Maths Week 2020
Survivor Series – Tuesday
Level 3
Questions
What to do for students
1 You can work with one or two others. Teams can be different each day.
2 Do the tasks and write any working you did, along with your answers, in your maths book.
3 Your teacher will tell you how you can get the answers to the questions and/or check your work.
4 When you have finished each day, your teacher will get a surprise word.
5 At the end of the week you will have five words. Put the words together and you will have a complete surprise message!
5 Good luck.
The Americas Cup
Question 1: America’s Cup Facts
Some questions will need access to on-line sites such as Wikipedia.
(a) The first race for the America’s cup was held in 1851. How many years ago was this?
(b) Speed at sea is measured in knots. The AC72 class used in the last America’s cup had a speed of over 40 knots. How fast is 40 knots in kilometres per hour?
(c) How many different countries have won the America’s cup? Name them.
(d)(i) Which of these international trophies is the oldest? The Ashes, The America’s Cup, The Wimbledon Trophy
(ii) How many years older than its nearest rival is this trophy?
Question 2
Switzerland is in the middle of Europe. Although it is landlocked (surrounded by land) it has won the America’s cup twice as it uses Lake Geneva as its home base.
The picture below gives a map of Switzerland and parts of some other nearby countries.
Using Google maps or an atlas will help to answer these questions.
(a) If you start at Lake Geneva, and travel due west, what country will you enter?
(b) What country is north of Zurich?
(c) Due south of the city of Zermatt is the city of ______in the country of ______.
(d) The smallest country in Europe is towards the south east of Zurich. What is its name?
Question 3
The map image below is from Google Earth and shows parts of the city of Auckland as well as a lot of the area at sea where the America’s Cup event will be held in 2021. Overlaid are gridlines showing latitude (horizontal) and longitude (vertical). Latitude and longitude are used to locate positions on maps. Here, they are being measured in degrees (°) and minutes (‘). With angles, a minute has 60 seconds, just like time. When reading coordinates, the first number is always the latitude and the second is the longitude.
On the map, the latitude measurements refer to the horizontal line immediately below the number. The longitude measurements refer to the vertical line immediately to the left of the number.
(a) What is the name of the island at 36° 43’ S and 174° 57’ E?
(b) What is the name of the suburb at 36° 47’ S and 174° 46’ E?
(c) What bay is located at 36° 51’ S and 174° 50’ E?
(d) What is the location of pin A?
(e) What is the location of pin B? Question 4
The name of the yacht Emirates Team New Zealand will use to defend the America’s Cup is Te Aihe. The Māori name Te Aihe means “The Dolphin”. It was chosen because it comes from the whakatauki "Mā te Aihe e tuitui ai i te ngaru moana, mā te Rangatira e tuitui ai i te tangata" ("As the dolphin sows through the seas so does a leader sew people together").
Te Aihe is an AC75 class sailboat, and is capable of travelling up to 50 knots without stopping. A dolphin’s top speed is 14.6 knots, which it can only reach by repeatedly leaping out of the water for up to 1500 m. By comparison, the world record for a human, set by César Cielo in 2009, is 46.91 seconds set over a distance of 100 m.
(a) One knot is approximately 0.5 metres per second. What is the speed of Te Aihe in metres per second?
(b) How much faster than a dolphin is Te Aihe? Give the answer in m/s.
(c) How much slower than Te Aihe is the fastest human? Give the answer in m/s.
(d) How many seconds will it take Te Aihe to sail 100m at its top speed? Question 5: America’s Cup Battleships
Each student chooses a partner. In turn, they try to guess the locations of the other player's ships on the grid. The boats named are all past winners of the America’s Cup (or potential winners, in the case of Te Aihe).
Step 1
Each player draws two 10 x 10 grids, labelled along the sides with letters and numbers as shown below.
Continued on the next page.
Step 2
One player plays for the Team NZ boats, and the other for the World boats. On the left-hand grid the player secretly draws their boats as below. Each boat occupies a number of adjacent squares (1 x 5, 1 x 4, 1 x 3, and 1 x 1) on the grid, horizontally or vertically (diagonal placements are not allowed).
Team NZ World
Aotearoa America
Te Aihe Alinghi
KZ7 USA17
NZL60 USA17
How to play
Players take turns to hit their opponent’s boats by calling out the coordinates of a square (eg D5). The opponent responds with "hit" if it hits a boat or "miss" if it misses. Each time a player scores a “hit”, the player gets another turn.
If the player has hit the last remaining square of a boat, the opponent must announce that a boat has been sunk and give its name (eg "You sank KZ7").
During play each player should record the opponent's shots on the left-hand grid, and their shots on the right-hand grid as "X" for a hit and "O" for a miss.
The first player to sink all of the opponent’s boats wins the America’s Cup!