Mathematics and Modelling

Question 1

when you are talking about “per unit” e.g. per litre what is this written as numerically?

Answer 1

the notation for the unit in question to the power of -1

Question 2

What is the most common base for logarithms?

Answer 2

10

Question 3

How do you work out logarithms?

Answer 3

log(X) = Y is like saying 10^Y = X

Question 4

What is the order of prefixes from 10^-9 to 10^9

Answer 4

10^-9 = nano
10^-6 = micro
10^-3 = milli
10^-2 = centi
10^-1 = deci
10^1 = deca
10^3 = kilo
10^6 = mega
10^9 = giga

Question 5

What must you remember to do when applying an operation to a quantity with units?

Answer 5

apply the same operation to the units

Question 6

What must you remember to do if you are converting between different levels of unit (e.g. metres squared to kilometres squared)?

Answer 6

It is not simply multiplying by 1000 to get there, you need to multiply by the power of the type of unit, so you multiply by 1000^2

Question 7

How do you calculate the area of triangle and then a triangular prism?

Answer 7

1/2 x base x height then to get volume multiply by the length of the prism

Question 8

How do you calculate the area of any prism?

Answer 8

Area of face x length or otherwise termed as height

Question 9

How do you calculate the rate of change?

Answer 9

Divide the latter (more recent value) by the former (older) value

Question 10

How do you convert radians to degrees? and degrees to radians?

Answer 10

/pi x 180 degrees

/180 x pi

Question 11

What does the E and the e represent?

Answer 11

E(x) = x10^(X)

e^x

Question 12

How do you calculate density

Answer 12

mass divided by volume

Question 13

what must you always remember to do when calculating density?

Answer 13

Appropriate the units so for example if it is per cm cubed then put cm^-3

Question 14

How do you calculate the vector resultant force and the angle of direction? (step-by-step)

Answer 14

1. Work out x and y coordinates of the initial force and the opposing force
2. Add the x and y values of the coordinates that make up these two forces
3. Pythagoras to work out the longest side (i.e. the changes in x and the changes in y)
4. Carry out inverse trigonometry to work out the angle between the changes in x and y of the total components