Summer Assignment 2017-2018

Course Title: IB Math Studies

Teacher Name: Nevin Jaffer

Teacher contact information: nevin.jaffer@apsva.us

Purpose of Assignment: The following summer assignment is designed to prepare you for the forthcoming IB Math Studies course. The IB Studies course is rigorous and fast paced and has a lot of content to cover before the exams in May 2017. This summer assignment contains content that has been covered in previous Algebra classes but must be mastered before entering IB Math Studies.

Estimated time to complete the assignment: On an average it will take 5 hours to complete the assignment.

Due date and Method of assessment: All completed problems should be turned in on the first Monday of school. It will be graded as a homework assignment.

Instructions for Assignment: Part I: Complete the following problem sets below: (see the problem sets) Do ALL your work on a separate sheet of paper. Show ALL your work where possible, for full credit.

Do review set 1A pg. 35, 36 # 1-12 all Do review set 1B pg. 36 #1-12 all Do review set 2A pg. 70 #1-11 all Do review set 2B pg. 71 #1-11 all Do review set 2C pg. 72 #1-11 all Do review set 3A pg. 89-90 #1-10 all Do review set 3B pg. 90 #1-10 all Do review set 4A pg. 124 #1-12 all Do review set 4B pg. 125 #1-13 all Do review set 4C pg. 126 #1-13 all

You will require the use of a TI-83 calculator to successfully complete the assignment.

Textbook: Haese Mathematics, Mathematics for the international student, Mathematical Studies SL, third edition. (If needed, this book is accessible online on the web)

PART II: IA (Internal Assessment Project) Readiness –Choosing a topic (see PACKET for topic ideas) and FORM AYou should start thinking of a creative and serious idea for your Internal Assessment (IA) Project (refer to the materials attached for some ideas). This packet includes: IBO online sites for project ideas, Assessment Details and Materials to assist you in choosing a topic for your IA.

Fill out the “Initial Planning” Form A document, which is after the problem sets

Turn in Form A (Part II) along with the above problems from Chapter 1, 2, 3 and 4. Part II of the assignment (FORM A), is worth 20 points and is also due the first day of school.

About the IA The IA is a piece of written work which will be based on your personal research from a wide variety of topics including, but not limited to investigations, applications, statistical studies and surveys. This IA will be done during the course of the year. The project is an independent research and data gathering project for which you will collect, prepare, organize, analyze, and evaluate data. The project is an integral part of the course and will count as 20% of your final IB grade.

During the summer however, you must come up with a project idea (topic) you wish to pursue. Refer to the attached packet to peruse through some ideas of IA topics. Write down your idea on Form A. Find a topic which interests you and which will be exciting to work with. Return the completed Form A with your homework.

Thank you.Have a brilliant Summer! Looking forward to seeing you in SeptemberMrs. Jaffer

Please note that this whole assignment is also accessible on my WL school website under Nevin Jaffer.

PROBLEM SETS FROM TEXTBOOK (Part1)

IB Math Studies Internal Assessment INITIAL PLANNING FORM A SUMMER ASSIGNMENT PART II

This should be completed and returned to me.

Name:

Area of interest:

Reason for choice:

Question or Hypotheses:

Method of Data Collection (interviews, observations, questionnaires, websites, internet etc…)

Sample IA topic ideas which have been done and other areas of interestPlease read all the following and think about a project idea you want to explore. Fill out the form above after reading.

Secondary data sources:1) The Census at School website is a fantastic source of secondary data to use.  If you go to the random data generator you can download up to 200 questionnaire results from school children around the world on a number of topics (each year’s questionnaire has up to 20 different questions).  Simply fill in your email address and the name of your school and then follow the instructions.2) If you’re interested in sports statistics then the Olympic Database is a great resource.  It contains an enormous amount of data on winning times and distances in all events in all Olympics.  Follow links at the top of the page to similar databases on basketball, golf, baseball and American football.3) If you prefer football, the the Guardian stats centre has information on all European leagues – you can see when a particular team scores most of their goals, how many goals they score a

game, how many red cards they average etc.  You can also find a lot of football stats on the Who Scored website.  This gives you data on things like individual players’ shots per game, pass completion rate etc.4) The Guardian Datablog has over 800 data files to view or download – everything from the Premier League football accounts of clubs to a list of every Dr Who villain, US gun crime, UK unemployment figures, UK GCSE results by gender, average pocket money and most popular baby names.  You will need to sign into Google to download the files.5) The World Bank has a huge data bank – which you can search by country or by specific topic.  You can compare life-expectancy rates, GDP, access to secondary education, spending on military, social inequality, how many cars per 1000 people and much much more.6) Gapminder is another great resource for comparing development indicators – you can plot 2 variables on a graph (for example urbanisation against unemployment, or murder rates against urbanisation) and then run them over a number of years. You can also download Excel speadsheets of the associated data.7) Wolfram Alpha is one of the most powerful maths and statistics tools available – it has a staggering amount of information that you can use.  If you go to the examples link above, then you can choose from data on everything from astronomy, the human body, geography, food nutrition, sports, socioeconomics, education and shopping.

Example Maths Studies IA Investigations:Some of these ideas taken from the excellent Oxford IB Maths Studies textbook.Correlations:1) Is there a correlation between hours of sleep and exam grades?Studies have shown that a good night’s sleep raises academic attainment.2) Is there a correlation between height and weight?The NHS use a chart to decide what someone should weigh depending on their height. Does this mean that height is a good indicator of weight?3) Is there a correlation between arm span and foot height? This is also a potential opportunity to discuss the Golden Ratio in nature.4) Is there a correlation between the digit ratio and maths ability?Studies show there is a correlation between digit ratio and everything from academic ability, aggression and even sexuality.5) Is there a correlation between smoking and lung capacity?6) Is there a correlation between GDP and life expectancy?Run the Gapminder graph to show the changing relationship between GDP and life expectancy over the past few decades.7) Is there a correlation between numbers of yellow cards a game and league position?Use the Guardian Stats data to find out if teams which commit the most fouls also do the best in the league.8) Is there a correlation between Olympic 100m sprint times and Olympic 15000m times?Use the Olympic database to find out if the 1500m times have go faster in the same way the 100m times have got quicker over the past few decades.9) Is there a correlation between sacking a football manager and improved results?A recent study suggests that sacking a manager has no benefit and the perceived improvement in results is just regression to the mean.

10) Is there a correlation between time taken getting to school and the distance a student lives from school?11) Does eating breakfast affect your grades?12) Is there a correlation between stock prices of different companies?Use Google Finance to collect data on company share prices.13) Does teenage drinking affect grades?A recent study suggests that higher alcohol consumption amongst teenagers leads to greater social stress and poorer grades.14) Is there a correlation between unemployment rates and crime?If there are less work opportunities, do more people turn to crime?15) Is there a correlation between female participation in politics and wider access to further education?16) Is there a correlation between blood alcohol laws and traffic accidents?17) Is there a correlation between height and basketball ability?18) Is there a correlation between stress and blood pressure?19) Is there a correlation between Premier League wages and league positions?

Normal distributions:1) Are a sample of student heights normally distributed?We know that adult population heights are normally distributed – what about student heights?2) Are a sample of flower heights normally distributed?3) Are a sample of student weights normally distributed?4) Are a sample of student reaction times normally distributed?Conduct this BBC reaction time test to find out.5) Are a sample of student digit ratios normally distributed?6) Are the IB maths test scores normally distributed?IB test scores are designed to fit a bell curve. Investigate how the scores from different IB subjects compare.7) Are the weights of “1kg” bags of sugar normally distributed?Probability and statistics1) The probability behind poker games2) Finding expected values for games of chance in a casino.3) Birthday paradox:The birthday paradox shows how intuitive ideas on probability can often be wrong.  How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? Find out!4)  Which times tables do students find most difficult? A good example of how to conduct a statistical investigation in mathematics.5) Handshake problemWith n people in a room, how many handshakes are required so that everyone shakes hands with everyone else?

Probability and statistics1) The probability behind poker games2) Finding expected values for games of chance in a casino.3) Birthday paradox:The birthday paradox shows how intuitive ideas on probability can often be wrong.  How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? Find out!4)  Which times tables do students find most difficult? A good example of how to conduct a statistical investigation in mathematics.5) Handshake problemWith n people in a room, how many handshakes are required so that everyone shakes hands with everyone else?

Other areas of interest