Simplifying expressions from $\left(\frac{x^m}{x^n}\right)^p$ to $x^{(m-n)p}$.

Simplifying expressions from $\frac{x^mx^n}{x^p}$ to $x^{m+n-p}$. 

Simplifying expressions from $(ax^n)^m$ to $a^mx^{mn}$, where $a$, $m$ and $n$ are positive integers.

This question is the one described in method 2 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

Simplifying algebraic expressions

Using $\cos^2\theta+\sin^2\theta=1$ to evaluate expressions.

This question is to practice order of precedence in mathematical expressions. 

Please use * for multiplication and / for division. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

Simplifying the trigonometric expression $\frac{\sin^2(x)}{1\pm \cos(x)}$ using the trigonometric identity $\sin^2(x)+\cos^2(x)=1$.

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.

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

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Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

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Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Dividing Cubic expressions to find the quotient

Dealing with expressions in online tests and in Matlab.