Maths Mock 1 Don't Know Flashcards
Give the formula you use when differentiating from first principles
Give 4 properties you need to know about a circle
1) the angle in a semi circle is a right angle
2) a tangent to a circle is perpendicular to the radius of the circle at the point of intersection
3) the perpendicular bisector of a chord will go through the centre of the circle
5) the shortest distance from the centre of the circle to the chord is the perpendicular distance
Give the formula for the cosine rule
How do you know when it’s an ambiguous case and what do you do about it
If the angles don’t up to 180, it’s an ambiguous case. This only happens when you are given 2 sides and the non included angle opposite the long side
Work out 180-x
Give the radian formula for arc length
Give the formula for sector area with radians
Give the rules for finding the second angle on a sin, cos or tan graph
Sin: 180- first angle
Cos: 360- first angle
Tan: First angle+180
Give and explain the formula you can use to test for mutually exclusive events
When this is true, the events are mutually exclusive
What
What are mutually exclusive events
Events that cant happen at the same time
What does a venn diagram look like for 2 mutually exclusive events
What are independent events
This is when one event has no effect on the other
Give and explain the formula to check if events are independent
When this is true, the events are independent
Give the formula for conditional probability
Give the formula for mean in discrete distributions
np
n is the number of trials
p is the probability of success
Give the formula for variance in discrete distributions
np(1-p)
n is the number of trials
p is the probability of success
What does X ~ B(n,p) mean
X is a random variable with a binomial distribution with parameters n and p, where n is the number of trials and p is the probability
Give 4 things that must happen for the binomial probability model to be used
There must be a fixed number of trials
There must only be 2 possible outcomes: success or failure
The trials must be independent
The probability can’t change
What is the null hypothesis test
This is H0
This is a statistical assumption that there is no change to the probability,
H0: p=x
What is the alternative hypothesis
H1
This is a statement that contradicts the null hypothesis. In this case, H1 will be one of the following:
- H1: p≠x (probability has changed)
- H1: p>x (probability has increased)
- H1: p<x (probability has decreased)
What is a one tailed test
Testing for an increase OR testing for a decrease in the probability
What is a 2 tailed test
Testing for any change in the probability
When do we reject H0 and why
When probability<level of significance
Because there is sufficient evidence at the x% level to suggest that….
What is the critical region in Binomial hypothesis tests
The range of values for which you accept H1
What is the acceptance region in Binomial hypothesis trials
The range for which you accept H0
