Things Seen On Past IB Exams

This page is a collection of tasks and questions that I have seen the IB ask on past exams. I have organized them roughly by topic. This could make for a quick check list while studying for your exams!

This list is by no means complete. Plus the IB ALWAYS comes out with some surprise questions.

I will add to the list as I teach through the syllabus and review past exams. This page has been ignored for awhile, but it's back on my radar (Feb 2013).



  • Find the vertex given the form $y=ax^2+bx+c$
  • Find x and y intercepts
  • Find or write the equation for the axis of symmetry
  • Given the axis of symmetry find the y-coordinate of the vertex
  • Write an equation for the quadratic given the zeros (from a graph)
  • Use a third data point (not one of the zeros) to find the ā€œpā€ in $p(x-r)(x-q)$

Exponential & Logarithmic Functions

  • Given $a^x$ solve for x $x= b \cdot log_a c$
  • Given logarithmic function find inverse - and the reverse
  • Find range of exponential and or domain of logs
  • Composite function of $a^x$ and $log_a x$
  • Simplifying logs: Solve for x $log_2 x + log_2 (x-2) =3$
  • Solve $a \cdot ln (4-a^2)=0$
  • Given data points find k for $e^{kx}$
  • Asymptotes of $a^x$ and $log_a x$

Derivative Calculus

  • Find the gradient at a specific point $(i.e. \: x=2)$on a function given the function
  • Calculating the 1st and 2nd derivatives of a given function
  • Derivative of $\frac{1}{sin^2 x}$
  • Identifying a inflexion point
  • Given max and min of $f(x)$ find x-int of $f'(x)$
  • Identify when $f'(x)$ is positive, negative or zero from a graph
  • Curvature from graph (concave up or down) or from value of $f''(x)$


  • Finding inverses (2x2 by hand, 3x3 with GDC)
  • Solving matrix equations of the forms: $AX=B$, $AX+X=B$ and $AX+B=C$
  • Determinants of 2x2 and 3x3 (with and with out GDC)
  • Solving systems of equations
  • Writing system of equations from points on a function given the form of the function.

If you have other tasks/question types to answer leave a comment below with a BRIEF description of the task or question and the general topic covered.

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