Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

Contains a video in Show steps.

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Questions which try to emphasise that f(x) does not mean f times x.

Expression of the (a+bx)^n is given and a couple of coefficients are asked for.

Practice with adding, subtracting and dividing basic algebraic fractions

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Some quadratics are to be solved by factorising

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

A quadratic function is given. The graph of the function is drawn with three coordinates on the graph, without any x or y ticks.  The $x$ coordinate is given for a couple and $y$ coordinate given for the third, and coordinates are asked for.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

Practice with adding, subtracting and dividing basic algebraic fractions

student is to re-arrange the equations $pV=nRT$ and $mgh = \frac{1}{2}mv^2$

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Some quadratics are to be solved by factorising

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Some quadratics are to be solved by factorising

A fill-in-the-blank style question to test vocabulary within the topic of Algebra.

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Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

Entering numbers and algebraic symbols  in Numbas.