• 1.

  Ready to use
  Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 
• 2.

  draft
  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 $(x+r)(px+b)(qx+d)$.
• 3.

  Ready to use
  Add/subtract fractions and reduce to lowest form.
• 4.

  draft
  Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.
• 5.

  draft
  Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.
• 6.

  Ready to use
  Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.
• 7.

  draft
  Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.
• 8.

  Ready to use
  Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.
• 9.

  Has some problems
  Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 
• 10.

  Ready to use
  Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$  
• 11.

  Ready to use
  Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.
• 12.

  Ready to use
  Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$.  Make sure that your choice is a solution by substituting back into the equation.
• 13.

  Ready to use
  Solve $\displaystyle ax + b = cx + d$ for $x$.
• 14.

  Has some problems
  Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.
• 15.

  Has some problems
  Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$
• 16.

  Ready to use
  Solve for $x$ and $y$:   $$\begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray}$$

There are no questions in this group.