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The theme for this year's Maths Week is Maths At Work. In order to demonstrate the intrinsic beauty and wide application of Mathematics, the River Valley Mathematics Society has organised a series of enriching and fun activities for all students to try out.
As part of the Maths Week programme, we have put up interesting Maths questions around the school for everyone to attempt. If you have no time to try the questions in school, please take a look at the questions listed below. If you know the answer to any one of these questions, just follow these simple guidelines and you stand to win yourself attractive prizes!
Step 1: Put on your thinking cap and try to solve as many questions as possible. Each question you solved correctly earns you points according to the number of stars it contains.
Step 2: Email your detailed solutions to catherine19_cyq@hotmail.com. Please also remember to include your name, gender, class and question number in your email submission to facilitate the collation process.
Step 3: Wait for the winners to be announced by the end of Maths Week 2011. We will send you a notification letter via email by 3 April 2011, so do check you email often!
Now, let’s move on to the questions, solve as many as you can! Good luck!
1. ★★★★Compare different pay scales. Decide if it is better to receive $300 a week or to be paid hourly at a rate of $7.50 per hour. What factors could affect your decision?
2. ★★Groups of campers were going to an island. On the first day 10 went over and 2 came back. On the second day, 12 went over and 3 came back. If this pattern continues, how many would be on the island at the end of a week? How many would be left?
3. ★★★There are about 20 potatoes in a 5 pound bag. A restaurant uses about 2 potatoes per order of French Fries. They charge $0.95 for an order of Fries. How much money does the restaurant take in on a day that they use 400 pounds of potatoes?
4. ★★I have a 5 scoop ice cream cone. Each of my 5 scoops is a different flavor of ice cream. The five flavors are blueberry, chocolate, strawberry, vanilla and bubble gum. You don't know what order my ice cream flavors are from top to bottom. However, here are some clues to see if you can figure out what flavors are from top to bottom:
5. ★★★★★Near the end of a party, everyone shakes hands with everybody else. A straggler arrives and shakes hands with only those people whom the straggler knows. Altogether sixty-eight handshakes occurred. How many other people at the party did the straggler know?
6. ★★★Suppose you have a grassy field, and cows eat grass at a constant rate. Keep in mind, the grass keeps growing continuously. 48 cows can clear all the grass off the field in 90 days. 120 cows can clear all the grass off the field in 30 days. How many cows would be needed to clear all of the grass in 16 days? Round up to the nearest whole cow.
7. ★★★★★A man dies and leave his estate to his sons. The estate is divided as follows:
1st son gets 100 crowns + 1/10 of remainder of estate.
2nd son gets 200 crowns + 1/10 of remainder of estate
…
(n)th son gets 100 ?(n) crowns + 1/10 of the remainder
Each son receives same amount. How many sons were there, what did each receive, and what was the estate?
8. ★★★Line L has a positive slope and passes through the point (0,0). If line K is perpendicular to line L, which of the following must be true?
a) Line K passes through the point (0,0)
b) Line K has a positive slope
c) Line K has a negative slope
d) Line K has a positive X-intercept
e) Line K has a negative Y-intercept
9. ★★★A certain triangle has two angles that have the same measure. If the lengths of two of the sides of the triangle are 50 and 30, what is the least possible value for the perimeter of the triangle?
10. ★★★What would be the least amount of money needed to purchase exactly 21 doughnuts?
a) $5.88
b) $6.68
c) $7.19
d) $7.38
e) $8.40
11. ★★If x is an integer greater than 1 and if y= x+1/x, which of the following must be true?
Ⅰ.y≠x
Ⅱ.y is an integer
Ⅲ. xy> x²
a)Ⅰonly
b) Ⅲ only
c) Ⅰ and Ⅱ only
d) Ⅰand Ⅲ only
e) Ⅰ,Ⅱand Ⅲ
12. ★★★If a+2b is equal to 125 percent of 4b, what is the value of a/b?
13. ★★★ After the first term, each term in a sequence is 3 greater than 1/3 of the preceding term. If t is the first term of the sequence and t≠0, what is the ratio of the second term of the first term?
a) (t+9)/3
b) (t+3)/3
c) (t+9)/3t
d) (t+3)/3t
e) (9-2t)/3
14. ★★★ What is (-1)1+(-1)2+…+(-1)2010 ?
A. -2010
B. -1
C. 0
D. 1
E. 2010
15. ★★★It takes 1.5 hours for Tim to mow the lawn. Linda can mow the same lawn in 2 hours. How long will it take John and Linda, work together, to mow the lawn?
16. ★★★A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is
a) 10
b) 15
c) 2100
d) 8
17. ★★★★A gardener laying out another bed of roses planted 10 rosebushes in 5 straight lines with 4 bushes in each line. How did she do it?
18. ★★★★ While flying over farmland, a pilot notices the rectangular shape of the fields below. She sketches the lines that divide the fields. When she returns to the airport, she wonders how many different rectangles can be formed by the lines drawn?
19. ★Conrad's Taxi Service charges $1.50 for the first mile and $.90 for each additional mile. How far could Mr. Kulp go for $20 if he gives the driver a $2 tip?
20. ★A team of scientists found that there were 4 oak trees for every 10 pine trees. How many oak trees were there if they counted 36 more pine than oak?
21. ★★ Mortimer wants some doughnuts. He is very cheap and likes to save even the smallest amount of money. He found a coupon in the paper for Dunkin' Donuts.The coupon was for $1 off a dozen. This week they are on sale for $3.99 a dozen without the coupon and $.35 a piece if you use the coupon. What do you think Mortimer will do and why?
22. ★ A picture that measures 12 cm by 18 cm is enlarged to 4 times its area. What are the new dimensions?
23. ★★ Find out how much per ounce each of these sells for. Then arrange them from the most expensive to the least expensive.
Gas $1.65 per gallon Snapple $1.29 for 16 oz.
Gatorade $1.59 for 20 oz. Lipton Iced Tea $1.19 for 16 oz.
Ocean Spray $2.54 for 30 oz. Evian Water $1.49 for 9 oz.
NyQuil $8.35 for 6 oz. Pepto Bismol $3.85 for 4 oz.
Whiteout $1.39 for .8 oz. Scope $$.99 for 1.5 oz.
24. ★★A frog jumped on several stones on his way to the pond. He did not land on the same stone twice. The product of all of the stones that he hopped on was 19,635. On which stones did he jump?
25. ★★★★Use each of the digits 1, 2, 3, 4, 5 and 6 once only, in this multiplication problem to make it correct.
? ?
x ?
——
? ? ?
26. ★★★★Decipher the equation:
SEND + MORE = MONEY
27. ★★Your heart pumps about 5 quarts of blood through its chambers every 60 seconds. A swimming pool (20 ft. x 60 ft.) will hold about 65,000 gallons of water. This represents the amount of blood pumped by your heart in approximately how many weeks?
28. ★★★How many times in a 12 hour period does the sum of the digits on a digital clock equal 6?
29. ★★An ice cream stand has 9 different flavors. A group of children come to the stand and each buys a double scoop cone with 2 flavors. If none of the children chooses the same combination of flavors and every combination is chosen, how many children are there? Show how you got your answer.
30. ★★Monday, the Produce manager, Arthur Applegate, stacked the display case with 80 heads of lettuce. By the end of the day, some of the lettuce had been sold. On Tuesday, the manager surveyed the display case and counted the number of heads that were left. He decided to add an equal number of heads. (He doubled the leftovers.) By the end of the day, he had sold the same number of heads as Monday.
On Wednesday, the manager decided to triple the number of heads that he had left. He sold the same number that day, too. At the end of this day there were no heads of lettuce left. How many were sold each day?
31. ★★★★★Eight married couples meet to lend one another some books. Couples have the same surname, employment and car. Each couple has a favourite colour. Furthermore we know the following facts:
1. Daniella Black and her husband work as Shop-Assistants.
2. The book "The Seadog" was brought by a couple who drive a Fiat and love the colour red.
3. Owen and his wife Victoria like the colour brown.
4. Stan Horricks and his wife Hannah like the colour white.
5. Jenny Smith and her husband work as Warehouse Managers and they drive a Wartburg.
6. Monica and her husband Alexander borrowed the book "Grandfather Joseph".
7. Mathew and his wife like the colour pink and brought the book "Mulatka Gabriela".
8. Irene and her husband Oto work as Accountants.
9. The book "We Were Five" was borrowed by a couple driving a Trabant.
10. The Cermaks are both Ticket-Collectors who brought the book "Shed Stoat".
11. Mr and Mrs Kuril are both Doctors who borrowed the book "Slovacko Judge".
12. Paul and his wife like the colour green.
13. Veronica Dvorak and her husband like the colour blue.
14. Rick and his wife brought the book "Slovacko Judge" and they drive a Ziguli.
15. One couple brought the book "Dame Commissar" and borrowed the book "Mulatka Gabriela".
16. The couple who drive a Dacia, love the colour violet.
17. The couple who work as Teachers borrowed the book "Dame Commissar".
18. The couple who work as Agriculturalists drive a Moskvic.
19. Pamela and her husband drive a Renault and brought the book "Grandfather Joseph".
20. Pamela and her husband borrowed the book that Mr and Mrs Zajac brought.
21. Robert and his wife like the colour yellow and borrowed the book "The Modern Comedy".
22. Mr and Mrs Swain work as Shoppers.
23. "The Modern Comedy" was brought by a couple driving a Skoda.
Who likes Violet? And can you find out everything about everyone from this?
We hope that you can appreciate the beauty of Mathematics through our activities! :)
