MATHS IB

Question 1

GOF

Answer 1

Are the outcomes in proportion to expected or is there a bias

Example: flipping a coin (we would expect there to be 50 heads/50 tails)

If we flipped heads 80 times (did this come about by chance or is the coin biased)

Null: The coin is not biased (we should expect even outcomes)

Alternative: Observed data does not follow expected distribution

Question 2

T test:

Answer 2

1 sample t-test:

Null hypothesis:mean of a single population is equal to a specified value

Alternative hypothesis: X1 > X2 OR X2 > X1

Two-sample t-test

Null hypothesis:

would be that the means of two populations are equal

Alternative hypothesis:

would suggest that the true means of the two populations are not equal.

Question 3

How to find the expected value in a chi-squared test?

Answer 3

GDC –> MAT B –> ONLY AFTER DOING THE TEST

Question 4

3sf

Answer 4

3sf

Question 5

How to perform GOF

Answer 5

STAT –> LIST 1 (TYPE IN THE OBSERVED FREQUENCIES) –> LIST 2 (TYPE IN EXPECTED FREQUENCIES LIKELY TO HAVE BEEN CALCULATED)

TEST –> CHI –> GOF –> FIX DF –> EXECUTE

Question 6

Scenario:

They have given a one tailed t-test.

Table:

	      Z  N X Y

If they say that Y is supposedly bigger than X, what does th expression look like

Answer 6

Y > X

They can be switched around

Question 7

Point slope form equation:

Answer 7

y-y1 = m(x-x1)

Point the line passes through (x,y)

Question 8

What is the x intercept and y intercept

Answer 8

X intercept (where y = 0)

Y intercept (where X = 0)

Question 9

Conditions for perpendicular bisector?

Answer 9

90’ right angle formed with the line it cuts through

Bisector –> it cuts halfway through

Question 10

Discrete vs Continuos

Question 11

Find the probability that at least one of the die rolls show white.

Answer 11

Do not forget to look at the first picks of White

Question 12

Conditional Probability equation

Answer 12

P(A|B) = P(A and B) / P(B)

The probability of A given that the probability of B has already occured

Probability that Arsenal win the league given they beat city

Question 13

Law of Total Probability

Answer 13

Pr(W)= Pr(R)⋅ Pr(W∣R)+ Pr(R’ )⋅ Pr(W∣R′ )

Question 14

The probability of the complement of event A is calculated as:

Answer 14

P(A’) = 1 - P(A)

Question 15

All set notation?

Answer 15

see

Question 16

How to construct a probability distribution table?

Answer 16

see

Question 17

How to convert percentage change into common ratio

Answer 17

% divided by 100 + 1

EG: 5.3/100 + 1

Question 18

Is Normal Distribution continuos?

Answer 18

Continuos

Question 19

Is Binomial Distribution discrete?

Answer 19

Discrete

Question 20

P(x=20) =

(Normal Distribution)

Answer 20

0

You can not find the probability of one value in Normal Distribution

Question 21

How to construct a bell curve

Answer 21

SEE

Question 22

What is the Z score

Answer 22

Z = x - mean/SD

How many SD’s are you away from the mean

Question 23

SD and data point relationship

Answer 23

2SD - 95%

1SD - 68%

3SD - 99.7%

Question 24

How to find the sd on a calculator

Answer 24

see

Question 25

How to find the range of a function

Answer 25

GDC –> THINK ABOUT INSIDE THE CURVE

IF THERE ARE TWO CURVES

THE ONE GOING UP (LOW–> HIGH)

THE ONE GOING DOWN LOW –> HIGH)

Question 26

y = -3/2x + 24 to standard form step by step

Answer 26

To convert the equation y = -3/2x + 24 into standard form, follow these steps:

Move the x term to the left-hand side:
3/2x + y = 24

Multiply both sides of the equation by 2 to eliminate the fraction:
3x + 2y = 48

This is the equation in standard form, where A = 3, B = 2, and C = 48. Note that it’s common to write the equation in standard form with integer coefficients, so you may also see this written as:

Question 27

Outliers Test

Answer 27

Q1 - 1.5 X IQR

Q3 + 1.5 X 1QR

Question 28

Different types of sampling

Answer 28

SEE

Question 29

Distribution of Box whisker diagram

Answer 29

see

Question 30

How to calculate Q1 and Q3

Question 31

For integration, how do you calculate the value of h

Answer 31

• H is the horizontal distance between each point

If x axis goes from 2, 3, 4, 5, 6

H = 1

Question 32

Maximum areas of triangles

Answer 32

Split the error diff

ALSO

with the angles –> lower angle bounds for maximum and vice versa

Question 33

Var(X)

Answer 33

Var(X) = np(1−p)

Question 34

range of r
−1

​

Answer 34

domain

Question 35

Simple random sampling

Answer 35

In this method, each individual in a population has an equal chance of being selected as part of the sample. A random number generator or a table of random numbers can be used to select the sample.