## 5 Steps to a 5: AP Physics 1: Algebra-Based 2017 (2016)

### STEP __3__

### Develop Strategies for Success

### CHAPTER 7

### Strategies to Approach the Questions on the Exam

**IN THIS CHAPTER**

**Summary:** This chapter contains tips and strategies that apply to both the free-response and the multiple-choice sections of the AP Physics 1, Algebra-Based Exam. First you”ll find information about the tools (calculator, equation sheet, and table of information) you can use on the exam and strategies to make the best use of these tools. Then you”ll find strategies for dealing with two common types of AP Physics 1 questions: ranking questions and questions about graphs. Both of these types of questions can be found in the multiple-choice section and in the free-response section of the exam.

**Key Ideas**

Although you can use a calculator on the exam, you should use it only when it”s actually required to do a calculation. It won”t help you answer the vast majority of the questions on the AP Physics 1, Algebra-Based Exam.

Questions involving a ranking task often require analysis more than calculation. Ranking questions can be multiple choice or free response. For free-response questions, be sure to indicate clearly the order of your ranking, and if two of the items to be ranked are equal, be sure to indicate that, too.

Graph questions are straightforward, because there are only three things you can do with a graph—take the slope, compute the area under the graph, and read one of the axes directly. Pick the right one, and you”re golden.

**Tools You Can Use and Strategies for Using Them**

Like all AP exams, the AP Physics 1, Algebra-Based Exam consists of both multiple-choice questions (Section I) and free-response items (Section II). The three tools discussed below can be used on both sections of the exam.^{ }^{1}^{ }Keep in mind that just because you *can* use these tools, it doesn”t necessarily mean you *should* .

**Calculator**

The rules of acceptable calculators are the same as those on the SAT or the AP math exams—pretty much any available calculator is okay, including scientific and graphing calculators. Just don”t use one with a QWERTY keyboard, or one that prints the answers onto paper.^{ }^{2}^{ }You”re not allowed to share a calculator with anyone during the exam.

**Wait! Don”t Touch That Calculator!**

Will a calculator actually help you? Not that much. Exam authors are required to write to the specific learning objectives in the “curriculum framework.”^{ }^{3}^{ }Of the 140 learning objectives in AP Physics 1 curriculum, *only 21 allow for calculation* ! For 119 of 140 learning objectives, something else entirely—qualitative prediction, semiquantitative reasoning, analysis and evaluation of evidence, description of experiment, explanation, etc.—is required. You will need to calculate, but not often.

And even then, the “calculation” on the AP exam usually does not require a calculator. For example, you”ll answer in symbols rather than numbers; you”ll be asked to do an “order of magnitude estimate” in which only the power of 10 matters^{ }^{4}^{ }; the numbers involved will be simple, like 4 × 2; or the choices will be so far separated that only one answer will make sense, whether or not you actually carry out the calculation.

But seemingly every problem we did for class required solving an equation and plugging values into that equation. My teacher assigned us a bunch of problems on the computer, with programs like WebAssign. I could never have done those problems without a calculator!

That”s very likely true. Being able to perform calculations is, in fact, a first step toward more difficult physics reasoning. But it”s very simple—the AP exam will only sometimes require a calculation. And when it does, a calculator will only sometimes be necessary. So wean yourself off of the calculator. Practice approaching every problem with diagrams, facts, equations, symbols, and graphs. Only use the calculator as a last step in a homework problem. Then you”ll be well prepared for the kinds of things you”ll see on the AP exam.

**The Table of Information**

There”s no need to memorize the value of constants of nature, such as the mass of an electron or the universal gravitation constant. These values will be available to you on the table of information you”ll be given.

**The Equation Sheet**

A one-page list of many relevant equations will be available to you on both sections of the exam.^{ }^{5}^{ }You will be able to see the official equation sheet ahead of time at the AP Physics 1 portion of the College Board”s website (__https://www.collegeboard.org__ ).

**Wait! Don”t Touch That Equation Sheet!**

Will the equation sheet actually help you? It won”t help you that much. Too often, students interpret the equation sheet as an invitation to stop thinking—“Hey, they tell me everything I need to know, so I can just plug-and-chug through the exam.” Nothing could be further from the truth.

First, the equation sheet will likely present most equations in a different form than you”re used to, or use different notation than your textbook or your class. So what—you”ve already memorized the equations on the sheet. It might be reassuring to look up an equation during the exam, just to make sure you”ve remembered it correctly, which is really the point of the equation sheet. But beware. Use your memory as the first source of equations.

If you must use the equation sheet, *don”t go fishing* ! If a question asks about a voltage, don”t just rush to the equation sheet and search for every equation with a *V* in it. You”ll end up using , where the *V* means volume, not voltage. You”d be surprised how often misguided students do this. Don”t be that person.

So you”re saying I”ll be given a calculator and an equation sheet, but neither will be much use. Why would I be given useless items?

Suffice it to say that many years ago, calculation was indeed the most important aspect of an AP Physics exam, so the calculator was indispensable. Back then, students were expected to memorize equations. As calculators became more sophisticated, students began to game the test by programming equations into their calculators, effectively gaining an unfair advantage. So the equation sheet was provided to everyone, negating that advantage. Now that calculation is a far less significant part of AP Physics, the calculator will only rarely be useful. But since you might need it a few times in an exam, it”s still allowed.

**Strategies for Questions That Involve a Ranking Task**

You already know there won”t be a lot of straight “calculate this” type of questions. So what kinds of questions will there be? One very different sort of question from the standard textbook end-of-chapter homework problem is the ranking question. It can be found among the multiple-choice questions of Section I or in Section II as a free-response question. Here”s an example:

Cart A takes 5 s to come to rest over a distance of 20 m. Cart B speeds up from rest, covering 10 m in 10 s. And Cart C moves at a steady speed, taking 1 s to cover 50 m. All carts have uniform acceleration. Rank the carts by the magnitude of their acceleration. If more than one cart has the same magnitude of acceleration, indicate so in your ranking.

Notice that you are emphatically *not* asked to calculate the acceleration of each cart. Usually, a ranking task can be solved more simply with conceptual or semiquantitative reasoning than with direct calculation.

In this example, the conceptual approach is probably best. Acceleration is defined as how quickly an object changes its speed. “Magnitude” of acceleration means ignore the direction of acceleration.^{ }^{6}^{ }Cart C doesn”t change its speed at all, so it has the smallest acceleration. Cart A goes farther than Cart B and takes less time to do so. Since both change their speeds from or to rest, Cart A must change its speed more quickly than Cart B.

The multiple-choice ranking tasks will have answer choices formatted as inequalities: A > B > C. If two were equal, then you”d see something like A = B > C, which would mean A and B are equal, but are both greater than C.

In the free-response section, you can format your answer to a ranking task any way that is clear. For example, you could list: “(Greatest) A, B, C (least).” Don”t forget to make some notation if two of the choices were equal; circle those two and write “these are equal” or something that is crystal clear.

**Exam Tip from an AP Physics Veteran**

For some people, semiquantitative and qualitative reasoning is much more difficult than just making calculations. You have every right to start a ranking task with several calculations! Then just rank your answers numerically. Sure, some questions will require you to explain your ranking without reference to numbers, but still, feel free to answer with numbers first, and *then* refer to the equations.

In the example above, you could make the calculation for each cart. Use the kinematics equations detailed in __Chapter 10__ . You can calculate that Cart A has an acceleration of 1.6 m/s per second. Cart B has an acceleration of 0.2 m/s per second. And Cart C has an acceleration of zero.

How could you follow your calculation with a nonnumerical explanation, then? Look at how the equations simplified. For carts A and B, the initial or final speed of zero meant that when you solved in variables for *a* , you got . Cart A has *both* a bigger distance to travel *and* a smaller time of travel. Cart A”s numerator is bigger, denominator smaller, and acceleration bigger than Cart B”s.

**Strategies for Questions That Involve Graphs**

Analyzing data in graphical form will be a skill tested regularly on the AP exam. Good graph questions are straightforward, because there are only *three things you can do with a graph* . Pick the right one, and you”re golden.

When you see a graph, the first step must be to *recognize the relevant equation* . In this situation, which equation from the equation sheet relates the *y* - and *x* -variables? I truly mean the equation, not just the units of the axes. Then, the equation will lead you to one of the following three approaches.

What are the three things we can do with this graph?

A box sits on a smooth, level surface. The box is attached to a spring. A person pushes the box across the surface, compressing the spring. For each distance the spring compresses, the force applied by the person on the box is measured.

**Take the Slope of the Graph**

You certainly understand that the slope represents the change in the *y* -variable divided by the change in the *x* -variable. But to really understand what the slope of a graph means, you can”t just say “it”s the change in force divided by the change in distance.” Slopes of graphs generally have a physical meaning that you must be able to recognize.

Always start with the relevant equation. If you suspect you”re looking for a slope, solve the relevant equation for the *y* -axis variable, then compare the equation to the standard equation for a line: *y* = *mx* + *b* . Here, we”re talking about the force of a spring and the distance the spring is stretched—that”s covered by the equation *F* = *kx. F* and *x* are the vertical and horizontal axes, respectively.

This process of circling the *y* -variable, circling the *x* -variable, and then circling the slope will work with any equation.^{ }^{7}^{ }Here, the slope represents *k* , the spring constant for the spring. So what is the numerical value of the spring constant? You can calculate the slope by drawing a best-fit line, choosing two points on the line that are not data points, and crunching numbers.

Using the two circled points on the line, the “rise” is (50 N – 16 N) = 34 N. The “run” is (3 cm – 1 cm) = 2 cm. So the slope—and thus the spring constant of the spring—is .

**Calculate the Area Under the Graph**

Always start with the relevant equation. The meaning of the area under the graph is generally found by looking at an equation that *multiplies* the vertical and horizontal axes. Here, that would be force times distance. Sure enough, the equation for work is at work here: *W* = *F* · Δ*x* _{||} . The force applied by the man is parallel to the box”s displacement, so the work done by the man is the multiplication of the vertical and horizontal axes. That means that to find the work done, take the area under the graph.

How much work did the man do in compressing the spring 3 cm? Usually, when you”re taking an area under a graph on the AP exam, just estimate by breaking the graph into rectangles and triangles. In this case the graph is an obvious triangle. The area of a triangle is (½)(base)(height) = (½)(0.03 m)(50 N) = **0.75 J** . If instead the question had asked for the work done in compressing the spring 2 cm, I”d do the same calculation with 0.02 m and 34 N.

Two things to note about that calculation: First, an area under a graph, like a slope, has units. But the units are *not* “square units” or “square meters.” The “area” under a graph isn”t a true physical area; rather, it represents whatever physical quantity is found by multiplying the axes. This area represents the work done by the man, so it should have units of joules. Second, you”ll note that I used 0.03 m rather than 3 cm in calculating the area under this graph. Why? Because without that conversion, the units of the area would have been newton centimeters (N·cm). I wanted to get the work done in the standard units of joules, equivalent to newton meters (N·m). So, I had to convert from centimeters to meters.

**Read One of the Axes Directly**

Often a question will ask for interpolation or extrapolation from a graph. For example, even though the man never used 60 N of force, how far would the spring compress if he *had* used 60 N? Just extend the best-fit line, as I already did, and read the horizontal axis: 3.6 cm.

**Exam Tip from an AP Physics Veteran**

When you draw a best-fit line, just lay your ruler down and truly draw the fit as best as you can. Never connect data point-to-point; never force the best-fit line through (0,0); never just connect the first and last data points. In fact, it”s best if you extend the line of best fit as far as you can on the graph, so that you can answer extrapolation questions quickly and easily.

Finally, note that many graphs on the AP Physics 1 Exam will include real data, not just idealized lines. Be prepared to sketch lines and curves that seem to fit the general trend of the data.

__ ^{1}__ This represents a change from previous AP Physics exams; you used to have access to a calculator only on the free response.

__ ^{2}__ Does anyone actually use printing calculators anymore?

__ ^{3}__ You can refer to the curriculum framework via the AP Physics 1 portion of the College Board”s website,

__https://www.collegeboard.org__.

__ ^{4}__ See

__Chapter 15__(Gravitation) for specific examples of order-of-magnitude estimates.

__ ^{5}__ Once again, this is a change for AP Physics 1; the equation sheet used to be for free response only.

__ ^{6}__ This can”t be determined here anyway, because although Cart A has acceleration opposite its motion, and Cart B has acceleration in the same direction as its motion, we don”t know which ways these two carts are moving. But who cares, for this particular question.

__ ^{7}__ And if there”s a leftover term with a plus or minus sign, you”ll recognize that as the

*b*-value, the

*y*-intercept of the graph.