Tuesday, June 12, 2007

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.

9 comments:

Jackie said...

Sounds like a comprehensive assessment. Out of curiosity, what is your calculator policy?

Dan Greene said...

On the MC portion, no calculator is allowed. It includes some questions that can be plugged into their graphing calcs, like operations on complex numbers, fractional exponents, logs, and the like.

Once they turn in this portion, they recieve the free response which allows calculators. Here I'm looking mainly for ability to solve problems, and a calculator won't be of much help if they don't know the correct processes. The graphing question is a piecewise one, which I know my students haven't figured out how to do on their TIs directly.

jackie said...

Thanks for the quick response. Next year is my first year teaching and I'm looking for exam ideas (I'm not happy with the tests I "inherited"). Your post was helpful!

Dan Greene said...

No problem, I'm proctoring finals all day, so not much else to do.. I can't concentrate enough to grade.

I have lots of exams I've written over the years for a variety of levels of math. Feel free to send me email if there's anything you want to see, and I'll send you some files. Good luck with your teaching.

Christopher said...

Yo, Captain Dan, congratulations to both of us on a(nother) year of teaching complete! I hope things are well for you.

Dan Greene said...

What up then... congrats to you too. What are you up to for the summer?

Hey, I noticed that you were posting some anti-vegan rhetoric.. watch out, or you may not get invited to the next dinner party :)

ps - I made fried tofu marsala for dinner tonight, served over brown rice, next to a romaine and spinach salad with a lemon-mustard dressing. Eat your heart out!

jonathan said...

For my algebra 2 (advanced) class, I ended up including asking for the derivation of the quadratic formula. At this point it is a gimme question. And it wasn't a waste, I don't think. Most of them think about completing the square when they see ugly expressions in x^2 and x...

On the other hand, all students reported struggling with some part of the exam. I will look this week, and maybe blog some of it. Twelve questions in 2 hours 15 minutes... I need to look at their tests.

Dan Greene said...

Jonathan,

I'd be very interested in seeing your final exam. I'd like to know if what I'm asking of my students is comparable to what is happening in other classrooms. And I'm happy to send you my final to look at if you're interested.

jonathan said...

Dan, I sent you mine. I'd be curious to see yours as well.