Maths

Question 1

What to remember when you have bearings?

Answer 1

ANGLES TO THE VERTICAL!!!

Question 2

What to remember when calculating the total normal when there is a particle on an angled plane?

Answer 2

Add together the component of the weight that is the normal contact, and then also if there is a rope holding it, then ADD THE VERTICAL FOR THAT AS WELL!!

Question 3

When 2 particles collide, and one is stationary, and then other is in motion

Answer 3

The particle with less momentum stays in motion.

Question 4

What to remember when you are trying to figure out the tension in the chain of a pulley

Answer 4

F=MA

but F = m(pulley) g + 2 x tension in the rope carrying the particles.

Question 5

What to remember when you are trying to figure out the tension in the chain of a pulley, but one is on the floor?

Answer 5

F = m(pulley) g

Question 6

Difference between positive and negatively skewed- and identifying it using a stem and tree diagram

Answer 6

If there are more items at the start - this is positively skewed.

If there are more at the end- this is negatively skewed.

Question 7

For testing hypothesis testing:

Answer 7

If they ask you why you shouldn’t use a specific significance level, find the Probability of less than or equal to 0, and compare to the significance level. Say that the critical region is empty.

Question 8

When finding a question for “reject / accept H0”

Answer 8

Then use the alternative hypothesis, and always use the <= or >=. Never use just < or >.

Question 9

When doing statistical hypothesis testing- and are asked to find a critical region, given a significance level…

Answer 9

, it will always be that he P(X=<> etc) < 0.05.

Question 10

When doing statistical hypothesis testing- and are asked to find the sample size

Answer 10

Usually, they will get you to P(X=0), and then this will mean that the (1- probability) ^ n <> etc.
They should give you this in the question.

Question 11

When doing statistical hypothesis testing- they give you that it is enough to reject H0, etc.

Answer 11

Use the significance level. If they have told you that it needs to be enough to reject H0, then decide whether it would be greater than or equal to the sig. level.

Question 12

Critical regions

Answer 12

When you have a value for the critical region, ALWAYS look at the sign for H1 AND USE THIS SIGN!!!

Also, this is the region in which you can reject H0.

Question 13

Dealing with logs-

Answer 13

If it is to the base x, then to get rid of the logs, you have to multiply both sides by x to the power of something. Doesn’t matter if it’s to thebase 10, 2, or 3.

Question 14

Whenever dealing with binomials

Answer 14

always remember that 2 entries that are the same, will count as only 1. So if you wanted to see how many ways you could get (4,3,3), you would use 3C2, as there are 3 things, and only 2 choices- the 3s become the same.

Question 15

STATS!!!

Always RTFQ carefully- if they ask you what is the probability of something happening

Answer 15

and then the probability of it not happening, then you should just do 1- P!!

Question 16

If they ever link something back to a progression

Answer 16

then think about how you could create or use a formulae to create a sequence. Then, find the a, r or d.

Question 17

Main translations

Answer 17

Reflection
Rotations
Translation
Enlargement

Question 18

How to prove that the velocity vector is perpendicular to the position vector

Answer 18

Calculate the position vector and the velocity vector.
Flip both of them, and say that when they are multiplied together, they are equal to -1.
Then solve for x.
You should get a quadratic equation.
Then, you should find its discriminant, if it is equal to 0, then you can have a solution for when the graph is perpendicular to each other.
If it is less than 0, then no solution.

Question 19

How to prove that the velocity vector is parallel ot the position vector?

Answer 19

Flip them both and say that they are equal to each other.
Then solve.
Get a quadratic, find its discriminant and if it is more than 0, then it has a solution.
If it is less than 0, then no solution.