Basic calculation from a sum given in Sigma notation.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Simplifying first is essential in terms of managing expressions that might need factorising.

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Rearrange a specific formula. No randomisation.

Substitute values into an algebraic expression and calculate the result.

Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$.

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Expand two brackets involving powers of $x$.

Expanding two linear brackets multiplied together.

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.

Exercises for HELM Book 2.6.2.

Find the highest scoring people over a course of days using the MAX, MATCH and INDEX functions

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Rewriting expressions from $\sqrt[m]{x^n}$ to $x^\frac{n}{m}$.

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Factorising a quadratic expression of the form $ax^2+bx+c$ by completing the square.

Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Maximaliseer output bij gegeven kosten

Minimaliseer de kosten bij een gegeven outputvolume

You can enter an equation in 2 or more variables and rearrange it in the following steps. Numbas checks that the lines of working are all equivalent to the original equation. 

You can enter an expression and rearrange it in the following steps. Numbas checks that each arrangement is equivalent to the original expression.

Two functions given in words. Write down the function definition. The numbers in the function definitions are randomised.

Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.