A formula is a recipe or a rule for doing something and it works
every time it gives the relationship between different
quantities. Some formerly a standard formally written down
by Mathematicians and scientists to cover a wide range of the
relationships between different
quantities. Others can be made up such as that for a washing
powder or a magician's memory
trick. More of that later.
Formally, usually use variables and letters instead of numbers,
and that gives the relationship. Let's have a look at.
The formula for the area of a circle A equals π R
squared, where a is the area of the circle.
And R is the radius of the circle.
This formula works every time and shows the relationship.
So we square the radius. We multiplied by pie and it
gives us the area and it will always work.
Imagine we have a circular lawn where the radius is 3 meters.
And we want to know how much turf in square meters that we
need to order so R is equal to 3
meters. So what we're going to do instead of writing are
in our formula. We're going to write the number 3, so A
is equal to Π * 3 squared. Now, it's really important
that we put the multiplication sign back in
as soon as we put numbers back in our formula.
Π * 3 squared is π * 9, giving us 28.3.
So the area of our.
Lawn is going to be 28.3 meters squared, so we're
going to need at least 29 meters squared of turf.
There are many formerly that relates to the area of 2D
objects and also to the volume of 3D solids.
Let's have a look at one. Now let's say we want to find the
volume of a football.
Now football is a sphere, so we want the formula for the volume
of a sphere and that's V equals 4 thirds of Π R cubed.
And let's say that the radius of a sphere are
football is 10 centimeters.
So in our formula to workout the volume instead of writing, are
we going to write 10 centimeters, so V equals 4
thirds π multiplied, again remembering to put the multiply
symbol in and instead of are we writing 10, so 10 cubed?
And if we calculate all of that.
We end up with the volume equaling 4189, so the
volume of the football since the radius was in centimeters
will be 4189 centimeters cubed.
There are many formerly relating to scientific principles.
And we're going to have a look at Newton's second law.
And that law relates force with mass and acceleration.
And the formula is F equals MA mass times acceleration.
Let's imagine a circus artist is going to be fired from the
barrel. And he's going to be fired horizontally
and the mass of a circus artist is 60 kilograms.
And he's going to be fired at an acceleration of 2.5
meters per second squared.
Our formula is F equals MA.
So instead of em, we're going to write 60.
And instead of a, we're going to
put 2.5. But again, because we're putting numbers in.
Instead of the letters, we must remember to put the multiply
sign back in so it'll be 60 times by 2.5.
That gives us 150, so the force on our circus artists is
150 newtons. And Newton is a unit of force.
Let's look at an equation of motion.
Z equals you plus 80.
Fee represents final speed.
You initial speed.
Hey, is acceleration.
Auntie is time.
And imagine that we've got some values for you A&T.
So you.
Equal to 5.
A is equal to two and T is equal to 3.
So to calculate V, the final speed, we're going to
substitute these numbers instead of these letters.
So instead of you, we write 5 instead of a. It's two, we must
write the multiply sign because we're now putting numbers
instead of letters.
And instead of T we write 3.
Now we've got a good opportunity here to look at
our order of operations. If we were to start from the
left and work through to the right, we would be in error
because we should do multiplying before we do
addition. So a quick reminder of our order of
operations with Bob Mass.
Where the B stands for brackets, the apfa powers.
Steve for divide and for multiply.
A for addition.
And S for subtraction.
So multiply comes before addition, so we need to do
2 * 3 before we do the addition, so it's 5 + 6,
giving us an answer of 11.
Let's look at another equation of motion. This time V squared
equals U squared plus 2A S.
Again, the final speed.
You initial speed.
Hey Accelleration.
And S distance traveled.
And imagine we've got a Cliff.
And we throw a stone off the top of the Cliff and we'd like to
know the speed with which it hits the water below.
And the Cliff is 100 meters high.
So we know that you are initial speed.
Is zero 'cause we're dropping the stone from rest at the top?
Our acceleration is the acceleration due to gravity, so
that's 9.8 meters per second
squared. And as the distance that it falls is 100 meters.
So instead of the letters in our formula, we
substitute the numbers.
UO
plus two times a 9.8 times
S 100.
That works out at 1960. Sophie squared is
1960. So to calculate V, the final speed when it
hits the water, we need to square root 1960 and that
gives us an answer of 44.
And because.
Our units are meters per second squared for acceleration in
meters for the distance that it's fallen, the velocity is 44
meters per second.
Another equation of motion is S equals UT plus a half 80
squared. What S is the distance?
You is the initial speed.
T is time.
A accelerations.
And the final to the same as
this one time. Not so much in this time that we have a well.
And we want to find out how deep the well is.
And what we do is we drop a stone down the well.
Use the initial speed of the stone is 0 because we dropped
it. It started at rest.
Let's say it takes 3 seconds for the stone to hit the bottom.
And AR acceleration is that due to gravity of 9.8 meters per
second squared. So instead of writing you T&A in our formula,
we're going to substitute and put these values in.
So S equals you 0 multiplied by T3.
Plus half multiplied by 9.8.
Multiplied by T squared.
So we put all the figures in. Now we can carry out the
calculation. 0 * 3 zero plus half of 9.8 four point
9 * 3 squared is 9.
That gives an answer of 44 to the nearest whole number. And
because our units are meters per second squared and
seconds, the depth of the world will be 44 meters.
Let's have a look at the formula for kinetic energy.
Kinetic energy equals 1/2 MV
squared. Where M represents mass and the is the speed that the
mass is traveling at.
The amount of work done, kinetic energy. Let's compare a sprinter
running and the work that is done by the sprinter running
with that of a truck. So the sprinter is mass 70 kilos.
And the running at a speed of 10 meters per second.
Another truck
has a mass of 2000 kilos.
And that's going forward at a speed of 20 meters per second.
So let's compare how much work they're doing. So for
this printer.
The kinetic energy equals 1/2. The mass is 70.
The velocity is 10 squared.
So we have 3500.
For the truck.
The kinetic energy again is 1/2 instead of the M
we write 2000.
And instead of the V, we've got 20 to be squared.
And that works out at 400,000.
So the kinetic energy of the truck is more than 100
times greater than that of the sprinter.
I haven't written the units down, but for kinetic energy
there jewels.
Let's look now at the formula for the period of a pendulum
where T equals 2π root L over G.
What city is the period of the pendulum?
And that means how long the
pendulum takes. To go from one side of its motion to the
other and then back again. So that's the period.
L is the length of the pendulum.
And she is the acceleration.
Due to gravity.
Which is 9.8 meters per second squared.
Let's imagine we've got a grand father Clock, and the
length of the pendulum L is equal to 1 meter.
So in our formula.
Going to put 2π multiplied by the square root L is 1
meter divided by G is 9.8.
And that gives us 2π. Now, if we calculate 1 / 9.8 and then
square root the answer.
We get 0.319 * 2 and by pie
and we end up with two .007.
So the period of the pendulum to the nearest second is T equals 2
seconds because we've used the units of meters per second
squared and meters.
That was a selection of standard formerly now for the magicians
memory trick. I've got a selection of 30 or so cards
here, each with eight digit numbers on, and if I could have
a helper to select one at random
for me. Now, if you could give me the two digit card
number which is on the top left hand corner, I'll tell
you the 8 digit number on the card number 14 #14.
OK, the 8 digit
number is
314-5943. 7, is that right? That's correct, very
good. OK would like to try another one, just to show that
it's not a fluke. Can you give me the two digit number again
#13 #13? So the 8 digit number
is 29101. 123, is that correct? That's correct, good thank you
very much. Well, I haven't actually memorized all 30
numbers that are here. I'm using a formula, so let's have a look
now at the numbers and show you what I did.
Now the only information I was given was the card number. This
number at the top left hand
corner. So I had to work out the 8 digit number from that card
number. Now the formula I was using was 2 N at
three. What end represents my card number?
So for example, the number 10 if N is equal to 10.
Then I would do 2 times by 10 at three, which gives Me 2 * 10 is
20 at 323, so that gives me my first 2 digits of the number two
and three, and then what I do is add the two digits to get the
third number. SO2AD3 gives me 5.
Then the next number comes from adding the previous 2 digits.
Three at 5 gives me 8.
Five at 8 gives me 13, so I'm going to take the 10 away and
just write down the three.
8 at three gives me 11. Again, I'm going to take the 10 away.
And write down the one three add one gives me four and one add 4
gives me 5, so there's my 8 digit number and all this I was
given was the card number.
OK, let's show you another one. Let's take this one an is 6.
So 6 is going into my formula to workout the first 2 digits, so 2
* 6 + 3 two 6 is a 12 add. Three gives me 15, so the
first 2 digits are one and five. Then I add one and five that
gives me 6 for the 3rd digit I add five and six. That gives me
11. I take away the 10 and one is the next digit.
Six at one.
Gives Me 7 for the next one.
One at 7 gives me 8.
7 add 8 gives me 15. I take the 10 away, so I write down just
the Five and eight, add 5 gives me 13 again. Take the 10 away
and I end up with three.
So there we have a magicians memory trick. Now you can
obviously make it as easy as complicated as you like for your
audience, so you can choose whatever formula you want.
And delight your audience.
So to summarize.
Working with formerly.
What you do is substitute numbers in instead of the
letters and do the calculation. But remember the order of
operations so that you are correct with your final answer.
And that's all you do.