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Differentiate a polynomial expression involving coefficients and, negative and fractional indices. 

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

Calculate an answer involving a fractional index.

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Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

https://numbas.mathcentre.ac.uk/question/22784/decimals-to-fractions/ by Lauren Richards

Translated to German.

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients.

Unmarked question, with advice.

Write down an example of a polynomial of given degree and given variable.

Write down a non-polynomial function.

Explain why a polynomial with a fractional index is not a polynomial.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Part of HELM Book 1.2

Simplify (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.

Part of HELM Book 1.2

Use a calculator to evaluate a number to the power of a fractional index. Both the number (a positive integer) and the index (a rational) are randomised.

Part of HELM Book 1.2

Part of HELM Book 1.2

Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

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

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution. $n$ is a positive or negative fraction.

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients

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