Pure Mathematics
Mathematical Techniques,Proof,
Mathematical Thinking
The Kangaroo Problem
PRIZE
Mathematician Kangaroo’s Solution
,...32
31,
16
15,
8
7,
4
3,
2
1
Engineer Kangaroo’s Solution
0.5, 0.75, 0.875, 0.938, 0.969, 0.984, 0.992, 0.996, 0.998, 0.999, 1.000
DecisionMathematics
Finding techniques for solving problems
Solving Problems Involving Networks
A Beautiful Mind
The story of John Nash
The Handcuffs ProblemThe Handcuffs Problem
Statistics
Reaching conclusions from data
Are girls more intelligent than boys ?
OR
Are boys more intelligent than girls ?
Stage 1
Select a Random Sample of 3 girls
Select a Random Sample of 3 boys
Random Sample
Stage 2
Carry out a suitable test to compare the two samples.
We will use 15 mathematical questions.
Question 1
Make the largest possible three digit number.
Question 2
Make the smallest possible three digit number.
Question 3
Make the largest possible three digit even number.
Question 4
Make the smallest possible three digit odd number.
Question 5
Produce the number zero.
Question 6
Produce the number 3.
Question 7
Produce the number one.
Question 8
Produce a number between zero and one.
Question 9
Produce a number between one and two.
Question 10
Produce the number one without using a fraction.
Question 11
Produce the 13th square number .
Question 12
Produce the 14th square number .
Question 13
Produce the 31st square number .
Question 14
Produce the numbernegative three.
Question 15
Produce the number that is nearest to 200.
Stage 3
Analysis of the results
Can we say that X are more intelligent than Y ?
Assume that males and females are equally intelligent.
Then the probability that a female
answers any question first is .
You could then generate a tree diagram.
2
1
M
M
M
M
M
M
MF
F
F
F
F
F
F
Tree Diagram for Three Questions
Table of Probabilities
P(15) = 0.0000 P(7 or more) = 0.6964P(14 or more) = 0.0005 P(6 or more) = 0.8491P(13 or more) = 0.0037 P(5 or more) = 0.9408P(12 or more) = 0.0176 P(4 or more) = 0.9824 P(11 or more) = 0.0592 P(3 or more) = 0.9963P(10 or more) = 0.1509 P(2 or more) = 0.9995P(9 or more) = 0.3036 P(1 or more) = 1.0000P(8 or more) = 0.5000 P(0 or more) = 1.0000
So on the basis of this sample we conclude that ...
Mechanics
Applying mathematics to statics and dynamics in the real world
Which way will the bike move ?
Which way will the drum move ?