H2 Math Summary Notes

Pure Mathematics
Unit 1 Inequalities1 Question 
Unit 2 Graphing Techniques7 Questions

Unit 3 Transformation of Graphs2 Questions

Unit 4 Functions6 Questions

Unit 5 APGP & Recurrence Relations6 Questions

Unit 6 Sigma Notation6 Questions

Unit 7 Techniques of Differentiation2 Questions

Unit 8 Applications of Differentiation9 Questions

Unit 9 Maclaurin Series2 Questions

Unit 10 Techniques of Integration6 Questions

Unit 11 Applications of Integration4 Questions

Unit 12 Differential Equations2 Questions

Unit 13 Vectors11 Questions

Unit 14 Complex Numbers6 Questions

StatisticsUnit 15 Permutation and Combinations7 Questions

Unit 16 Probability5 Questions

Unit 17 Discrete Random Variable4 Questions

Unit 18 Binomial Distribution5 Questions

Unit 19 Normal Distribution7 Questions

Unit 20 Sampling and Estimation8 Questions

Unit 21 Hypothesis Testing6 Questions

Unit 22 Correlation and Linear Regression5 Questions
Worked Example 4
In a game, \(3\) green balls and \(7\) yellow balls are placed in a bag. A player draws \(4\) balls at random and without replacement. The number of green balls that she draws is denoted by \(G\). Find the probability distribution of \(G\) and show that \(P\left( G\ge 2 \right)=\frac{1}{3}\). Show that \(\text{E}\left( G \right)=\frac{6}{5}\) and find the variance of \(G\).
Alice scores \(5\) points for each green ball that she draws and Bob scores \(2\) points for each yellow ball that he draws.
Alice’s score is denoted by \(A\) and Bob’s score is denoted by \(B\).
Without finding the probability distribution of the number of yellow balls, find the expectation and variance of \(AB\) if
(a)
Alice and Bob play two separate independent games to decide their scores,
(b)
Alice and Bob decide their score in the same game.
Responses