# 翰林学院Alevel Further Math-S进阶数学S辅导

### 翰林学院 Further Math-S进阶数学S辅导大纲

 Topic Subtopics Hours* Homework Expectation algebra Expectation & Variance of a Function of Combinations of Random Variables Expectation & Variance of Sample Mean Poisson distribution Suitability of a Poisson Distribution Expectation & Variance Addition of Poisson Distributions Relationship of Inequalities Poisson Approximation of a Binomial Distribution Normal Approximation of a Poisson Distribution Continuous random variable Probability Density Functions (pdf) Cumulative Distribution Function (cdf) Expectation and Variance Obtaining f(x) from F(x) Distribution of a Function of a Random Variable Geometric & exponential distribution Geometric Distribution Cumulative Probabilities Mean & Variance of a Geometric Distribution Exponential Distribution Mean & Variance of an Exponential Distribution Sampling & Central Limit Theorem Central Limit Theorem Point and interval estimation The Variance Point Estimate & Confidence Interval Percentage Points for a Normal Distribution Confidence Interval for a Population Mean Confidence Interval for a Population Proportion Percentage Points for a t-Distribution Confidence Interval for a Population Mean with a Small Sample Hypothesis tests Null & Alternative Hypothesis Hypothesis Testing with Different Distributions Hypothesis Tests and Confidence Interval Type I and Type II Errors Comparison of Two Means Goodness of fit Chi-squared Test Comparing the chi-square Value Goodness of Fit to Prescribed Distribution Type Contingency Table Regression and correlation Regression Calculating the Regression Coefficient Two Regression Lines Correlation Product-Moment Correlation Coefficient Total

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## Further Math进阶数学相关国际竞赛

AMC10

American Mathematical Competition 10，10年级及以下学生参加，前2.5%可以晋级AIME

AMC12

American Mathematical Competition 12，适合12年级及以下学生参加，全球前5%可以晋级AIME

AIME

American Invitational Mathematics Examination, AMC10和AMC12优胜者参加的数学邀请赛

HiMCM

High School Mathematical Contest in Modeling，美国高中生数模竞赛，历史悠久，每年超千支队伍，Outstanding特等奖不足1%

Euclid数学竞赛

Euclid Mathematics Contest,滑铁卢大学欧几里德数学竞赛，参赛对象12年级学生

Yau Science Awards (Mathematics),每年一届，研究报告的形式参赛。旨在发现有前途的全球华人年轻科学天才。

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