Advanced Placement Format

Sample Assessment Questions

10th Grade TAKS - High School

The free response section of an Advanced Placement Exam is worth 50% of the entire score. Our current assessment tools do not meet the challenges of this type of assessment. Preparing our future AP students early with an AP assessment format, will promote a greater understanding of the challenges of a rigorous Advanced Placement Math Course.

What Makes a Good Pre-AP* Mathematics Problem?

After reading the goals of the Pre-AP* mathematics program, seeing how AP* problems can be adapted for use at other levels. After examining exemplar problems for particular TEKS, we hope you have a better understanding of what makes a problem or activity particularly appropriate for use in the Pre-AP mathematics classroom. Below you will find some of the criteria that the committee used in selecting the problems and activities for this document.

A good Pre-AP mathematics problem or activity

  • has a clear connection to the vocabulary, skills, concepts, or habits of mind necessary for success in AP mathematics courses;
  • goes beyond a minimalist approach to addressing the TEKS;
  • can serve multiple purposes, such as addressing an Algebra I TEKS, reviewing a middle school geometry skill, and introducing an AP Calculus concept;
  • should go beyond simple drill and recall (There should be a greater emphasis on analysis, application, and synthesis of material.);
  • requires students to engage in an extended chain of reasoning (Problems should require more than one step and might cover more than one topic.);
  • might be completely different from problems that the teacher has demonstrated in class, though based on the same concept (Students are expected to apply their knowledge in novel situations with very little teacher direction.);
  • requires students to develop their reading and interpretation skills using verbal, graphical, analytical, and numerical prompts;
  • asks students to communicate their thoughts orally and/or in writing (Students must be able to justify their work in clear, concise, and well-written sentences.);
  • stretches the students in ways that might make them uncomfortable (The solving of problems might take several attempts. They might have to hear someone else's explanation (preferably one of their peers) before they begin to develop understanding.);
  • should be graded based on the process and methods as well as the final answers; and
  • might require the thoughtful use of technology.

Advanced Placement Free Response Questioning Guide

  • Indicate units of measure.
  • Why or why not?
  • Show the computations that lead to your answer.
  • Explain your reasoning.
  • Give a reason for your answer.
  • Explain the meaning of ______.
  • Explain your answer.
  • Justify you answer. (most commonly used)

10th Grade Spring 2003 Released Exam

Answer: B

10th Grade Spring 2003 Released Exam Problem 5

(a)Write the vertex form and the standard form of the given parabola.

(b)Give the domain and range for the above quadratic function in interval form and inequality form.

(c)Estimate the area bound by the function and the x-axis.

(d)Plot points M(-1, -2) and N(3, 5) and write the equation of the line that passes through both points in slope-intercept form and point-slope form.

(e)Sketch the line tangent to the graph at x = – 3

(f)The point (-2, -1) lies on the line tangent to the graph at x = – 3. Find the equation of this line.

10th Grade Level Spring 2004 Released Exam

Answer: B

10th Grade Level Spring 2004 Released Exam Problem 3

(a)For each section of the graph find the corresponding interior angle.

(b)If the radius of the circle is 45 cm, find the area for each sector.

(c)If the center of the circle is placed on the origin, find the rate of change of each radii.

(d)Sketch a line segment tangent to the point where the radii meets the circle. You will have a total of 4 line segments. Determine the rate of change for each tangent segment.

10th Grade Level Spring 2004 Released Exam

Answer: F

10th Grade Level Spring 2004 Released Exam Problem 10

(a)Where should point Z be locate to create a square similar to square PQRS?

(b)Explain why the two squares are similar.

(c)Find the area of square PQRS.

(d)Draw segment and determine its length and rate of change.

(e)Find the area of a circle whose radius is and its center is located at S.

(f)Draw segment to create triangle WXY. Find the area and perimeter of the triangle.

Exit Level Feb 2006 Released Exam

Answer: F

Pre-AP / AP Modifications for Problem 2

(a)If the domain is (0, 6], make a table of values for each quadratic function and find the first non-zero integer output and plot the point.

(b)For all four functions, draw a line segment from the origin to the point you plotted in (a) and draw another line segment from the point to the y-axis. You should have 4 triangles.

(c)Find the perimeter and area of each triangle.

(d)Describe what needs to be done with these areas to obtain right circular cones.

(e)Find the volume for each cone.

(f)What is the ratio of the smallest cone volume to the largest cone?

Answer: B

Pre-AP / AP Modifications for Problem 9

(a)Approximate the area of the triangle bounded the two lines and the y-axis. Then calculate the actual area.

(b)If you rotate the shaded area about the y-axis, how would you describe the 3-D figure created?

(c)Find the volume of the figure.