Group equations by their solutions. Given six different equations, pupils determine which have the same solutions. Scholars explain why some are the same and some are different.

Four 4s represent the counting numbers. Pupils attempt to write equivalent expressions to as many counting numbers as possible using only four 4s. Scholars then determine whether the same feat is possible using only three 3s.

What will that cost in the future? The scenario provides pupils with a growth as a Consumer Price Index. Learners create functions for a given item to determine future prices and graph them. Class members then compare their functions to...

Take a coordinated look at rectangles. The task asks pupils to plot the length and width of created triangles in the coordinate plane. Using their plots, scholars respond to questions about rectangles and their associated points on the...

Reflect upon the graphs of quadratic functions. Given a quadratic function to graph, pupils determine whether the graph after a horizontal and vertical reflection is still a function. The final two questions ask scholars to describe a...

Create polynomials with specific values. The task consists of writing three polynomial functions that evaluate to specific values for any given number. Scholars first find a polynomial that evaluates to one for a given value, then a...

Sometimes the solution is all a matter of perspective. The short assessment task presents a problem to pupils that requires them to make sense of a diagram. Once learners see two similar triangles, the rest of the solution is solving a...

How many ways can you make 10? Class members tackle three problems to find all possible ways three numbers add to be 10. The first is with positive integers, secondly with non-negative integers, and finally with real numbers. Pupils also...

Graph growth in the US. Given population and area data for the United States for a period of 200 years, class members create graphs to interpret the growth over time. Graphs include population, area, population density, and population...

Let's give parameters a second try. Scholars take a second look at a system of linear equations that involve a parameter. Using their knowledge of solutions of systems of linear equations, learners describe the solution to the system as...

Chase the traveling solution. Pupils analyze the solutions to a system of linear equations as the parameter in one equation changes. Scholars then use graphs to illustrate their analyses.

Just how far can I see? The short assessment question uses the Pythagorean Theorem to find the distance to the horizon from a given altitude. Scholars use the relationship of a tangent segment and the radius of a circle to find the...

Root for young mathematicians learning about functions. A set of two problems assesses understanding of polynomial functions and their roots. Scholars select values for a, b, and c, and then create two functions that meet given...

Develop a deeper understanding of statistics. The six released free-response items from the 2002 AP® Statistics Form B involve several concepts that are currently in the regular statistics standards. Teachers see how...

Over the years, data analysis has been important. Looking back to the 2004 AP® Statistics Form B free-response questions, pupils and teachers see the importance of analysis of data sets. The six questions contain analysis of data on...

Here's another great way to learn from the past. Released free-response questions provide a look into how concepts measured on the 2005 AP® Statistics Exam on Form B. Teachers and pupils review questions that cover concepts such as...

So that is how they do it! Pupils and teachers see how College Board assesses topics using the free-response questions from Form B of the 2007 AP® Statistics test. The six questions are divided in two sections, the first five being...

To know what is on the test would be great. The six free-response question from the second form of the 2008 AP® Statistics gives pupils an insight into the format and general content of the exam. Each question requires the test...

How does one factor in the social costs of a product? What factors influence price? Learners consider the question and others using authentic College Board materials. Other questions examine profits and competition in the market and the...

Imports often affect the production of domestic goods. Scholars consider the variables in this situation with a scaffolded prompt from College Board. Other items examine factors in production and compare the production advantage between...

Monopolies may have an advantage in some markets, but what are they? A scaffolded problem set examines the effects monopolies have on a market. Other authentic College Board problems examine labor markets and how a variety of factors...

The government catches a firm in the act of polluting. What will happen to the company's profits? Learners consider the question and others using authentic College Board materials. Other problem sets examine wages and labor and price...

Inventors with patents have a distinct advantage in the market. But what happens when the patent expires? A series of questions from College Board asks learners to consider the effects of a patent expiration. Other practice prompts...

How are monopolies and competitive firms similar and different? Scholars consider the question using authentic College Board materials. Other prompts consider supply and demand curves and the relationship between wages and output.