.

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

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Calculating the integral of a function of the form $ax^b$ using a table of integrals. 

Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Calculating the integral of a function of the form $\frac{a}{bx}$ using a table of integrals.

Integrating an exponential function of the form $ae^{bx}$ using a table of integrals / anti-derivatives.

Calculating the integral of a function of the form $a \sin(bx)$ using a table of integrals.

Calculating the integral of a function of the form $a \cos(bx)$ using a table of integrals.

Calculating the integral of a function of the form $a \sec^2(bx)$ using a table of integrals.

Calculating the integral of a function of the form $\frac{a}{\sqrt{b^2-x^2}}$ using a table of integrals.

Calculating the integral of a function of the form $2ax(ax^2+b)^n$ using integration by substitution.

Calculating the integral of a function of the form $x(ax^2+b)^n$ using integration by substitution.