The Final

Tomorrow, my students are taking their Algebra 2 Honors final exam. It was hard, as always, to try to distill a year's worth of material into a test that is comprehensive yet fair, that can be completed in 2 hours.

I decided to give them 25 multiple choice questions that cover lots of the smaller topics, like dividing complex numbers, simplifying radicals, powers of i, associative/commutative properties, etc. These questions are worth 50 points, or 1/3 of the total. I expect students to finish them in 30 - 45 minutes.

The remaining time should be spent on the free-response, worth 100 points. To be as fair as possible, I gave students a sheet listing the content that would be tested in these 11 problems. Though it does not include all of the material we covered this year, I tried to pull out the topics we focused most heavily on.

1. Place numbers in the correct locations on a Venn Diagram of the complex number system.
2. Given 3 points on a parabola, find the function of the parabola in standard form. You must be able to write and solve a 3 x 3 system of equations to do this.
3. Graph a piecewise function.
4. Answer graphical analysis questions (given a graph, determine domain, range, values of x and f(x), find when f(x) <0, etc.)
   
5. Solve a polynomial inequality with a number line model.
6. Given a verbal situation, set up a model of an exponential function and then solve with logarithms. For example: the current value of my car is $12,000 and it is decreasing by 9% each year; how long will it take for my car to be worth only $9000?
7. Solve a logarithmic equation using properties of logs, and eliminating extraneous solutions.
8. Translate/transform a graph. For example, given the graph of f(x), draw the graph of y = 2f(x + 3) – 7.
9. Simplify a rational function, indicating values excluded from the domain. Determine intercepts, holes, and asymptotes, and make a graph.
10. Solve a quadratic equation (with the quadratic formula) that has imaginary solutions.
11. Divide with polynomial (or synthetic) division.
    

Extra credit:

1. Given a rational function, determine its inverse, and the domain and range of both.
2. Prove the quadratic formula by completing the square.

This afternoon is our final review session, which I expect to be very well attended. Looking over that list of topics reminds me how proud I am of what these students have been able to accomplish this year - especially those students I was teaching fractions to last year.