Paper 5 is a written paper to test the practical skills that you acquired during your Cambridge International A Level course.

## Question 1: [Planning – 15 marks]

This question of paper 5 tests your ability to plan experiments. If you have done a good amount of practical work during your A Levels, this question won’t be much of a concern for you (especially if you paid good attention to your paper 3 of Physics). Whatever you practically perform in your paper 3, you have to write it in this paper.

While solving this question, keep these pointers in mind:

- Defining the problem [3 marks]
- Methods of data collection [4 marks]
- Setup for the apparatus [1 mark]
- Method of Analysis [2 marks]
- Safety considerations [1 mark]
- Any additional details [4 marks]

We’ll now describe these pointers one by one. The experiment described in this paper 5, question 1 : (**May/June 2018 Paper 5 Variant 2**) is used as an example for an explanation of the above pointers in the sections that follow.

### Defining the problem:

Here you are required to identify the variables in the experiment:

**Independent variable:**it is a variable whose variation does not depend on that of another.**Dependent variable:**it is a variable whose value depends on that of another.

In simpler terms, the independent variable is the variable you are going to *vary* in the experiment, and the dependent variable is the variable you are going to *measure* in the experiment (pay attention to the words ‘vary’ and ‘measure’).

After the identification of variables, you are required to identify the quantities you are going to keep constant. Any quantity which may vary your results, other than quantities involved in the experiment, must be kept constant. Mention ‘how’ you are going to make sure it does not change, and ‘why’ you think it should be kept constant. While you do this, keep in mind one thing that there may be a lot of such quantities that need to be kept constant; always mention that quantity which DIRECTLY affects the variables being measured.

### Methods of data collection:

Now that you have mentioned the variables, you need to describe how to measure them. Describe the method to vary the independent variable, and a method to measure the effect on the dependent variable. State all instruments used.

In the example question, two variables are involved in the experiment, λ (independent) and h (dependent). λ can be *varied* by using different colored LEDs/lasers (red, green, blue, etc) and using the values for λ given on these LEDs/lasers for any calculations/analysis. The corresponding values of ‘h’ can be measured using a meter rule/plastic ruler.

As you can see now, I described above ‘HOW’ I am going to vary the independent variable, and ‘HOW’ I am going to measure the dependent variable. I also stated all the instruments used too. Along with all this, you are also required to mention the SETUP (discussed below) for the experiment; for instance, how you are going to place the LEDs/lasers (any appropriate method to support the light source, like clamping the light source using a retort stand, etc.), how you are going to place the ruler (placing the ruler close to the maxima on the screen).

You also need to describe how any errors possible may be prevented; these points you mention are counted as *additional details*.

Also include details on how you are going to keep constant quantities you mentioned before constant (In the example experiment described above, the constant quantity was the angle of the incident light. It can be kept constant by holding the light source using a retort stand, and not changing its position the entire experiment)

In some cases, there are no proper instruments available for the measurement of dependent quantity. For example, resistance cannot be measured using a conventional piece of apparatus directly. So for that purpose, mention all the measurements you need to take for its calculation and the instruments used (ammeter used for measurement of current, voltmeter used for measurement of p.d. across the resistor. R is then calculated using the equation: R = V/I).

### Setup for the apparatus:

Draw a diagram with all the equipment you mentioned / might use during the experiment. A basic, well-labeled diagram could score many marks; even if the explanation is weak! Therefore, don’t think that the diagram is of little importance.

### Method of analysis:

In all papers, an equation is given which you need to test or experiment about. Algebraically manipulate the given equation to form a linear relationship (Y = mX + c) – choose what quantity should be on each axis to give a straight line graph.

Relationship |
Linear form |
Graph |
Gradient |
y-intercept |

y = mx + c | y = mx + c | y against x | m | c |

y = ax^{n} |
g y = (n)lgx + lg a | lg y against lg x | n | lg a |

y = ae^{kx} |
ln y = kx + ln a | ln y against x | k | ln a |

Once you are done algebraically manipulation the equation into a linear form, describe what the graph will look like if the given relationship is true, e.g.

Relationship given is : y = ax^{n} ; linear form : lg y = (n) lgx + lg a

The graph will be linear if lg y is plotted against lg x.

Also mention, where the line will intersect the y-axix, and what will the gradient of the plotted relationship.

If quantities are asked to calculated, as in the example question given above, that can be done as follows:

The equation given in the example question is:

h = n λ/d + B

Converting this linear form; (y = mx + c) form, we get:

(*the given equation is already in the linear form, so I’m just making it look like one by the use of brackets*)

h = n/d (λ) + B

h is plotted on the y-axis against λ on the x-axis.

By comparing it with linear form, we know that, n/d = m = gradient, and B = c = y-intercept.

Therefore,

d = n/gradient

and

B = y-intercept

These all steps of conversion to linear form, graphical form, gradient, y-intercept, and calculation of quantities come under ‘*Analysis of Data*’.

### Safety considerations:

Any hazards/harms involved while performing the experiment go here; for every hazard/harm, mention a way to avoid it.

For the example question, the safety precautions needed are:

- Looking directly at the bright light source may damage your eyes [safety precaution: wear goggles, do not look directly, safety screens, etc.]

Other common safety issues for other experiments may be:

- In electricity experiments, electrocution may occur [safety precaution: wear gloves]
- If heating is involved, burns may occur; fire [safety precaution: wear gloves, use holders for picking up hot objects; turn off heating instruments between taking measurements]
- For experiments involving heavy objects, moving objects, they may fall on your foot if slipped from bench/table, sand bucket for falling masses or moving objects may hit you, resulting in eye injuries or other face injuries [make sure heavy objects not placed near edges, supports are strong, wear goggles to prevent moving objects hitting your eyes]

There may be many more such harms possible, and many more precautions necessary depending on the experiment.

### Additional details:

All the improvements possible, preventions of errors, etc. come under this heading.

Make yourself acquainted with the following list of apparatus (these apparatus/additional details are taken from Znotes – https://znotes.org/cie-a2-physics-9702/)

#### General Experiments Apparatus:

**Signal generator:**can be used to produce a sound/voltage/current and can vary frequency settings on the device**Micrometer:**can be used to measure small distances**Vernier calipers:**can be used to measure small distances**Set square:**used to make sure apparatus perpendicular**Magnets:**can be used with metal objects in the experiment**Balance:**can be used to weigh a mass**Burette:**accurately measuring the volume of liquid**Diffraction grating:**can be used to measure the wavelength of a monochromatic light source

#### Additional Details:

**Measuring amplitude and period using a c.r.o**- Adjust time-base and 𝑦-gain to achieve a suitable waveform
- Calculate amplitude by finding height in terms of boxes on a grid of waveform and multiplying by 𝑦-gain
- Calculate period by counting boxes of grid occupied by a full waveform and multiply by time-base setting

**Measuring diameter:**repeat measurements in different positions and average- Wear safety goggles/use a safety screen to protect eyes when heating/pouring liquids or handling stretched wire
- Ensure apparatus stable & not easily knocked over by placing weights (e.g. on retort stand) and working on a flat surface
- Use a sand tray under heavyweights and make sure weights don’t fall on your foot
- Keep radioactive substances in a lead-lined container
- To ensure the surface is horizontal, use a spirit level
**Sound experiment:**perform the experiment in a quiet room**Light experiment:**perform the experiment in a dark room- Repeat experiment & determine the average

#### Pressure Experiments Apparatus:

**U-Tube (manometer):**measures pressure difference between two fluids**Bourdon gauge:**measuring the pressure of a gas or liquid**Pump:**can be used to alter the pressure in a container

#### Electrical Experiments Apparatus:

**Variable resistor (rheostat):**can be used to alter voltage/current supplied in a circuit or can be used to keep current constant**LDR:**resistance decreases with increasing light intensity**Photocell:**sensors that allow you to detect light – generate an e.m.f when light is incident

#### Additional Details:

- Use a protective resistor to reduce current
- Switch off currents when not in use so that wires/coil do not overheat
- Use microammeter and galvanometer for small voltages and currents
- When using an ammeter and voltmeter to measure resistance, a power supply is required
**Type of current to use:**- Large current to create a large magnetic field
- Large current to produce measurable e.m.f./voltage
- Small current to reduce the heating effect

#### Magnetic Field Experiments:

**Hall probe:**used to measure magnetic fields- Keep Hall probe at right angles (perpendicular) to the magnetic field by fixing to rule
- Calibrate Hall probe in a known magnetic field
- Repeat experiment with Hall probe reversed and average
- In magnetic experiments, avoid external alternating magnetic fields

#### Falling Bodies & Oscillations Experiments

**Measuring velocity using light gate:**- Measure distance between light gates
- Connect light gates to time loggers
- Calculate the time of fall by using data from loggers – time difference between when the first and second beam is broken

- For experiments with light weights or wind, close windows & switch off the air conditioning to avoid draughts
- For measuring the time period of oscillations, find time for 10 oscillations and then divide
- Use fiducial markers to time oscillating objects
- To measure quantities in an experiment with fast motions, record the experiment with a video camera and playback in slow motion
- In an experiment with an object being dropped, make sure the object released with no/constant velocity. Can use electromagnets or a spring-loaded device
- For falling objects, use a guide to keep motion in the correct direction

An example question 1 solved is provided at the following link:

## Question 2: [Analysis – 15 marks]

This question has a number of parts. For solving this question, you need to have a strong grip on the following things. Using the same paper for explanations:(**May/June 2018 Paper 5 Variant 2**).

### Conversion to linear form:

Firstly, you should be comfortable with transforming ANY given equation to linear form (Y = mX + c). Make yourself familiar with the logarithmic rules to help you in this.

In the example paper, the equation given in question 2 is:

It can be arranged into linear form like this (t is *measured*, hence a dependent quantity, and resistance (nR) is *varied*, hence an independent quantity):

Taking ln on both sides,

Using the power rule of logarithm on the right side, we get,

Comparing this final equation with linear form (Y=mX + c),

This shows that if a graph of ‘t’ against ‘nR’ is plotted, we will obtain a straight line graph passing through the origin (it can then be deduced that ‘t’ is *directly proportional* to ‘nR’)

### Treatment of uncertainties and significant figures:

Secondly, you should be familiar with the treatment of uncertainties and significant figures.

For finding the percentage/absolute/fractional uncertainty, keep in mind the following rules:

- in case of addition / subtraction:
- We add the individual uncertainties of the quantities added or subtracted. Take the following example:

a = 5 ± 0.2 & b = 2 ± 0.3

We are given, c = a + b

Find the absolute uncertainty & percentage uncertainty in c.

c = 5 + 2 = 7

absolute uncertainty in c = 0.2 + 0.3 = 0.5

percentage uncertainty in c = 0.5/7 * 100 = 7.14% (up to 3 sf.)

- We add the individual uncertainties of the quantities added or subtracted. Take the following example:

Note: whatever the case (subtraction or addition), the individual uncertainties are always ADDED never subtracted!

- in case of multiplication / division:
- We add the fraction uncertainties of the involved quantities. Take the following example:

a = 2 ± 0.2 & b = 3 ± 0.3

We are given, c = b/a

Find the absolute uncertainty & percentage uncertainty in c.c = 3/2 = 1.5

fractional uncertainty in a = Δa/a = 0.2/2 = 0.1

fractional uncertainty in b = Δb/b = 0.3/3 = 0.1

fractional uncertainty in c = (Δa/a + Δb/b) = 0.1 + 0.1 = 0.2

absolute uncertainty in c = (Δa/a + Δb/b) * c = (0.1 + 0.1) * 1.5 = 0.3

percentage uncertainty in c = (Δa/a + Δb/b) * 100 = 0.2 * 100 = 20%

- We add the fraction uncertainties of the involved quantities. Take the following example:
- in case powers are involved:
- When powers are involved in the given expressions, we find the uncertainties in the same way as above, with just a small change: we multiply the power with the fractional uncertainty of the value which is raised to that power. For example:

P = I2R

when finding the percentage uncertainty of P, we’ll do it like this:

percentage uncertainty in P = (**2**(ΔI/I) + ΔR/R) * 100

Just see how everything is done exactly the same, except that inclusion of power 2.

- When powers are involved in the given expressions, we find the uncertainties in the same way as above, with just a small change: we multiply the power with the fractional uncertainty of the value which is raised to that power. For example:
- in case of logarithmic uncertainties:
- We are given: a = 2 ± 0.2

log a = log 2 = 0.301

uncertainty in log = log (2+0.2) – log(2) = 0.0414

log (2±0.2) = 0.301 ± 0.041

- We are given: a = 2 ± 0.2

Calculate all the data in 3 significant figures (generally done) or to one s.f. more or equal to the s.f of the raw data.

However, in the case of logarithmic calculations, the number of d.p for the calculated log is the number of s.f in the raw data. Hence for raw data of 3 s.f. the log should be calculated to 3 d.p.

The significant figures of uncertainty are usually ignored in the marking scheme but stick to 1 or 2 s.f.

### Graphs:

Thirdly, make sure you know how to draw the graphs for this question.

The general instructions for drawing graphs are:

- Use small encircled dots or crosses to plot the points.
- Use a sharp pencil.
- If a gradient is to be calculated, draw a triangle and mentioning the points of the vertices on the best-fit line. The hypotenuse should be greater than half the length of the best-fit line.

#### Drawing worst-fit lines:

Once you are done plotting the best-value points, add or subtract the error from the best point, and plot this above or below, or left or right the best-value point, depending on the question.

Join the three points together to form the error bar.

The worst-fit line can then either be the shallowest (*drawn by joining the bottom of the topmost bar, and top of the bottommost bar*) or steepest (*drawn by joining the top of the topmost point’s error bar and the bottom of the bottommost error bar*) possible line that passes through every error bar.

Draw either the shallowest or steepest worst-fit line, NOT both. Both lines should be clearly labeled.

For calculation of error in gradient, calculate the gradients for both lines by drawing triangles with hypotenuses greater than half the lengths of both lines and mentioning the points of vertices on both the best and worst fit lines. Find error by subtracting the gradient of best-fit from worst-fit. All calculations should be to 3 s.f.

Take special care of units and powers of tens. Don’t forget to mention the units along with answers!

This was all about paper 5 of A Level Physics. We really hope it proves useful.

Thanks for the notes. Question: if two values of the same variable are taken (time period of oscillations for example and we are given t1 and t2) what is the procedure for calculating the uncertainty for the average of the variables.

What if I got an anomalous point due to a mistake in plotting, and just ignored the point and drew the best fit line for other points? Will I get 0 for graph? Is it even possible to get an anomalous point in paper 5?

there are no anomalous points in P5, the points are predetermined and a mark is deducted for incorrect plotting.

Very useful link.

Do the worst and best fit lines need to overlap?

Yes

if i write 12×10^4 instead of 1.2×10^5 will i lose marks?

You may lose marks depends on the question and what it requires. But not always. I would suggest the Second one is always better!

should the line of worst fit be a dotted line?

No, you dont need to draw a dotted line. You can just mention that this is the line of worst fit.

Can you kindly please add the method of finding the uncertainty of equations that include trigonometric or logarithmic functions?

wow, very thorough breakdown of the paper 5. Has everything I need to know. Thank you so much for compiling this. I really am grateful.

can we use normal pencil to draw the best fit line and use color pencil to draw the worst fit line??

same question

You only use hb pencils on the graphs in the exam. If you even use a pen or any other colour pencil, dosent matter if your graph is write or wrong, there will be no marks awarded.

nope, Cambridge examiners won’t even check it.