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You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
Let’s work in the City!
1) How could you model the salary of each offer?
2) What will Paul’s annual salary be in 2025 if he chooses company A?
3) When will Paul’s annual salary reach £60,000 if he chooses company B?
4) Paul plans to stay for eight years in London. Figure out which job offer would be the most interesting for him.
Paul, a young French trader, wants to work in the City (London).
He has applied for a job in two companies, has been interviewed, and has finally been offered a job in both companies. Now he has to choose between the two job offers.
Conditions of the job offer in company A:
Start of the contract : 01/01/ Monthly salary : £ 4,
Each year, on the 1st of January, the monthly salary increases by £60.
Conditions of the job offer in company B:
Start of the contract : 01/01/ Monthly salary : £ 4,
Each year, on the 1st of January, the monthly salary increases by 3%.
You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
Malthus’s theory
Thomas Malthus (1766-1834) was an English political economist who was concerned about what he saw as the decline of living conditions in nineteenth century England. Malthus published «An essay of the Principle of Population » in 1798. He blamed this decline on the rising of human population and the inability of feed resources. According to Malthus, the population will increase by 3% every year and the feed resources will increase by 0. million every year.
Year Population (million) Feed resources (million of people) 1800 10 12 1801 10.3 12.
1802 10.609 12.
1) According to Malthus’s theory:
a) Which kind of sequence P describes the population growth? Give its characteristics. b) Deduce the population in 1830 and in 1850. c) When did the population amount to 30 million?
2) According to Malthus’s theory:
a) Which kind of sequence R describes the feed resources growth? Give its characteristics. b) How many people did the resources feed in 1830 and in 1850? c) When did the resources feed more than 40 million people? Use an algebraic method.
3) Here is a graph extract from Malthus’s essay:
When did what Malthus predicted as « the point of
crisis » occur? Use your calculator.
4) Actually, the following table shows real
population growth in England during the nineteenth
century.
How can you explain such a difference between Malthus’s theory and reality?
http://blogs.isb.bj.edu.cn/fional/thomas-robert-malthus/
Year 1800 1820 1840 1860 1880 1900 Population (million) 10 15.5 20.2 24.5 33 41.
You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
The pig pen
Suppose a rectangle pig pen is 4 feet longer than it is wide and its area is more than 32 square feet. The question is the dimensions of the pen. Let x represent the width of the pen. 1) Using ݔ, give the pig pen length and
area.
2) Explain why ݔ ଶ^ + 4 ݔ− 32 0.
3) Sketch the graph of the function ݔ = ݕ ଶ^ + 4 ݔ− 32 and shade the ݔ-values that satisfy the inequality ݔ ଶ^ + 4 ݔ− 32 0. What could the dimensions be? Pig pen, Source : Haley McCready Outreach and Development Fund http://haleymccreadyfund.com/?m=
The farmer gets more pigs and increases the dimensions of his pen. The pig pen is now 10 feet longer than it is wide and its area is exactly 96 square feet. 4) Explain why x^2 + 10 x − 96 = 0. 5) Solve this equation. 6) What are the new dimensions?
If you have time : Explain how living condition of factory farming animals could be improved.
Factory Farming: Misery for Animals
On today’s factory farms, animals are crammed by the thousands into filthy, windowless sheds and stuffed into wire cages, metal crates, and other torturous devices. These animals will never raise their families, root around in the soil, build nests, or do anything that is natural and important to them. Most won’t even feel the warmth of the sun on their backs or breathe fresh air until the day they’re loaded onto trucks headed for slaughterhouses.
The factory farming industry strives to maximize output while minimizing costs—always at the animals’ expense. The giant corporations that run most factory farms have found that they can make more money by squeezing as many animals as possible into tiny spaces, even though many of the animals die from disease or infection.
Source: People for the Ethical Treatment of Animals (PETA) http://www.peta.org/issues/animals-used-for-food/factory-farming/
You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
The path of a punted ball
When a football player punts* a football, he hopes for a long “hang time”. (Hang time is the total amount of time the ball stays in the air). A time longer than 4.5 seconds is considered good.
The height of the ball in feet after t seconds can be modeled by the following function: ݐ ܽ= ሻݐሺܪ ଶ^ +ݐ ܸ + ℎ
where ܸ is the initial velocity of the ball and ℎ is the initial height of the b all.
Buzzstard.com
We suppose that a punter kicks the ball with an upward velocity of 80 feet per second and his foot meets the ball 2 feet off the ground. The height of the ball is 98 feet after 2 seconds.
1) What is the hang time of the ball? 2) Conclude. 3) How could the football player increase his “hang time”?
- a punt is a kick in which the ball is dropped and then kicked before it touches the ground.
If you have time:
Do you know other sports where the paths of projectiles, as well as their heights over time, can be
modeled by quadratic functions?
Source: The Guinness Book of Records
On September 21, 1969, Steve O’Neal set a National Football League record by punting the ball 98 yards.
You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
Broadway
The director of a famous Broadway theatre notices that the
number of the audience members depends on the price of
the ticket :
If the price is $30, there are 500 persons in the audience.
Each increase of $1 implies a loss of 10 persons.
1) What will the revenue be if the price of the ticket is $32?
2) The director wants to find the best price to obtain the biggest profit.
If n is the number of $1 increases, show that the revenue is: R n ( ) = − 10 n^2 + 200 n + 15000.
What is the best price? And what will the revenue be like for this price?
3) The director wants to earn $15000 or more for each show. In which interval should he set the price of the ticket to reach his goal?
www.pixabay.com
You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
The third royal baby
On Tuesday 16 th^ February 2016, in the library of an American High school, a group of students read the article from IB TIMES:
Then they decided to start the rumour about “the third royal baby”.
The spread of this rumour throughout the school could be modelled by the function: ݊ ሺݐሻ = ଼
ଵାଷଽ ష where ݊ is the number of students who have heard the rumour as a function of time, ,ݐ in days.
1) Assuming that every student at school eventually hears the rumour, determine: a) The number of students in the library who started the rumour. b) The student population of the school. c) How long it will take for the rumour to reach half of the school’s population.
2) This function is represented by the graph below:
a) Explain why the shape of the curve is reasonable in the context. b) Why doesn’t it keep rising exponentially?
3) Complete the table:
Day 1 2 3 4 5 6 7 8 9 Speed of the spread a) Determine the day when the rumour spread the fastest. b) Was this rumour true?
You have to talk for ten minutes about this subject. Which mathematical notion(s) do you recognise? The questions may help you, but answering all of them is not compulsory: you can simply explain a way to solve an exercise, even if you can’t find the solution
Celsius versus Farenheit
Anders CELSIUS Daniel FAHRENHEIT
Felicia, who was born in the United States and Carlo, of Spanish origin are sharing a flat in Paris where they are both studying French over the summer. They don’t use the same temperature scale: Felicia uses Fahrenheit degrees while Carlo uses Celsius degrees. They decide to buy two different thermometers in order to choose suitable clothes each morning: a warm jumper or not… When they leave the flat together at 9.00 am, they both write the temperature of the day on the fridge door. The measures are rounded to the nearest value. Here is what they wrote last week:
Carlo Felicia Monday 7 45 Tuesday 12 54 Wednesday 15 59 Thursday 11 52 Friday 17 63 Saturday 14 57 Sunday 10 50
1) Taking Carlo’s column as X and Felicia’s as Y and using your calculator, give the equation of the regression line to get Y with respect to X. 2) The French weather forecast is predicting 19 °C for the next Wednesday. Convert this temperature into Fahrenheit for Felicia. 3) Felicia tells Carlo that 70 °F is not so hot, what do you think of that?
If you have time: Carlo is planning to visit Felicia next summer. Find the formula to help him convert °F into °C.
