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).

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• 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pā 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 $f''(x)$

### Matrices

• 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.