Maths Mock 1 Don't Know

Question 1

Give the formula you use when differentiating from first principles

Answer 1

Question 2

Give 4 properties you need to know about a circle

Answer 2

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

Question 3

Give the formula for the cosine rule

Answer 3

Question 4

How do you know when it’s an ambiguous case and what do you do about it

Answer 4

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

Question 6

Give the radian formula for arc length

Answer 6

Question 7

Give the formula for sector area with radians

Answer 7

Question 9

Give the rules for finding the second angle on a sin, cos or tan graph

Answer 9

Sin: 180- first angle

Cos: 360- first angle

Tan: First angle+180

Question 11

Give and explain the formula you can use to test for mutually exclusive events

Answer 11

When this is true, the events are mutually exclusive

Question 12

What

Question 13

What are mutually exclusive events

Answer 13

Events that cant happen at the same time

Question 14

What does a venn diagram look like for 2 mutually exclusive events

Answer 14

Question 15

What are independent events

Answer 15

This is when one event has no effect on the other

Question 16

Give and explain the formula to check if events are independent

Answer 16

When this is true, the events are independent

Question 18

Give the formula for conditional probability

Answer 18

Question 19

Give the formula for mean in discrete distributions

Answer 19

np
n is the number of trials
p is the probability of success

Question 20

Give the formula for variance in discrete distributions

Answer 20

np(1-p)

n is the number of trials
p is the probability of success

Question 21

What does X ~ B(n,p) mean

Answer 21

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

Question 22

Give 4 things that must happen for the binomial probability model to be used

Answer 22

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

Question 25

What is the null hypothesis test

Answer 25

This is H0 This is a statistical assumption that there is no change to the probability, H0: p=x

Question 26

What is the alternative hypothesis

Answer 26

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

Question 27

What is a one tailed test

Answer 27

Testing for an increase OR testing for a decrease in the probability

Question 28

What is a 2 tailed test

Answer 28

Testing for any change in the probability

Question 31

When do we reject H0 and why

Answer 31

When probability

Question 33

What is the critical region in Binomial hypothesis tests

Answer 33

The range of values for which you accept H1

Question 34

What is the acceptance region in Binomial hypothesis trials

Answer 34

The range for which you accept H0