More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients.

Inputting algebraic expressions into Numbas.

evaluate a function with randomised alphanumeric expressions as inputs.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Apply the factor and remainder theorems to manipulate polynomial expressions

Expand something like a(b+c) or (b+c)a or a(bc), where a, b and c can be +ve or -ve expressions. Part of HELM Book 1.3

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Removing brackets from expressions of the form (a+b)(c+d). Part of HELM Book 1.3

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewiting expressions involving sums or differences of surds into the form $a \sqrt{b}$.

Rewiting expressions involving sums or differences of surds into the form $a \sqrt{b}$.

Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) + (a_2 + b_2 \sqrt{c})$.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) - (a_2 + b_2 \sqrt{c})$.

Simplifying surds from $a\sqrt{b^2c}$ to $ab\sqrt{c}$, where $a$, $b$ and $c$ are positive integers.

Simplifying surds from $\sqrt{a^2b}$ to $a\sqrt{b}$, where $a$ and $b$ are positive integers.

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

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Two BODMAS questions. Part of HELM Book 1.1.