[PLS NOTE: Several edits have been made. This version should be accurate!]
Two new documents are now available on Achieve's Algebra 2 Test Overview web site:
Released Items Oct. 2008
Released Items Oct. 2008 Commentaries
I strongly encourage our readers to download these pdf documents. The 2nd document is particularly useful since it contains excellent discussions of each question, scoring rubrics, sample student solutions and detailed explanations and alternate methods.
There will be endless arguments about over-testing, open and fair testing, who's making the profit from these tests, quality and authenticity of assessments, the politics of how results will be used (programmatic vs. comparing teachers, schools, states). In the end, we need to get past the rhetoric. For me the bottom line is that these released questions are high quality and require youngsters to demonstrate both mechanical skill and conceptual understanding. Further, they include several open-ended (extended response each counting 4 pts) and short constructed response items (each counting 2 pts) that give students the opportunity to display what they know, not how skillful they are at eliminating answer choices.
Released items often contain more difficult questions. I found many of these questions required some sophisticated thinking and analysis.
I'm not permitted to reproduce any of the items however I will attempt to categorize each problem and enumerate topics (you may disagree with some of these classifications so please read the documents).
- Imaginary solutions of quadratic equation
- Graph of inverse of a linear function
- Meaning of rational exponents
- Solving absolute value equation which includes a linear expression outside the absolute values (leading to an extraneous solution)
- Relationship between a polynomial function and its graph
- (Short answer) Solving a quadratic equation resulting from a Pythagorean application
- (Short answer) Constructing the graph of a simple rational function, e.g., f(x) = k/x2
- Recognizing an exponential function from its characteristics (domain, range, intercepts, asymptotes, etc.)
- Determine the slope of a linear-type function involving absolute values
- Graph of a system of linear inequalities
- Associating a function involving the greatest integer function with a problem situation
- Roots of a quadratic equation with a negative discriminant
- Matching the graph of a quadratic function with characteristics involving its coefficients
- (Short answer) Determining an expression for the volume of a cube whose original dimension is increased by a variable amount (also, expand the expression).
- Determining the zeros of an exponential function
- Solving for a variable in a literal equation involving a radical
- Solving an applied problem (physics-type) involving a given quadratic function
- Domain of a composite function
- Simplify a 'complex' fraction (Mechanical skill)
- Analyzing functions of the form cxd (including end behavior)
- (Short answer) Construct a piecewise function to model a given problem situation
- (Extended Response) Applied problem involving interpretation of a given quadratic model
- Simplifying rational expression (Mechanical skill)
- Recognizing graph of a linear programming application (simple)
- Matching a given exponential function (involving a parameter) to a function table (conceptual)
- Application of concept that the product of a complex number and its conjugate is real
- Exponential growth application
- Analyzing the effect on the zeros of a quadratic subjected to different transformations (conceptual)
- (Extended response) Applied problem involving percent increase and an exponential model