Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.

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

Express $\displaystyle b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle ax+b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

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

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

First part: Express  $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d},\;a=-c$. Numerator is an integer.

Second part: $\displaystyle \frac{a}{px + b} +\frac{c}{qx + d}+ \frac{r}{sx+t}$ as single fraction 

First part: express as a single fraction: $\displaystyle \frac{a}{x + b} +  \frac{c}{x + d},\; a \neq -c$.

Second part: Find $\displaystyle \frac{a}{x + b} + \frac{c}{x + d}+\frac{r}{x+t}$ as a single fraction.

First part: express as a single fraction: $\displaystyle \frac{a}{px + b} +  \frac{c}{qx + d}$.

Second part: Find $\displaystyle \frac{a}{px + b} + \frac{c}{qx + d}+\frac{r}{sx+t}$ as a single fraction.

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{x + b} +\frac{c}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

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

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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.