## Get the most from your friendly calculator

This helpsheet is on the front page in the general resources but I forgot, so I’ll repost it here so that those who are looking for it get a double chance. ENJOY

Your calculator can go in to all Physics exams unless it is one that isn’t allowed. Here are the two most common calculators and how to set them up. Learning these tips will give you the edge in the exam.

No programmable calculators are allowed in the Physics Exam!

## Significant Figures

Watch the video below on significant figures.

Figure 1: The red and brown is called a counting stick and can only measure to 10 cm.

Figure 2: The top part of this metre stick can read to the nearest 1 cm, the bottom to the nearest mm.

When Physicist use numbers it is usually because they have measured something. Significant figures tell us how precise our measurement.

For example a student uses a metre stick to measure the length of a jotter.

If the student measures a jotter with the â€ścounting stickâ€ť (in the top picture in the red and brown) which is marked in 10 cm graduations they will not be able to get a very good value. You would get that the jotter was just under 30 cm long but you wouldnâ€™t be able to say much more.

If the student uses a ruler marked in centimetre marks they could say that the jotter was over 29 cm but less than 30 cm and closer to 30 cm than 29 cm, youâ€™d say it was about 30 cm long.

If the jotter was measured with a metre stick marked in millimetres the jotter could be measured as 29.7 cm long

You need to look at significant figures with rounding which I will cover this week too.

30 cm is one significant figure and means a number between 25 cm and 34 cm which would be rounded to 30 cm. This is how you could record the number if you used the counting stick.

29 cm is two significant figures and means a number between 29.5 cm and 30.4 cm, which would be rounded to 29 cm. This is how you could record the number if you used the metre stick marked in cm only

29.7 cm is three significant figures and means a number between 29.65 cm and 29.74 cm, which would be rounded to 29.7 cm. This is probably the best measurement we should aim to make and to do this we would need a metre stick with millimetre graduations.

29.76 cm is four significant figures and means a number between 29.755 cm and 29.764 cm, it is unlikely that you could measure a jotter to that level of precision as the pages would vary by more than this. You would need a better piece of apparatus than a metre stick to measure this.

## How many Significant Figures?

The simple rule is this: Your answer should have no more than the number of significant figures given in the question.

If different numbers in the question are given to a different number of significant figure you should use the number of significant figures in the value given to the smallest number of significant figures.

### Example

Question: A rocket motor produces 4,570 N (3 sig fig) of thrust to a rocket with a mass of 7.0 kg (2 sig fig). What is the acceleration of the rocket?

The calculated answer to this question would be 652.8571429 ms-2 . However the least accurate value we are given in the question is the value of the mass. This is only given to two significant figures. Therefore our answer should also be to two significant figures: 650 msâ€“2 .

You might not think that this makes a difference, but during the SQA Intermediate 2 paper in 2006 Q25 was written to test significant figures.

## Me and my calculator part 2

I was rather shocked to find that myÂ new S1 class are really lovely but had never heard of the term average. Maybe I ought to have used the term mean, but I don’t think that would make much difference. So out came the calculators and I explained that mean average was all the numbers shared out evenly.
The mean is the average of the numbers.

It is easy to calculate:
add up all the numbers, then divide by how many numbers there are.

IÂ askedÂ student to use calculators to find the meanÂ average of:

600,Â Â  100,Â Â  900,Â Â  450,Â Â  50

The mean average should be 420, the mean must be bigger than the smallest number and smaller than the largest number.

Some students got 2060. These are the ones that didn’t push the equals button between adding them up and dividing by 5 (as there are 5 numbers). So the calculator did the sum

600+100+900+450+ (50Ă·5)=600+100+900+450+ 10=2060

So using your calculator either do

600+100+900+450+ 50= ansĂ·5 =420

or

(600+100+900+450+ 50)Ă·5=420

Now this is OK with nice round numbers but we were using time, so students needed to fix their calculators to prevent calculator diarrhoea! (this is a Mrs Physics term and not a recognised scientific term)

We can FIX calculator diarrhoea (the tendency to write down everything that comes up on the display) using the FIX button on your calculator.

Here goes (I’m using my Casio fx85 or fx83)

Step one: Press the SHIFT and then MODE button on this line under the screen. ThisÂ will bring up the menu.

Step 2: Make sure that the calculator is in line mode, so press 2

Step 3: Repeat step one but this time press the 6 on your calculator which brings up the FIX button. It will then ask you to record how many decimal places you need. This will depend on your values and measurements, but a suggest 2 is a safe bet.

Step 4: Select the number of decimal places you want to use.

Step 5: You’re ready to go.

Step 6: If you want to return to normal. Press the SHIFT followed by the MODE button and then 8 for return to normal. You will have 2 options, 1 (maths mode, good if you want fractions), 2 (line mode, good if you don’t want the fractions)

Try it and let me know how you get on!

## Me and My Calculator copied for N5!

Whilst working with the Police Crash investigator team I had a meeting with Pete Monteith, now known as calculator Pete, whom I decided must be of a similar age to me, as he had the same calculator I’d had at school. The difference was, he was still using his, whilst I was enjoying the delights of an updated calculator.

These days calculators are more technical than the computers I was brought up with. However, I think fewer people know how to use them, which isn’t surprising given the poor quality of the instruction manual. I am on a one woman campaign to get my students to fully utilise this great resource. When I started teaching Physics it used to take two weeks to teach resistance in parallel, now the students are happy in under a lesson- the reason? Their calculators “do as it says on the tin”!

Here are a few things to check out and try. (I am using a Casio, and I know the brighter amongst you would much prefer a Sharp, but I’ve never got on with them). You can draw your own conclusions!

Let’s check out using the calculator how to find total resistance in parallel. The equation is

1/Rt = 1/R1 + 1/R2 + 1/R3… etc.

How can your calculator to do this easily?

Let’s try adding a 7 ohm resistor in parallel with a 28 ohm resistor.

1. Make sure your calculator is in MATHS IO mode. To do this go SHIFT -> MODE->1. I’ll assume you know to turn it on.
2. Press the fraction button, two rectangles one on top of the other with a line between. (see image below)
3. Now type in the first value which will be 1/7 (7 is the resistance but the equation tells us to find 1/Rt we need to put in the value of 1/R1)
4. The up and down arrows allow you to move between the top and bottom parts of the fraction.
5. Now we need to add the 1/28 to this value. Use the right arrow to make sure that you are out of the fraction.
6. Press the + symbol.
7. Then press the fraction button again and add in the 1/28, using the up and down arrows as before.
8. Now when you press equals you ought to get the answer for 1/Rt, in this case 5/28.
9. Remember this is not the answer. This is the value for 1/Rt. We need to find 1/ans to find the value Rt. Luckily we have a button for that too.
10. Press the X-Âą button (see below)
11. When you press the equals this gives the answer 28/5. This is indeed the right answer but the SQA does not like you leaving things as a fraction. So press the S<->D button to reveal the answer 5.6
12. So adding a 7 ohm and a 28 ohm resistor in parallel gives a total resistance of 5.6 ohms.

Yes that really did take nearly two weeks to teach before the age of super calculators.

Remember, your calculator can be a great asset to you during your exam and your career but only if you know how to use it.

Here is another of my favourite buttons, the degrees, minutes and second button.

1. With this button we can easily add times together and convert between time and decimals of time.
2. For example, we all know that 2 hours 30 minutes is 2.5 hours so we’ll just use this to prove it works!
3. With this button, you must remember that you have to enter a number for hours, minutes and seconds even if they are not needed.
4. Enter 2 (for the hours) and press the . Then put in the 30 minutes and press the button again.
5. Now two hours thirty minutes doesn’t have any seconds, but we need to input this into the calculator, so press 0 and the
6. The odd bit, that is easily forgotten, is you now need to press the equals button which reveals 2Â°30Â°0Â°.
7. Press the button and this gives 2.5. Well we knew that but other numbers aren’t so obvious.
8. Try 0 hours, 45 mins and 0 seconds. Yes you ought to get 0.75 hours.
9. But does it work the other way? Yes it does.
10. Type in 0.75 press the equals and then push ;the calculator displays 0Â°45Â°0Â° or 45 minutes.
11. Here’s another use… An AH student wanted to convert 2973s into hours and mins, so press 0Â  Â 0Â  Â 2973Â  = the answer comes up as 0Â°49Â°33Â° which means no hours, 49 minutes and 33 seconds.
12. You can add time too. Try adding 3 hours 49 minutes to 7 hours 25 minutes. This will tell me the time I will be at Euston Station if I catch the 7:25 train to London, which takes 3 hours and 49 minutes. Now I could just check the timetable or I can use the calculator and I rapidly find I will be in London at 11:14am (or I will if the train is on time: and if it is over half an hour late, remember to reclaim your train fare)

My final fun button that is now a favourite of my classes, although they are right to be a little nervous, if they don’t know what they are doing. These tips cut the time to find resultants or components of vectors and their angles. The teaching of SOHCAHTOA (which incidentally I have to spell out using Six Old Horses, Clumsy And Heavy, Trod On Albert because I can’t spell SOHCAHTOA) appears to have gone by the wayside in Maths. But once you know your Pythagoras and SOHCAHTOAs from other Greek Philosophers then this button can save loads of time, but please don’t use it unless you’re sure you know what you’re doing.

I am sure many of you know that a right angled triangle with sides 3cm and 4cm will have a hypotenuse (or large side) of 5cm, but what will the angle be between the X axis and hypotenuse?

For this we want to use the rectangular to polar coordinate buttons.

We want to find the hypotenuse of a 3,4 triangle and the angle it subtends. so therefore we need the Pol button.

1. Press shift and then +, this causes a Pol( to appear on your screen.
2. Enter 4 for along the bottom and then a comma ( which is shift and close brackets) ie shift )
3. Then add the second digit, the 3 up.
4. Close the brackets or just press equals.
5. This gives an r=5, Î¸ = 36.86989765 , which you’d certainly know to round up to 37Â°.
6. If you know the 5cm and the angle, just use the Rec button (shift and the minus).
7. So Rec(5,37) =X=3.99317755, Y=3.009075116, which for a Physicist is fine as 4cm along and 3cm up!

Practice using these buttons and when you need some more handy calculator hints let me know!

To Calculator Pete, if you ever want a race, I’ll time you with your factorial button anytime! When I was at school my Casio beat my friends Texas calculator by about 45 seconds every time I pressed 69 and then the factorial button (!). This then multiplied 69 by 68,by 67 etc. all the way down to 1. Funny, my new super calculator can still only manage factorials up to 69 before running out of digits, but the speed is remarkable. My question to myself, is why did me and my friend Deb Faulder, ever race regularly- as if we expected one day her calculator to beat mine.

Here are some documents to help you through the maths that you’ll need for your Physics. Don’t panic! You can easily learn the maths, but you’ll need to practice it regularly.

Need a piece of graph paper? Download it here multiwidth graph grey

The Relationship Sheet and Data Sheet. Why not make some flashcards using the information and leave them as a pile by the biscuit tin. Before tucking in set yourself a target of how many to get right!

Physics N5 Relationship SheetÂ The relationship sheet you’ll have during your SQA exams. Make sure you’ve got an annotated copy.

Physics N5 Data SheetÂ The data sheet will be on page two of your section 1. It is important that you get used to using it.

basic maths with answer. Here is a document for you to test out whether you can know your prefixes, scientific notation and significant figures.

### Prefixes

 Prefix Symbol Multiple Multiple in full Tera T Ă— 1012 Ă— 1 000 000 000 000 Giga G Ă— 109 Ă— 1 000 000 000 Mega M Ă— 106 Ă— 1 000 000 kilo k Ă— 103 Ă— 1 000 centi c Ă— 10-2 Ă· 100 milli m Ă— 10-3 Ă· 1 000 micro m Ă— 10-6 Ă· 1 000 000 nano n Ă— 10-9 Ă· 1 000 000 000 pico p Ă—10-12 Ă· 1 000 000 000 000

Above is a table of prefixes, which you will commonly find in Physics.
NB THE STANDARD UNIT FOR MASS IS THE KILOGRAM. Do not try changing it to grammes!
Watch out for ms which is not metres per second but milli seconds

### Setting out Mathematical Questions

Always set out maths problems using the structure given below. It may seem to take longer but it will save time in the long run as it makes the question clearer.

1. (Information)- Summarise the question.
2. Change any units that are not standard.
3. (Equation) -Write out the formula.
4. (Substitution) -Put the numbers in.
5. Use the magic triangle to rearrange the formula..
6. (Solution)- Work out the answer.
7. Write out the answer, but not to too many sig fig.
9. (Underline) Underline the answer

Here is the same information but in a little more detail for thoseÂ whom require it.

1. Information– Summarise the question by writing down what you know from the information given. Use the letter that goes with the quantity and this will help you be able to work out the correct formula. Don’t forget at this point to ensure that all units are in their basic form and you are using SI units, such as metres, ohms, Grays, NewtonsÂ etc. The only exceptions are km/h and those involving half life that can have any units of time. There might be a few others, but you can tell me what they are! Basically it is vital you learn the list of Quantity Symbol unit and unit symbol and know the difference between these.
2. Equation â€“ write down the equation as it occurs in the data sheet. Do not attempt to rearrange it. At National 4 there shouldnâ€™t be too much rearranging. At N5 there could be. The one mark is for copying down the correct equation, so why throw this away, when it is one mark in the bag for sure! After you’ve summarised the information it should be easy to select the correct equation.
3. Substitution â€“ put the numbers into the equation as they appear in the formula: just like in football you’re taking off one player (the letter) and replacing it with a number!
4. Solution â€“ work out the answer. You are ALWAYS allowed to use a calculator. If you are not good at knowing which number dividesÂ  into which, then turn on maths (see blog post) and add it in as an fraction equation.
5. Units– you will need to use the correct units so will need to learn these. No, or wrong, units =Â no mark for the answer, i.e. you might as well have not bothered working out the answer if you don’t know the units, they’re that important.
6. Underline â€“ underline, with 2 lines, the answer to make it clear what your final answer will be.

A little out of date, maybe he’ll update it for the three mark question

### Using the exp / Ă—10x button

The speed of light in air is 300 000 000 ms-1 (fast) We will use this number loads of times over the nextÂ year. It is a big number and must be entered carefully into your calculators.
300 000 000 means 3 Ă—108 or 3 Ă—10Ă—10Ă—10Ă—10Ă—10Ă—10Ă—10Ă—10 THIS IS NOT THE SAME AS 38 WHICH EQUALS 6561

There are various ways of putting this number into your calculator.
1. Obviously you can do 300 000 000
2. you can use the xy or yx Here you would do 3Ă—10 yx 8. This should give you the correct answer.
3. The EASIEST WAY IS USING THE exp / ee/ 10x button. Here you go 3exp8 or 3ee8 or 3Ă—108 PLEASE NOTE. The exp / ee/ 10x button meansÂ  1Ă—10x . DO NOT ADD TOO MANY 10S ON HERE!

###### Happy Counting!

Q: What happened to the plant in math class?
A: It grew square roots.

Q: How do you make seven an even number?
A: Take the s out!

Q: Why should the number 288 never be mentioned?
A: It’s two gross.

Q: Why is a math book always unhappy?
A: Because it always has lots of problems.

Q: Why did I divide sin by tan?
A: Just cos.

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