AP Precalculus free-response questions: how they are scored

Section II has four questions of 6 points each, in two parts of 35 minutes: Function Concepts and Modeling a Non-Periodic Context with a graphing calculator, then Modeling a Periodic Context and Symbolic Manipulations without. Points come in pairs, often an answer and the reason for it.

Part A	Questions 1 and 2, graphing calculator, 35 minutes
Part B	Questions 3 and 4, no calculator, 35 minutes
Points	6 per question, 2 in each of parts A, B and C
Weight	37.5% of the exam score

What earns the points

An answer and a separate reason: name the property that justifies it, such as constant second differences over equal-length input intervals for a quadratic model.
End behavior in limit notation, such as the limit of h(x) as x increases without bound equals 2.
Units and context in an interpretation: from t = 0 to t = 5 minutes, the temperature of the tea fell on average by 2.4 degrees per minute.
Decimals to three places after the decimal point, without rounding the steps in between.
The work that leads to each answer, especially in the no-calculator questions.

The periodic question, step by step

Read the maximum, minimum and the time of one cycle from the context.
Label the five points across two cycles: the midline value d is halfway between the maximum and minimum, and the amplitude a is half the difference.
Find b as 2π divided by the period and choose c from where the graph starts.
Say whether the function is increasing or decreasing on the interval and whether the graph is concave up or down.

Try 2 questions

Question 1

A linear regression is used to model a data set, and the residual plot for the regression is shown. Which of the following conclusions is supported by the residual plot?

Question 2

Values of r(x): x = 10, 100, 1000, 10000 give r(x) = 2.6474, 2.5127, 2.5013, 2.5001.
$x$	$r(x)$
10	2.6474
100	2.5127
1000	2.5013
10000	2.5001

The table gives values of a rational function

r

for selected large values of

x

. The values continue the same pattern as

x

increases. Which of the following is the best estimate of

\lim_{x \to \infty} r(x)

Next step

Take the free diagnostic Try the free-response lesson

College Board's AP Precalculus exam page

Questions people ask

How many FRQs are on the AP Precalculus exam?

Four: Function Concepts and Modeling a Non-Periodic Context with a graphing calculator, then Modeling a Periodic Context and Symbolic Manipulations without, each worth 6 points.

How much is the free-response section worth?

37.5% of the exam score; the 42 multiple-choice questions are the other 62.5%.

Can you use a calculator on the AP Precalculus free response?

On Part A (Questions 1 and 2) a graphing calculator is required. On Part B (Questions 3 and 4) no calculator is allowed.