AP Physics 1 & 2 FRQ Templates for 2024-2025 CED

Table of Contents

Translation Between Representations (TBR) Question 5

Experimental Design and Analysis (LAB) Question 10

Qualitative/Quantitative Translation (QQT) Question 16

NOTES:

The information in this document comes from the CED Free-Response Question descriptions and point distributions shared at various APSIs this summer. Sample language is drawn from the two FRQ Progress Checks and one Practice Exam for each course that have been added to AP Classroom. The overall point distribution and task (justify, derive, sketch,etc.) will be consistent across questions, though language will adjust to fit the physics scenario described. Also, since only the progress checks for early units have been shared, there will likely be other representations tested on the exam that are not included here (Energy Bar Charts, I am looking at you!) As much as possible I have tried to share the range of language I’ve seen in the examples available to us AND tried to highlight differences in language between AP Physics 1 and AP Physics 2. I hope this is helpful to physics teachers.

Kris Newton

Cambridge Rindge and Latin School

Cambridge, MA

Mathematical Routines (MR) Question

The Mathematical Routines (MR) question assesses students’ ability to use mathematics to analyze a scenario and make predictions about that scenario. Students will be expected to symbolically derive relationships between variables, as well as calculate numerical values. Students will be expected to create and use representations that describe the scenario, either to help guide the mathematical analysis (such as drawing a free-body diagram) or that are applicable to the scenario (such as sketching velocity as a function of time).

For AP Physics 1 and AP Physics 2, the MR question will ask students to make a claim or prediction about the scenario and use appropriate physics concepts and principles to support and justify that claim. The justification is expected to be a logical and sequential application of physics concepts that demonstrates a student’s ability to connect multiple concepts to each other.

Mathematical Routines FRQ Summary of Points

The Mathematical Routines question assesses students’ ability to use mathematics to analyze a scenario and make predictions about that scenario.

(ai) Students will be expected to symbolically derive relationships between variables, as well as calculate numerical values. (5pts)

(aii) Students will be expected to create and use representations that describe the scenario, either to help guide the mathematical analysis (such as drawing a free-body diagram) or that are applicable to the scenario (such as sketching velocity as a function of time). (2pts)

(b) For AP Physics 1 and AP Physics 2, the Mathematical Routines question will ask students to make a claim or prediction about the scenario and use appropriate physics concepts and principles to support and justify that claim. The justification is expected to be a logical and sequential application of physics concepts that demonstrates a student’s ability to connect multiple concepts to each other. (3pts)

NOTE: Section (a) might have parts i, ii, and iii if the derivation is split into two parts.

Mathematical Routines (MR) question (10 points, ~25 minutes)

This will be question #1 on the AP exam.

Show all your work for each part of the question. The parts within the question may not have equal weight.

NOTE: Part A includes 7 points, 5 of which are one or more derivations. (It is also possible - but not common - for those 5 points to be split between a derivation and calculation). The remaining two points are for creating a representation of the scenario. These 7 points will not always happen in the same order. Some questions might ask students to draw a free-body diagram first to aid in the derivation, whereas other questions will ask students to derive first and then make a drawing or sketch related to the scenario.

PART A (7 points)

[Include descriptions and images of the scenario as appropriate. Specify appropriate assumptions.]

(ai)

Derive an expression for _____ in terms of _____ and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

NOTE: AP Physics 1 students might also see the following language:

Starting with _____, derive an expression for _____. Express your answer in terms of _____ and physical constants, as appropriate. [Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.]

(aii) Some examples are included here of the types of representations students might be asked to draw/sketch. It does not include all examples:

On the following axes, sketch a graph of ____ as a function of time from _____ until _____. Take the upward direction as _____.
On the following dot, which represents _____, draw, and label the forces (not components) that act on _____ when _____ is at the position shown in Figure . Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. Draw the relative lengths of the vectors to reflect the relative magnitudes of the forces exerted on the sphere for any relative values known.
On Figure _____, do the following.

Draw an arrow to represent process _____.
Label State ____.
Draw an arrow to represent process _____.

PART B (3 points)

(b) The scenario is then changed by _____. Indicate a choice among possible listed outcomes OR indicate if a claim is correct or incorrect. Justify your claim/answer/response.

Scoring Guidelines

Question 1: Mathematical Routines 10 points

NOTE: These are example scoring guidelines. Not all of these will apply to every problem and in many cases the 5 points for the derivation will be split into two steps.

Part A (7 points)

Derivation points:

_____ 1 point is earned for a multi-step derivation starting with _____.

_____ 1 point is earned for attempting to find the components of _____.

Scoring Note: The trigonometry does not have to be correct to earn this point.

_____ 1 point is earned for the substitution of _____ into _____.

_____ 1 point is earned for one of the following:

Solving two _____ equations for _____ and setting them equal to each other
Solving one equation for _____ and substituting that expression into a second equation

_____ 1 point is earned for a correct expression for _____ in terms of given variables.

Representation points: (This part is worth 2 points, but this includes more than two examples of what might earn points)

_____ 1 point is earned for drawing a downward arrow labeled as the gravitational force.

Scoring Note: Examples of appropriate labels for the force due to gravity include FG, Fg, Fgrav, “grav force,” “F Earth on sphere,” “F on sphere by Earth,” FEarth on sphere, FEarth, sphere, Fsphere, Earth. The labels G or g are not appropriate labels for the force due to gravity.

_____ 1 point is earned for drawing an arrow that points along the direction of the string labeled as the tension force.

_____ 1 point is earned for drawing and correctly labeling the _____ arrow so it has _____ times the length as the correctly labeled _____ arrow.

_____ 1 point is earned for a graph of _____ as a function of time that is _____.

_____ 1 point is earned for a graph of _____ with a _____ slope starting at _____.

_____ 1 point is earned for a monotonically increasing curve that is concave _____.

_____ 1 point is earned for drawing a vertical line from _____ to _____ with an arrow pointing upward and labeling the final state as _____.

Example Response:

Include an example response here.

Part B (3 points)

_____ 1 point is earned for indicating that the claim is _____ with an attempt at a relevant justification.

_____ 1 point is earned for indicating a specific point of physics relevant to the problem.

_____ 1 point is earned for indicating a different specific point of physics relevant to the problem.

Translation Between Representations (TBR) Question

The Translation Between Representations (TBR) question assesses students’ ability to connect different representations of a scenario. Students will be expected to create a visual representation that describes a given scenario. Students will derive equations that are mathematically relevant to the scenario. Students will draw graphs that relate quantities within the scenario. Finally, students will be asked to do any one of the following:

Justify why their answers to any two of the previous parts do/do not agree with each other.
Use their representations, mathematical analysis, or graph to make a prediction about another situation and justify their prediction using that reasoning or analysis.
Use their representations, mathematical analysis, or graph to make a prediction about how those representations would change if properties of the scenario were altered and justify that claim using consistent reasoning or analysis.

Translating Between Representations FRQ Summary of Points

The Translating Between Representations question assesses students’ ability to connect different representations of a scenario.

(a) Students will be expected to create a visual representation that describes a given scenario. (3 pts)

(b) Students will derive equations that are relevant to the scenario. (4pts)

(d) Finally, students will be asked to do any one of the following: (2pts)

Justify why their answers to any two of the previous parts do/do not agree with each other.
Use their representations, mathematical analysis, or graph to make a prediction about another situation and justify their prediction using that reasoning or analysis.
Use their representations, mathematical analysis, or graph to make a prediction about how those representations would change if properties of the scenario were altered and justify that claim using consistent reasoning or analysis.

Translating Between Representations (TBR) question

(12 points, ~30 minutes)

This will be question #2 on the AP exam.

Show all your work for each part of the question. The parts within the question may not have equal weight.

PART A (3 points)

[Include descriptions and images of the scenario as appropriate. Specify appropriate assumptions.]

(a) Some examples are included here of the types of representations students might be asked to draw/sketch. It does not include all examples:

AP Physics 1:

Figure shows the position of _____ at times ____, _____, and _____. Draw corresponding dots to represent the position of _____ at times ____, _____, and _____.

AP Physics 1 and 2:

The dot in Figure _____ represents _____. Draw and label the forces (not components) that act on _____ when _____ is at the position shown in Figure . Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. Draw the relative lengths of the vectors to reflect the relative magnitudes of the forces exerted on the sphere for any relative values known.

AP Physics 2:

On the dot in Figure _____, which represents the position along the -axis, draw arrows to represent the electric field created by _____. Label the arrows _____ and _____ to indicate the fields created by sphere _____ and _____, respectively. The relative length of each vector should reflect the relative magnitude of the electric field from each sphere.
In the space below, draw two circuit diagrams, one for Circuit 1, and one for Circuit 2. Clearly label the circuit elements in each diagram.

PART B (4 points) - NOTE: This section might be split into two parts, bi and bii.

(b)

Derive an expression for _____ in terms of _____ and physical constants as appropriate. [Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.]

NOTE: AP Physics 1 students might also see the following language:

(continued on next page)

PART C (3 points)

(c) Some examples are included here of the types of graphs students might be asked to sketch. It does not include all examples:

AP Physics 1:

Sketch and label a graph of the velocity of each car as a function of time between times _____ and _____.
Figure 2 shows a graph of the linear speed of _____ as a function of time between t = 0 and _____. On the same grid, sketch the linear speed of _____ as a function of time between t = 0 and _____.

AP Physics 2:

Sketch and label a curve or line starting on the dot (which represents the initial state of the gas) to represent Process _____. Sketch and label a curve or line to represent Process _____.
On Figure _____, sketch a graph of the total electric potential due to the two charged spheres as a function of position on the -axis for _____ < x < _____.
On the grids in Figure 1, sketch the current IR in the resistor and the potential difference ΔVC across the capacitor as functions of time for the circuit in part (b). Label any intercepts and/or asymptotes in terms of given quantities.

PART D (2 points) - NOTE: There are 3 possible options for this part of the question. Examples of each are included below.

Justify why answers to any two of the previous parts do/do not agree with each other.

Justify how the force diagram created in part (a) is or is not consistent with the graph drawn in part (c).
Indicate whether the graph of Process _____ in part (c) is consistent with the derivation for the work done by the gas on the piston during Process _____ from part (b). Briefly justify your answer by referencing both your derivation from part (b) and the graph in part (c).

Use representations, mathematical analysis, or a graph to make a prediction about another situation and justify their prediction using that reasoning or analysis.

At time _____ the cars have traveled distances _____ and _____ , respectively. Indicate whether _____ is greater than, less than or equal to _____. Justify your claim by using evidence from the graph sketched in part (c).

Use representations, mathematical analysis, or a graph to make a prediction about how those representations would change if properties of the scenario were altered and justify that claim using consistent reasoning or analysis.

Indicate how the shape of the graph between _____ and _____, sketched in part (c) would change, if at all, if the angle of the ramp were increased. Justify your claim.
The scientist modifies the circuit from part (b) by adding _____ in series/parallel with the other circuit components. Indicate how _____ compares to that in the circuit from part (b). Briefly justify your answer.

Scoring Guidelines - AP Physics 1

Question 2: Translating Between Representations 12 points

NOTE: These are example scoring guidelines. Representations tested will vary based on the physics scenario.

Part A (3 points)

AP Physics 1 - Motion map example.

_____ 1 point is earned for at least three dots where the spacing between the dot closest to zero and the next point is smaller than the distance between the next two points.

_____ 1 point is earned for at least one point plotted at the correct location.

_____ 1 point is earned for a correct plotting of all 4 points.

AP Physics 2 - Electric field vector example

_____ 1 point is earned for drawing two vectors of equal magnitude pointing in opposite directions at x = 0.

_____ 1 point is earned for drawing a leftward pointing vector labeled E1 with a greater magnitude than a rightward pointing vector labeled E2 at x = -a/2.

_____ 1 point is earned for 1 point is earned for drawing the vector labeled E1 at x = -a/2 with a magnitude that is four times as large as vector E1 at x = 0.

Example Response:

Include an example response here.

Part B (4 points)

_____ 1 point is earned for a multi-step derivation that starts with _____.

_____ 1 point is earned for a substitution of _____ into an appropriate _____ equation

_____ 1 point is earned for relating _____ to _____.

_____ 1 point is earned for a correct final expression of _____.

Example Response:

Include an example response here.

(continued on next page)

Part C (3 points)

AP Physics 1:

_____ 1 point is earned for a straight line for Car A with a positive slope.

_____ 1 point is earned for a straight line for Car B with a negative slope.

_____ 1 point is earned for lines for cars A and B and where the magnitude of the slope of the line for Car A is twice the slope of the line for Car B.

AP Physics 2:

_____ 1 point is earned for a graph of potential that is negative everywhere in the region.

_____ 1 point is earned for a graph of potential that is concave down.

_____ 1 point is earned for a graph of potential that is symmetrical about the vertical axis with zero slope at x = 0.

Example Response:

Include a correct graph here.

Part D (2 points)

_____ 1 point is earned for indicating _____, with an attempt at a relevant justification.

_____ 1 point is earned for a justification that includes _____.

Example Response:

Include an example response here.

Experimental Design and Analysis (LAB) Question

The Experimental Design and Analysis (LAB) question assesses students’ ability to create scientific procedures that can be used with appropriate data analysis techniques to determine the answer to given questions. The LAB question can roughly be divided into two sections: Design and Analysis. In the Design portion of the LAB question, students will be asked to develop a method by which a question about a given physical scenario could be answered. The experimental procedure is expected to be scientifically sound: vary a single parameter, and measure how that change affects a single characteristic. Methods must be able to be performed in a typical high school laboratory. Measurements must be made with realistically obtainable equipment or sensors. Students will be expected to describe a method by which the collected data could be analyzed in order to answer the posed question, by either graphical or comparative analyses.

Students will then be given experimental data collected in order to answer a similar, but not identical, question to what was asked in the Design portion of the question. Students will be asked to use the data provided to create and plot a graph that can be analyzed to determine the answer to the given question. For instance, the slope or intercepts of the line may be used to determine a physical quantity or perhaps the nature of the slope would answer the posed question.

Experimental Design FRQ Summary of Points

Experiment 1

• Describe an experimental procedure including multiple IV values (Part A-2pts)

• Describe how the data can be graphed and analyzed (Part B-2pts)

Experiment 2

• Indicate which measured or calculated quantity could be plotted to yield a linear graph (Ci-1pt)

• Scale & Label all axes and Plot the quantities (Cii-2pts)

• Draw a best fit line (Ciii-1pt)

• Calculate an experimental value using an equation and the graph-slope (D-2pts)

Experimental Design and Analysis (LAB) question

(10 points, ~25 minutes)

This will be question #3 on the AP exam.

Show all your work for each part of the question. The parts within the question may not have equal weight.

A group of students are given _____ and are asked to take measurements to create a graph that could be used to determine _____. The students have access to _____ and/or only have access to _____. [Images and/or additional descriptions of the scenario added as needed.]

NOTE: Students may be asked to determine either a specific quantity OR determine if a particular claim is supported.

PART A (2 points) - AP Physics 1

(a) Describe an experimental procedure for collecting data that can be graphed to determine ____. Include any steps necessary to reduce experimental uncertainty. [If needed, you may include a simple diagram of the setup with your procedure.]

PART A (2 points) - AP Physics 2

(a) Design an experimental procedure that the students could use to collect the data needed to determine _____. Provide enough detail so another student could replicate the experiment, including any steps necessary to reduce experimental uncertainty.

NOTE: For experimental uncertainty, students are expected to specify that the independent variable will be changed multiple times.

PART B (2 points) - AP Physics 1

(b) Describe how the data collected in part (a) would be graphed, and how that graph would be analyzed to determine _______.

PART B (2 points) - AP Physics 2

(b) Describe how the students could analyze the collected data to determine ____.

PART C (4 points) - AP Physics 1

Another group of students is given _____. [Include details about the experiment, as necessary.] The following table shows the data collected by the students.

The students correctly determine that the relationship between _____ and _____ is given by _____. The students create a graph with _____ plotted on the _____ axis.

(c)

i. Indicate which measured or calculated quantity could be plotted on the _____ axis to yield a linear graph whose slope can be used to calculate _____. You may use the remaining columns in the table, as needed, to record any quantities (including units) that are not already in the table.

Vertical: __________ OR Horizontal: __________

NOTE: For AP Physics 1, students will be provided with either the horizontal or vertical variable and will need to specify the other. The provided variable will also be labeled and scaled on the graph.

ii. On the grid shown in Figure _____, plot the data points for the quantities indicated in part (c)(i) that can be used to determine _____. Scale the graph as appropriate. Clearly label the _____ axis, including units.

iii. Draw a best–fit line for the data graphed in part (c)(ii).

PART C (4 points) - AP Physics 2

In a second experiment, the students _____. [Include details about the experiment, as necessary.]The students record _____. The data are shown in the table.

(c)

i. Indicate what measured and/or calculated quantities could be graphed to yield a straight line that could be used to calculate _____. Use the blank columns in the table to list any calculated quantities you will graph other than the data provided.

Horizontal Axis:__________ Vertical Axis:__________

ii. Plot the data points for the quantities indicated in part (c)(i) on the graph provided. Clearly scale and label all axes, including units, as appropriate.

iii. Draw a best–fit line for the data graphed in part (c)(ii).

PART D (2 points) - AP Physics 1

(d) Calculate an experimental value for ____, using the best fit-line you drew in Figure ___ in part (c)(iii).

PART D (2 points) - AP Physics 2

(d) Using the best-fit line calculate ____.

Scoring Guidelines - AP Physics 1

Question 3: Experimental Design 10 points

Part A (2 points)

_____ 1 point is earned for describing a procedure that indicates one of the following as a reasonable method of reducing experimental uncertainty.

Complete multiple trials using different values of the independent variable
Repeat measurements for each trial of a single height

_____ 1 point is earned for describing a plausible procedure that includes measurements that can be made with the provided materials.

Example Response:

Include an example response here.

Part B (2 points)

_____ 1 point is earned for describing an analysis that involves a graph that could be used to determine the _____.

_____ 1 point is earned for a statement that includes the correct analysis of the graph that would lead to _____.

Example Response:

Include an example response here.

Part C (4 points)

_____ 1 point is earned for listing a quantity that could be plotted on the _____ axis to produce a linear graph whose slope can be used to determine _____.

_____ 1 point is earned for labeling the horizontal axis correctly (or consistent with quantities indicated in part (c)(i)) (including units) with a linear scale.

_____ 1 point is earned for 1 point is earned for correctly plotting data points consistent with quantities indicated in part (c)(i).

_____ 1 point is earned for drawing an appropriate straight best–fit line that approximates the trend of the data.

Example Response:

Include a correct graph here.

Part D (2 points)

_____ 1 point is earned for correctly relating the slope of the best-fit line (or the y-intercept, if applicable) to the value of _____.

_____ 1 point is earned for calculating a value of _____ within a range of _____ to _____.

Example Response:

Include an example response here.

Scoring Guidelines - AP Physics 2

Question 3: Experimental Design 10 points

Part A (2 points)

_____ 1 point is earned for describing a plausible procedure that includes measurements of _____.

_____ 1 point is earned for a reasonable method of reducing experimental uncertainty by using several independent variable values.

Example Response:

Include an example response here.

Part B (2 points)

_____ 1 point is earned for indicating appropriate values that could be graphed to determine _____.

_____ 1 point is earned for correctly indicating how the slope of the graph can be used to calculate/determine _____.

Example Response:

Include an example response here.

Part C (4 points)

_____ 1 point is earned for indicating appropriate quantities that can be plotted on the graph to determine _____.

_____ 1 point is earned for labeling the axes correctly (including units) with a linear scale such that the plotted points are spread over at least half of the horizontal axis and at least half of the vertical axis.

_____ 1 point is earned for correctly plotting the data points.

_____ 1 point is earned for drawing an appropriate best-fit line that approximates the data.

Example Response:

Include a correct graph here.

Part D (2 points)

_____ 1 point is earned for correctly relating the slope of the best-fit line of the graph to _____.

_____ 1 point is earned for calculating a value of _____ to be approximately _____.

Example Response:

Include an example response here.

Qualitative/Quantitative Translation (QQT) Question

The Qualitative/Quantitative Translation (QQT) question assesses students’ ability to connect the nature of the scenario, the physical laws that govern the scenario, and mathematical representations of that scenario to each other. Students will be asked to make and justify a claim about a given scenario, as well as derive an equation related to that scenario. Finally, students will be asked to do any one of the following:

▪ Justify why their answers to any of the previous parts do/do not agree with each other.

▪ Use their representations or mathematical analysis to make a prediction about another situation and justify their prediction using that reasoning or analysis.

▪ Use their representations and mathematical analysis to make a prediction about how those representations would change if properties of the scenario were altered and justify that claim using consistent reasoning or analysis.

While students may not be directly assessed on their ability to create diagrams or other representations of the system to answer the QQT, those skills may still help students to answer the QQT. For instance, some students may find that drawing a free-body diagram is useful when determining the acceleration of a system. However, the student will earn points for the explanation and conclusions that diagram indicates (or perhaps the derivation that results from the diagram), rather than for creating the diagram itself.

Qualitative/Quantitative Translation FRQ Summary of Points

(a) Students will be asked to make and justify a claim about a given scenario. (3 pts)

(b) Students will then be asked to derive an equation related to that scenario. (3 pts)

• Justify why their answers to the previous parts do (do not) agree with each other.

• Use their representations or mathematical analysis to make a prediction about another situation and justify their prediction using that reasoning or analysis.

• Use their representations and mathematical analysis to make a prediction about how those representations would change if properties of the scenario were altered and justify that claim using consistent reasoning or analysis.

QQT FR

Qualitative Quantitative Translation (QQT) question

(8 points, ~20 minutes)

This will be question #4 on the AP exam.

Show all your work for each part of the question. The parts within the question may not have equal weight.

PART A (3 points) NOTE: A few examples of possible wording are included below.

[Include descriptions and images of the scenario as appropriate. Specify appropriate assumptions.]

AP Physics 1

(a) Indicate whether _____ is greater than, less than, or equal to _____ (or will increase, decrease, or remain the same). Justify your answer using qualitative reasoning beyond referencing equations.

AP Physics 2

(a) [Description of a physics phenomenon.] Indicate why this happens. Justify your reasoning in terms of the interaction between _____ and _____.

PART B (3 points)

AP Physics 1

(b) Starting with _____, derive an expression for _____. Express your answer in terms of _____, _____, _____, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

AP Physics 2

(b) Derive an expression for ______ in terms of _____, ______, _____, and physical constants, as appropriate. [Begin your derivation by writing a fundamental physics principle or an equation

from the reference booklet.]

PART C (2 points) NOTE: There are 3 possible options for this part of the question. Examples of each are included below.

Justify why their answers to any of the previous parts do/do not agree with each other.

(c) Indicate whether the derived expression in part (b) is consistent with your reasoning in part (a). Briefly justify your answer.

Use their representations or mathematical analysis to make a prediction about another situation and justify their prediction using that reasoning or analysis.

(c) A group of students want _____ to be as small as possible. Describe the relative masses of _____ that will result in the smallest _____. Justify your answer using your derivation from part (b).

Use their representations and mathematical analysis to make a prediction about how those representations would change if properties of the scenario were altered and justify that claim using consistent reasoning or analysis.

(c) [Description of a change in the scenario.] Indicate the process that is responsible for this. Justify your response by referring to the equation derived in part (b).

Scoring Guidelines

Question 4: Qualitative/Quantitative Translation 8 points

NOTE: These are example scoring guidelines. Not all of these will apply to every problem.

Part A (3 points)

_____ 1 point is earned for selecting _____ with an attempt at a relevant justification.

_____ 1 point is earned for indicating a specific point of physics relevant to the problem.

_____ 1 point is earned for indicating a different specific point of physics relevant to the problem.

Example Response:

Include an example response here.

Part B (3 points)

AP Physics 1

_____ 1 point is earned for a multi-step derivation starting with _____.

_____ 1 point is earned for substitution of one of the following: ______ or ______ (or for one of the following physics steps).

_____ 1 point is earned for correct expression for _____, [in terms of the given variables].

AP Physics 2

_____ 1 point is earned for an expression that includes _____ (or that relates _____ and _____).

_____ 1 point is earned for correctly substituting _____, _____, and _____ into _____.

_____ 1 point is earned for correct expression for _____, in terms of the given variables.

Example Response:

Include an example response here.

Part C (2 points)

_____ 1 point is earned for attempting to address the functional dependence between ______ and ______.

Scoring Note: It is not necessary to use the functional dependence correctly to earn the first point.

_____ 1 point is earned for correctly using functional dependence to evaluate the relationship between ______ and ______, consistent with the reasoning in part (a) and the derivation in part (b).

Example Response:

Include an example response here.

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