The AP® Physics Free Response section is composed of 5 questions; you are given 90 minutes to answer them. Knowing the physics is crucial, but beyond that, here are five techniques to minimize errors and maximize points on the AP® Physics Free Response section. We apply all of these techniques to 2015 Free Response Question 1.

Draw the Correct Picture

The AP® Physics Free Response section is set up such that you are often required to draw a picture which will be used later in an algebraic equation or expression. The algebra is often used later in a paragraph explaining the physical meaning behind a certain result. Therefore, drawing the correct picture is of utmost importance in order to get correct results in later parts of the question.

Here are the prompt and grading scheme for part (a) of 2015 Free Response Question 1:

You can imagine that most everyone drew two arrows on each dot with the correct directions. The point of this question is to see if you know (and can show) that the tensile forces on both blocks are the same: the two vectors representing tension must have the same length. Notice that you are provided with dashed lines to “measure” the length of your arrows – use them!

List Relevant Equations

Here are the prompt and grading scheme for part (b) of 2015 Free Response Question 1:

Notice that performing the algebra and arriving at the correct acceleration expression is worth the same as listing the force equations, even though doing the algebra is harder. The AP® Physics Exams test your knowledge of physics – setting up physical equations is physics, and doing math isn’t.

Another way to approach this problem is to treat both masses as part of the same system and consider only external forces on the system:

$\left( { m }_{ 1 }+{ m }_{ 2 } \right) a={ m }_{ 2 }g-{ m }_{ 1 }g$.

This also yields the correct acceleration expression, is faster, and would score full points. It is not acceptable just to write down the acceleration

$a=\dfrac { \left( { m }_{ 2 }-{ m }_{ 1 } \right) g }{ \left( { m }_{ 1 }+{ m }_{ 2 } \right) }$.

The prompt says to “derive” the acceleration expression, which is a good clue that you should show work.

On the other hand, do not write down irrelevant equations – if the prompt asks for two equations, for example, graders will score only the first two equations you write down.

Check Limiting Cases

Limiting cases are typically not taught as part of the AP® Physics curriculum, but they are easy and quick ways to check if your expression is reasonable. The idea is to push a single variable to an extreme and see if the answer that follows would make sense in the real world. This is easier to see in practice:

Take the acceleration expression for the two-block system obtained above,

$a=\dfrac { \left( { m }_{ 2 }-{ m }_{ 1 } \right) g }{ \left( { m }_{ 1 }+{ m }_{ 2 } \right) }$.

We test two limiting cases.

1. ${ m }_{ 1 }$ is small. If ${ m }_{ 1 }$ approaches zero, then the expression for a reduces to

$a=\dfrac { \left( { m }_{ 2 }-0 \right) g }{ \left( 0+{ m }_{ 2 } \right) } =g$.

This makes sense: if ${ m }_{ 1 }$ has no mass, then we expect ${ m }_{ 2 }$ to accelerate down in free-fall with acceleration g.

2. ${ m }_{ 1 }={ m }_{ 2 }$. If the masses are equal, the expression reduces to

$a=\dfrac { \left( { m }_{ 2 }-{ m }_{ 2 } \right) g }{ \left( { m }_{ 2 }+{ m }_{ 2 } \right) } =0$.

This makes sense: the masses are stationary because neither is more massive. The system is in equilibrium with equal masses hanging on either side of the table.

Now, let’s see what happens when the expression tested is incorrect. Suppose you made an algebra mistake and came up with an expression like one of the two below:

$a=\dfrac { \left( { 3m }_{ 2 }-{ m }_{ 1 } \right) g }{ \left( { m }_{ 1 }+{ 2m }_{ 2 } \right) }$.

$a=\dfrac { \left( { m }_{ 2 }+{ m }_{ 1 } \right) g }{ \left( { m }_{ 1 }+{ m }_{ 2 } \right) }$.

1. ${ m }_{ 1 }$ is small. If ${ m }_{ 1 }$ approaches zero, then the first incorrect expression for a reduces to

$a=\dfrac { \left( { 3m }_{ 2 }-0 \right) g }{ \left( 0+{ 2m }_{ 2 } \right) } =\dfrac { 3g }{ 2 }$.

This makes no sense: if ${ m }_{ 1 }$ has no mass, then the expression says that ${ m }_{ 2 }$ accelerates faster than under the influence of gravity. Something is wrong, and we must check our work.

2. ${ m }_{ 1 }={ m }_{ 2 }$. If the masses are equal, the second incorrect expression reduces to

$a=\dfrac { \left( { m }_{ 2 }+{ m }_{ 2 } \right) g }{ \left( { m }_{ 2 }+{ m }_{ 2 } \right) }=g$.

This makes no sense: the masses should be stationary because neither is more massive than the other. Since the (incorrect) expression says the system accelerates with acceleration g, something is wrong and we must check our work.

A disclaimer: checking limiting cases can only tell you if your answer is incorrect. It cannot say whether an expression is right – it’s perfectly possible for a wrong expression to be right in a limiting case. For example, $a=\dfrac { \left( { m }_{ 2 }+{ m }_{ 1 } \right) g }{ \left( { m }_{ 1 }+{ m }_{ 2 } \right) }$ is correct when ${ m }_{ 1 }=0$. Limiting cases are simply quick smell tests that discard expressions that don’t pass the test. They won’t earn you points on the AP® Physics Free Response, but they might alert you to a mistake.

Use Correct Vocabulary

Physics is not like other subjects in which you are asked to use specific vocabulary words – in physics, you usually have no choice but to use physics vocabulary when describing physical phenomena. However, you must use correct vocabulary – if you use an incorrect word, you risk losing points on an explanation portion of an AP® Physics Free Response question. You should review the differences among the following terms:

•  Displacement vs. distance traveled

•  Gravitational acceleration vs. gravitational force (do not just say “gravity”)

•  Speed vs. velocity

•  Moment of inertia vs. inertia

•  Potential energy vs. potential difference vs. electric potential

•  Electric field vs. electric force

•  Impulse vs. momentum

(AP® Physics 2 Only)

•  Reflection vs. refraction

•  Interference vs. diffraction

•  Real image vs. virtual image

Redo the Algebra

Simply looking over your work doesn’t cut it – if you have time, start from the basic equations and redo any algebra you had to perform to arrive at the answer. In the best case, arrive at the same answer using a different method: say that for our example FRQ, you correctly set up the two $F = ma$ equations,

${ m }_{ 1 }a=T-{ m }_{ 1 }g$,

${ m }_{ 2 }a={ m }_{ 2 }g-T$.

If you first solved this system by solving for T in the first equation and substituting in the second,

$T={ m }_{ 1 }g+{ m }_{ 1 }a$

${ m }_{ 2 }a={ m }_{ 2 }g-\left( { m }_{ 1 }g+{ m }_{ 1 }a \right)$

you could solve it again by solving for T in the second equation and substituting in the first,

$T={ m }_{ 2 }g-{ m }_{ 2 }a$

${ m }_{ 1 }a=\left( { m }_{ 2 }g-{ m }_{ 2 }a \right) -{ m }_{ 1 }g$

and you could even solve it again by adding the equations together,

${ m }_{ 1 }a+{ m }_{ 2 }a={ m }_{ 2 }g-{ m }_{ 1 }g$.

All three methods yield the same result, as they should.

Wrapping Up Five Techniques to Beat the AP® Physics Free Response

Draw the Correct Picture

•  For vectors, both length and direction matter. Make sure to label all parts of the drawing.

List Relevant Equations

•  Start from the basic equations of physics. Do not skip steps!

Check Limiting Cases

•  Push one variable to an extreme to check that your expression yields a reasonable answer.

Use Correct Vocabulary

•  Words in physics have specific meanings – use the correct word.

Redo the Algebra

•  Don’t just look over your math – do it again, using a different method if possible.

Looking for AP® Physics 1 & 2 practice?

Kickstart your AP® Physics 1 & 2 prep with Albert. Start your AP® exam prep today.