Advanced Placement Format
Sample Assessment Questions
9th 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
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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)
9th Grade TAKS - 2006
AN
ANSWER: G
Pre-AP/AP Modifications for problem #46
(a) Graph the translated figure in the grid below. Label it f(x).
(b) Graph the lines x = 2 and y = 0 in the same grid above.
(c) Describe the solid created by f(x), x = 2 and y = 0 when such figure is rotated about the x-axis.
(d) Describe the solid created by f(x), x =2, x = 0 and y = 0 when such figure is rotated about the y-axis.
9th Grade TAKS - 2006
ANSWER: G
Pre-AP/AP Modifications for problem #2
Point K is the midpoint of JL .
(a) Graph a line with slope of -1 passing through point J. Label this line as f(x).
(b) Graph a line with slope of 2 passing through point L. Label this line as g(x).
(c) Graph y = 7. Label this line as h(x).
(d) Find the equation of f(x) using the slope-intercept form. Find the equation of g(x) using the pointslope form.
(e) Determine algebraically the point of intersection of all three lines. Show the work that determines
your answers.
(f) Find the length of each side of the figure bounded by the lines (HINT: Use Pythagorean theorem).
Show the work that leads to your answers.
(g) Determine the area of the figure bounded by the lines.
9th Grade TAKS - 2006
ANSWER: C
Pre-AP/AP Modifications for problem #37
(a) Label the graph as f(x).
(b) Graph h(x) = f(x) + 1
(c) Devise a plan for finding the area bounded by the x-axis, the y-axis, the curve h(x) and the line
x=28. Explain your plan.
(d) Calculate the area described in question (c). Show the calculations that support your answer.
(e) Graph g(x) = f(x) + 3
(f) Devise a plan for finding the area bounded by the x-axis, the y-axis, the curve g(x) and the line x=28.
Explain your plan.
(g) Calculate the area described in question (f). Show the calculations that support your answer.
(h) Compare your answers from questions (c) and (f). By looking at the differences in the two figures,
give a reason why the difference between the two answers is 56.
(i) Write a short story describing Lynne’s trip.
9th Grade TAKS – 2003
ANSWER: D
Pre-AP/AP Modifications for problem #3
Based on your answer to problem #3, answer the following questions. Refer back to the graph if
necessary.
(a) Find the length of the radius.
(b) Find the area of the circle.
(c) Verify that point (-5, 4) lies on the circle.
(d) Find the value of y when x = -6.
(e) For which values of x is y = -1?
(f) Find the slope o the line tangent to the circle at (0, 2).
(g) Graph g(x) = 3. On the graph, shade the area enclosed by the graph of the circle and
g(x)  3 .
(h) Estimate the area enclosed by the circle and g(x)  3 . Explain the procedure used to arrive
at your solution.
(i) Is your answer to question (h) an overestimation or an underestimation? Justify your answer.
9th Grade TAKS – 2004
ANSWER: D
Pre-AP/AP Modifications for problem #41
(a) Based on the data, estimate the value of f(x), when x = 15. Show the computations that lead to your
answer.
(b) For 1  x  2 , does the function change direction in any of the subintervals indicated by the data in
the table? If so, identify the subintervals and explain your reasoning. If not, explain why not.
(c) Determine the concavity of this function. Justify your answer algebraically.
(d) Find the total units traveled by this function from x = -1 to x = 4.
(e) Is there any point at which the graph returns to the origin? Justify your answer.
(f) Using the data from the table, on what intervals is the graph decreasing?
(g) Sketch a line tangent to f(x) at x = 2. Find the slope of this line.
(h) Repeat part (g) for x = 0, x = 1, x = -1, x = -2. Create a table of values for x and the slope of the
lines tangent at x.
(i) Is there a pattern n the table created in part (h)? If so, describe the pattern.
(j) Predict the slope of the tangent line at x = 100.