1
Table of Contents STORY START
3
CHAPTER 1
4
NORTH AMERICA -1-2-3-
4 4 8 10
CHAPTER 2
15
SOUTH AMERICA -1-2-
15 15 17
CHAPTER 3
21
AUSTRALIA -1-2-3-4-
21 21 25 26 27
CHAPTER 4
30
ASIA -1-2-3-
30 30 33 35
CHAPTER 5
36
ANTARCTICA -1-2-3-4-
36 36 38 39 40
CHAPTER 6
41
AFRICA -1-2-3-4-
41 41 42 45 48
CHAPTER 7
52
EUROPA -1-2-3-4-
52 52 53 54 55
2
Story start Today we are invited by Math Expert. We are going to the tropical waters of the Atlantic Ocean. This journey will be not only for fun, we need to guess some riddles. It will not be difficult for you. English Expert will ask the riddles. -What is the name of this wonderful land? -asked Math Expert. English Expert started to explain in details: - Christopher Columbus discovered our island in 1492. If you are eager to find out the name of our island that was discovered by Christopher Columbus as one of the first ones, you should solve these tasks: 4 2 3 1 1)
125.34 + 11.534 =
2)
2.526 – 1.9 =
3)
7.25 – 3.263 =
4)
6.2 – 1.899 =
Keys: 142.8 – G; 61.32 – B; 0.626 – U; 3615.5 – O; 338 – P; 3281.3 – E; 3.618 – M; 136.874 – A; 3.987 – B; 95.76 – T; 4.301 – C; 4.62 – I - You have arrived to our land from the North. Do you know the name of the sea, which washes our island from the South? -asked English Expert. 514463217 1)
724.1*5 =
2)
4.38*14 =
3)
0.315*306 =
4)
16.9*30 =
5)
0.074*55 =
6)
1.46*105 =
7)
36.24*0.2 =
Keys: 153.3 – I; 61.32 – E; 7.248 – N; 3620.5 – A; 507 – R; 3281.3 – S; 3.618 – F; 137.874 – U; 3.989 – M; 96.39 – B; 5.301 – K; 4.07 - C
3
Chapter 1 North America -1After visiting some of the beautiful Caribbean islands Mr. Quick and Calculator 300 decided rent a yacht and sail north. 'Bring your sense of adventure and get ready to set off on our trip!' - said Mr. Quick to Calculator 300 and they began their voyage. 'It is a pity that we have not enough time to visit the whole continent so we have to choose some best known places' - Calculator 300 said 'I have an idea! Let's visit one of the biggest city, the highest mountain and the lowest place there' - Mr. Quick answered on second thoughts.
Finally they reached New York - not only the largest city in the United States but one of the most amazing cities in the world. If you solve all these math exercises, you can find the touristic place where they are right now. 6x + 5 = 35 10x + 12 = 5x + 27 3x - 35= -2x + 64 + 1*1 1= canyon, 2 = beach, 3 = of, 4 = grand, 5= statue, 6 = park; 7 = virginia, 8 = york, 9 =valley, 10 = national, 11= bridge, 12 = new, 13 = death, 14 = las, 15 = golden, 16 = los, 17 = vegas, 18 = gate, 19 = angeles, 20 = liberty.
'Look, the Statue of Liberty! This monument was a gift to the city of New York from the people of France - Mr Quick explained 'Do you know that in 1626, the Dutch purchased Manhattan Island from the Lenape Native Americans?' - English expert asked Yes, but first the name of this city was different. It was not New York but...
Â
4 Â
To know the name solve the puzzle you find below. Arrange results from the smallest to the highest with letters connected with them. By doing that you'll get the earlier name of New York.
15 ⋅ 0.165 = 0.01 ⋅ 0.101 = 2.35 ⋅ 8.5 = 58.6 ⋅ 9.456 = 99.9 ⋅ 6.6 = 69.69 ⋅ 6.9 = 85.5 ⋅ 4.8 = 57.58 ⋅ 2.2 = 999.8 : 0.2 = 58.78 : 0.02 = 102.1 : 0.5 = 2120.13 : 3 =
E N W E R T S A M A M D
After seeing the beautiful statue in New York City. They crossed the border for a while, and travelled to the capital of Canada:..... 5=o 3=a 7=t 9=w 25x=125 2 X =49 38.5-183 2 X =9 7+87-85 63:21 Back in the USA they wanted to see a beautiful piece of nature so they went to Yellowstone. They saw several pretty things like animals, geyser and a vulcano. It was super fun to be there and educative! But the coolest part was.... 55126*561= 5*5*5*5*5*5*5*5*5*5*5= 97813+465721= 838160/5= 56/2= 36472+6247= 89765-4321=
Solutions 48 828 125=A 94 444 =O 42 719 =N 28=C 4444 = E 1 029 255=L 30 925 686=V 167 632=U
5
If you want to know the name of the tallest point on the continent we visited solve each problem by working from left to right. When you finish a problem, locate the answer in a box below, then write the word above the answer and you will find out the name of this place.
Take 6.34 → Add 0.36 → Multiply by 34 → Divide by 17 Take 27.2 → Multiply by 0.8 →Subtract 7.08 → Add 5.22 Take 84.55 → Divide by 5 → Add 6.81 → Subtract 4.63 Take 69.3 → Subtract 48.8 → Divide by 5 → Add 14.7 Take 0.945 → Add 99.45 → Divide by 5 → Subtract 4.359 Take 981.9 → Divide by 9 → Add 64.9 → Divide by 6 Take 34.44 → Add 4.04 → Multiply by 0.4 → Add 4.048 Take 9.6 → Multiply by 60.9 → Add 3.42 → Subtract 575.76
19.09
19.44
13.4
18.8
15.72
29
= = = = = = = =
12.3
K Y M I N L C E
19.9
After visiting so cold place in Alaska they continued their trip and went to California. At 280 feet (855 meters) below sea level in Death Valley National Park is the lowest point in this continent.
After seeing al of the wonders of nature they went back to one of the US’ big cities. San Francisco is a lively town and there are many people that come to visit a great piece of architecture. It’s red, it’s big and you can drive on top of it, it is… √49 2x+3=5 2*2*2*2= 21*21 196/14= 7x+15=50 2000*2000= 6x+60=120 2100-999= 12*12*12*12= 4000-555= Calculate the exercises. The results of the excercises are letters you can find in the legend! Don’t forget, put them in order! The outcome is red, big and you can drive on it. O=20 736; G=7; L=3445; E=441; N=1101; A=5; R=10; D=4 000 000; T=1; B=14; I=16
6
To know the name solve the riddle, draw a straight line between each fraction on the left and an equivalent fraction on the right. Each line will go through one number and one letter. At the bottom, write the letter on each line below the number.
1
Â
2
3
4
5
6
7
8
7 Â
-2Mr. Quick and Calculator 3000 arrived in the next city is in the North of USA by plane after a four hours trip. They saw the city from the plane and it was beautiful and very big. — There was a very important film with the name of this city –said Mr. Quick-. Playing the next game you will have the name. Jumping in the alphabet Example: +3 means 3 jumps to the right -2 means 2 jumps to the left
a b c d e f g h i j k l m n o p q r s t u v w x y z After doing the next operations jumping, you will get the name of the city (at the beginning you are on a) +16-8+1+3-11+3+1+7+4-8+1-8 City __ __ __ __ __ __ __ __ __ __ __ __
— Mr. Calculator 3000, do you know the name of an important scientist that was born and worked in this city? The next riddle will give you the answer. Factorize the numbers and complete: 8=2
□
Find the numbers you put in the box above in the grid below
0
5
8
6
1
2
6
3
4
0
9
8
1
9
7
9
8
Take the letter in the same cell as the number above a
r
l
p
j
c
n
e
k
m
v
w
s
x
t
g
Do the same with these numbers: 9=3
□
16=2
□
27=□
25=□
2
49=□
2
3
Write the letters that match with the numbers to get the name of the scientific 8=2
□
9=3
□
16=2
□
27=□
3
25=□
2
49=□
2
Letters
— I met this scientist once –said MR. Calculator 3000- He told me that he invented the first computer in the world with John Mauchly. The name of that computer is hidden in the boxes below.
Shades the cells corresponding to each fraction D
F
H
K
E
U
N
I
V
Z
A
C
9
-3After this trip they wanted to have a little more fun in Las Vegas, there are a lot of big buildings, fountains, hotels and even a replica of the Eiffel tower. After a while they realised: “What happens in Vegas stays in Vegas!” So they went to the most famous thing in Vegas the ….. (solve this rebus)
+ -h
+
-d and -saur
A couple days later they went to the city of movies: Los Angeles. They saw the walk of fame, the beach and so much more. And when they arrived in Hollywood they met Jennifer Lawrence. She thought that they were so cool that she asked if they wanted to play along in the movie, called… Red= ck; Orange= j; Green=in; Blue=ay; Purple=g; Yellow= mo; 9=yellow; 8=orange; 1=purple; 5= red; 3=green; 2=blue Hint: It is the title of 3th film from a famous trilogy.
After this amazing expirience they went near another country, it’s called Mexico. There was an big event going. It’s colourful, it’s beautiful and it’s super fun! During this event people like to dress up, it’s …... 15 * 2,4= 2,6*45= 45:25= 349- 173= 92:23= 2x+5 =9 55+62= 86-12 :2= c= 36; y=69; a = 117; r= 1,8; n=176; h=96; i= 4; v=2; a= 117; l= 80; q=0.218568; u= 33333; p=6
10
After this festival they went to Texas. This state is famous for the western movies that were made here and these movies were usually about... This is braille-writing. The braille-alphabet is given. Try to find the people who live there.
They are called:
When they left the friendly people of Texas and were on the road, they suddenly saw a sign saying: “Disney World 40 miles.” They got really excited and wanted to go to this huge amusement park. There were many attractions like a ferris wheel and and many fastfoodtrucks but the most amazing part was the …..
When they moved on, it was very hot! So when they came in Virginia they wanted something that was sunny and refreshing. So they went to…
11
The number you find when you solve these exercises is the number of which letter it is in the alfabet: 1=a, 2=b, 3=c… etc. 6x + 7 = 139 3^2= 144/8= v49= 3^2= 2x + 4 = 32 3^2= 1^1= Before they went back to New York, they made a last stop in the most important building of the entire USA. They went to the …. -Caesar code
Znk cnonk nuayk
12
English Expert invited Math Expert to visit the storage of fruit and vegetables. The trip continued here. -Do you know, -asked English Expert, -that there are fruit- travelers? Many of them travelled very far by the sea. 1) 0.4+0.3
2) 0.72-0.32
3) 6.5-3.3
-0.2
*4
:4
+1.5
+4.8
*6
4) 0.32:4
5) 1.1 +7.9
6) 2.2 – 1.6
+0.11
:9
*4
*3
-0.4
+2.8
7) 0.09*4 +0.44 :5
0.57 - pineapple 5.2 - tomato 0.16 - sunflower 2 - pumpkin 0.6 - pepper 4.8 - corn 6.4
–
potatoes
13
-Guess, what is the homeland for these plants. The keys for this crosswords will be the parts of the world where these vegetables and fruit came from.
4) 6) 7) 5) 1) 3) 2)
-I want you to ask the question which is connected with the Sargasso Sea. -I have been several times there, - Math Expert interrupted English Expert. -This is the sea without shores, which is found in the Atlantic Ocean and makes a part of it. Every ship, which travels from Europe to the Central America, should cross the Sargasso Sea. This sea is also called so because its surface is covered by the huge amount of the algae-Sargasso. -But now-the next riddle. -said English Expert. -This sea is also famous for the spawning place of one also in Latvia well-known fish. It travels thousand kilometers to reach the Sargasso Sea. When the small fish hatch from the eggs they travel form the Sargasso Sea to Europe. These fish can be found not only in the Baltic Sea but also in Latvian rivers. The fish eat and grow there in order to make the long journey as their parents did.
3421 1) 2) 3) 4)
2.53:11 = 75.5:5 = 13.2:24 = 120.03:15 =
Keys: 15.01 – R; 8.002 – R; 0.505 – P; 0.023 – D; 0.55 – G; 15.1 – I 8.02 – A; 6.41 – K; 6.041 – T; 0.23 – G.
14
Chapter 2 South America -1Mr Calculator and Mr Quick went on a new journey - to South America! -English Expert, in my opinion, there are just jungles in South America. There are probably only the natives who live there. - said mister Quick. - Are you kidding? Firstly, South America is also famous for its Andes - the most extended mountains in the world - and the Atacama Desert - the driest place on Earth. It is also a modern continent with a population of 837 million people! - Wow! And how many countries are there in South America? -Let’s find it out! You need to fill in a pyramid of addition – put the "bricks" with a common side and write the answer in the "brick" on the top! Several numbers have been already given! The answer is in the green "brick"!
-17
-7
43 3
1
14
- Wow! What is the area of this continent then? - asked Mr. Quick. If you want to find it out, do this simple operation: 249 907 952 : 14! - Do you know what place the continent of South America takes among the continents ? - Asked English Expert - I know it! –said Mr Calculator 300 – If you do my task, you will know! 5
5
2
(32937 – (-43 / (-43 )) – (-54) ) [3373-12336] - Well, I think we should get acquainted with the cuisine of South America.- offered Mr Calculator 300
15
And I have prepared information about some dishes! – was glad English Expert – Just a moment ... Oh, that's a bad luck! The names of the dishes have messed up with their descriptions! Let’s help English Expert! Join the expression and the answer! -1653*(-5) Itapoa
-562*265 Chorizo
-96*(-6)*(-3) Churrasco
-859*(-35)*1 Chinhuine
1*(-1)*1*(-5)*1 Carapulcra
(1)*(1)*(-1)*(1)*(5) Mate
-1728 Cubes of meat roasted on coals
8265 Crab Pudding
-5 Strong Tea
30065 Roast beef intestine
5 Spicy soup
-148930 Long sausage
potato
- Thank you so much, my friends! - said English Expert. - And now I have one wish! No matter what, I want to see capybara alive!
-Who? - stared Mr. Calculator 300 and Mr. Quick - Capybara. It is the largest rodent in the world, which is found only in South America! You know what, let's draw it on the coordinate plane! Here are the coordinates of capybara! Join the dots! (7;0),(6;-4),(7;-7),(5,5;-7),(5;-6),(5;-3),(4;-3),(1;-4),(-2,5;-4,5),(-2,5;-5,5),(-1;-7), (-2,5;-7),(-4;-4,5),(-4,5;-5,5),(-4,5;-7),(-6;-7),(-6;-6),(-7;-4,5),(-8;-3),(-8;1),(-7;3), (-5;4),(-3;4,5),(0;4),(2;4),(4;5),(6;5,5),(8;5),(10;4),(11;2),(10;0),(9;0),(7;0) And now some details: join (-2,5;-4,5) and (-2,5;-5,5); joint the dot (4;-6) with (5;-6) and (4;-3). Draw the eyes, mouth, ears, nose, and your capybara is ready! - Of course, dear expert, we will find Capybara for you! - Catching up on that! Well, I think now we are just ready for a trip to South America! - summed up English Expert.
16
-2-
It was a sunny day. Mr Quick and Calculater 3000 were sitting in a café in San Francisco and drinking coffee. 'It's delicious' - English expert said 'Do you know that in the world is said the best coffee to come from one of the country we are visiting?' - asked Maths expert ‘If you want to know where we are going solve this puzzle’ – he encouraged Write each answer, then mark it in the answer column. For each set of exercises, there is one extra answer. Write the letter of this answer in the corresponding box at the bottom.
1
2
3
23-23 = 52-44 = 19+ (-15) =
(-25)+(-25) = 14-56 = 55-69 =
78+(-33) = (-69)+115 = 31+(-66) =
C S
P R
U I
5
Answers: 8
5
0
4
S
(-99)-(-89) = (-99)-89 = (-31)-(-66) =
4
H
Answers: (-42) (-14)
T
(-34)
36
O E
2
5 (-50)
J
Answers: 46
55-14 = 14+55 = 65-(-14) =
-35 45
6
1
3
V -188
B
X
L
K
41
G 79
Answers: 142
Q 72
169
N 35
Answers: 56
D 69
56-(-16) = 85-49 = 79-(-63) =
6
F
Answers: (-10)
Y
36
A 161
4
'You should know that this country is the largest country in South America.' -‐ said the English expert -‐ 'Its name means “red like an ember,” comes from pau brasil -‐ a tree that once grew abundantly along the coast that produced a deep red dye.' 'It has almost 7,500 km of coastline, making it the longest continuous coastline in the world' -‐ Calculator 2000 added
'They have also beautiful beaches' - sighed Mr Quick Then they decided to travel through the rainforests along a huge river .
17
'Let's hope we would not meet the piranha. This river is also home to anaconda, more than five thousand different species of fish, crabs, turtles and caiman and it can be dangerous' - said English expert 'Do you know that it is the second longest river in the world?' - asked Maths expert - 'Do you know its name? If not you can to solve this puzzle to find out the name.' 'Work each exercise. Find the code letter for that answer and write the code letter in the blank by the exercise' - explained Calculator 2000 1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6. Later on they were going to Venezuela. 'Do you know that there is a waterfall almost 1000 meters high, one of the highest in the world?' - asked English expert - 'It was discovered by an American in 1937 named Jimmy Angel' 'If you want to know the name solve the puzzle' suggested Calculator 2000. Each row across has 6 boxes. Only two or three of them contain a number divisible by the given number. Circle these numbers in each row. Notice the numberletter above each circled number. Write the letter in the matching numbered box at the bottom of the page and you will find out the name of the waterfall.
Divisible by 2
2-N 196
10 - B 825
11 - S 4374
7-C 9,701
1-M 65,253
10 - L 125,823
Divisible by 3
1-N 46
7-F 51
3-Y 913
5-L 834
8-P 4,991
7-O 7,822
Divisible by 5
4-E 325
10 - M 608
6-N 5,273
9-O 49,249
9-F 52,891
11 - S 94,305
Divisible by 4
4-K 73
2-I 69
9-L 548
8-A 7,624
10 - L 12,308
6-B 24,875
Â
18 Â
1-A 78
Divisible by 6
1
2
3
5-P 62
4
6-S 3,054
5
11 - K 5,453
6
7
3-G 23,826
8
9
11 - D 5,553
10
11
‘Hey, look!’ - said Mr Quick - ‘This is an amazing place! Where exactly are we?’ ‘This is the driest place on the Earth. It’s also 50 times drier than the Death Valley. It is the world’s largest supply of Sodium Nitrate. The average rain fall in this region is just one millimeter per year. Do you know where we are?’ ‘No’ - replied English Expert ‘Then solve my riddle.’ To know the name draw a straight lines between each Maths operations on the left and results on the right. Each line will go through one number and one letter. At the bottom, write the letter on each line below the number. (-13) + 40 •
• 49
1
(-12)⋅(-2) •
2
4 ⋅ (-3) •
(–88) : (–4) •
4
34 – (–15) •
A
(-50)-(-123)•
7
A
(-56) – 11• (-72) + 66 • (- 12) + 109 • (-19) – (-45)•
2
4
5
6
9
• 24
S
10 00 R 0 11
T
3
• 129
5
Solution: 1
T
A
D
98 – (-31)•
6
E
47 + (-22)•
• 27
C
3 M
(–27) : 3 •
• 22
A
7
E
• 73 • 97
12
• (-12)
• (-67)
8
• (-9)
• 25
13
8
• 26 • (-6)
9
10
11
12
13
19
‘Of course! Now I know! We are in Chile!’ ‘I’m happy to hear that. Can you tell me more about wildlife in South America? – ask Calculator 3000 - South America is home to more plant and animal species than anywhere on earth, and there are countless places to observe them in their natural habitat, said English Expert. I have a homework at Geography: writing about the Amazon jungle. Can you help me? - I read somewhere that in the north, the Amazon rainforest encompasses more than “x” million square kilometres and straddles “y” countries – said Math Expert. I can tell you that “x” is the solution of the first Math trick and “y” is the solution of the second Math trick. Math trick 1 Add a number (x) to double and triple the number. Subtract the number 17. Divide by 5 to get the number 5. Do you know the number (x)? Math trick 2 Add 7 to a secret number (y). Multiply by 6. Subtract 10. Divide by 4. Add 5 and the result is 25. Can you find the secret number (y)? Home to macaws, monkeys, snakes, sloths and even jaguars, it’s the most biodiverse place on earth. Tropical cloud forest in Ecuador house an astounding variety of birds, while high-altitude grasslands in the Andes are home to foxes, deer and vicuña. Wetlands like Brazil’s Pantanal may be the best place to observe wildlife due to their visibility. The waters off Patagonia are rich with marine life like whales, sea lions and charismatic penguins. And all manner of strange creatures can be found on the Galápagos. I hope that all my information was useful for you! - Yes, thank you! You are a really friend! Can we go to our next stop?’ ‘Where are we going this time?’ ‘You’ll see.’ Our mascots got to the plane and went to another amazing journey.
20
Chapter 3 Australia -1Finally, after a long flight across Pacific Ocean our experts came to Australia. First they took a sightseeing tour seeing Sydney Harbour Bridge, Sydney Opera House, the historic Rocks district. Later on they decided to go to beach and plan the rest of their visit in Australia.
When they were strolling along the Bondi beach they met two boys: Mandu (which means the Sun) and Orad (which means The Earth) − Aboriginal Australians − which told them about the most fascinating places in Australia, history and nature. The Aborigines were the oldest folks in this land. They had the continent to themselves for 50,000 years. 'You should know that Australia is home of three unique animals: platypus, mammal that lays eggs, the kangaroo, which carries its young in a pouch, the emu, a large bird that does not fly' - said Mandu. Orad showed the experts a river on the map. 'It begins as a small stream in the Australian Alps − he explained − and it meanders and carves steep river banks to the Mallee, where it touches the Australian desert and our great outback region.
'You will discover unique Aboriginal culture that reveals the story of mankind and ancient fossilised limestone cliffs before it finally enters the Southern Ocean at Goolwa and the Coorong − Mandu added − 'In this river region you can spot Aboriginal artifacts such as canoe trees, fish traps and boundary markers.
21
Orad said: ' It is the longest river in Australia. It is 2,228 kilometers long. And if you want to know the name of this river, you must do a riddle." Each ordered pair at the bottom of the page represents a point on the coordinates below. Above each ordered pair, write the letter that appears at the point.
Before going along the river they explored the rugged alpine landscape of the National Park which is an area of outstanding beauty. It is one of the best known and best loved national parks in Australia. 'Look! Over there!' said Maths expert and pointed at a huge mountain.
'Oh, this is the highest mountain in Australia. Mandu and Orad told about it' − said Mr Quick 'Yes, it was discovered and named by the Polish explorer Paul Edmund Strzelecki in 1840, in honour of the Polish national hero and hero of the American Revolutionary War General. Do you want to know, how is it called?' − Maths expert added 'I'd love to.' 'Then solve my riddle.' - explained the Maths expert - 'To solve the puzzle for each exercise, plot the three given points, then draw a line through them. The line, if extended, will cross a letter the grid. Write this letter in each box containing the exercise number.'
22
Now I will remember the name' − said Maths Expert. After amazing trip along the river they went north and visit the third amazing place. 'Do you know that it lies at 15 meters below sea level. It is Australia's lowest point and it has only filled to the brim three times in the last 150 years?' - English expert asked.
'Seasonal rainfalls attract waterbirds such as Australian pelicans, silver gulls, red-necked avocets, banded stilts and gull-billed terns. The best way to this area and take in its vastness is from the air. Flights provide spectacular views across the park and showcase the seasonal wildlife' - he added.
If you want to know the name of this place solve the riddle. Each pair of numbers stands for a point on the coordinates below. Above each pair of numbers, write the letter that appears at that point.
Â
23 Â
(−8, 6) (7, 3)
(2, 3)
(−4, −6)
(−4, −6) (−5, 3) (0, 4)
(−4, −6)
B T
C
Z
T J
R
A
K
Y U
1
P
S
1 M
O N
W N
L
E D
I
H
24
-2“I know something interesting facts about Australia!”, said Calculator 300. “If you also want to know it, play my game!”
Find out what points do not belong to the graph y= 2x + 7, without drawing the graph, and cross them out! The remaining points will tell you the Australian animal with population more than 1000 000.
S(-2;2) M(2;-2) H(2;-11) E(1;-9) K(1;3) L(-2;-2) E(1;-9) P(0;4) T(-6;0) Done? Try again with the graph x=6! Now you can learn what Australian dollar is made of!
P(6;-9) J(-5;-6) L(6;0) A(6;5) O(4;6) R(-3;1) S(6;-6) G(0;6) T(6;3) I(6;-3) C(6;6) D(5;-3) And now find out the biggest part of what continent belongs to Australia! You can use the graph!
S(0;1) A(-1;1.4) D(2;2) N(-1.7;2) T(0;0.7) E(0.3;-1) A(-1;1.4) R(0.8;0) C(1;-0.9) T(0;0.7) J(2;2) I(2;-1) L(-0.5;-0.6) C(1;-0.9) Y(-2;-1.8) W(1;-0.5) A(-1;1.4)
Wow! there even more! So, let us put on our ugg boots and go ahead! – Mister Quick said. Draw your ugg boots connecting the points on the coordinate plane:
Now I want to go
(-2;6) (3;7) (8;6) (3;6) (-2;6) (-2-;4) (-6;-5) (-8;-7) (-8;-9) (7;-7) (-8;-6) (7;-3) (7;0) (8;6) Details – connect (-8;-8) и (-8;-6), (3;6) и (3;-8), (-2;-4) и (3;-5), (7;-3) и (3;-6)! Don’t forget to draw a pair, otherwise you will freeze! Although now, when it is winter here, they enjoy summer)
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-3Mr. Quick and Calculator went on their adventure at the airport. They didn’t know where they were exactly, just that they were somewhere in Australia. Then Mr. Quick asked a woman: — What is the name of this city? —said Mr. Quick— — If you check the GPS coordinates Latitud:-35.281535 and Longitud:149.132449, you will find the name of this city. You are in the capital of Australia. — the woman added— — Oh, thank you! The two experts went to the city, where they met a man while they were visiting the Centre for Mathematics & Its Applications in the Australian National University. Calculator started to talk to him: — Do you work here? —said Calculator. — Yes, I do. If you want, I can show you this building and explain something about my work to you— said the man. — I will be very pleased. While the man was getting ready, Mr. Quick told Calculator that he knew the man and he could discover the name in the next riddle: Represent the following points in the coordinate plane with the letters. After that, read the letters from left to right and you will get the name of the scientist. A(-3,2) A(3,1) D(0,3) D(5,-2) I(-2,0) L(4,0) M(-4,1) N(-1,-1) N(2,3) O(1,5) After some minutes, the man was back. They started the tour along the big building. — Ok. My name is John —said the man— — I am Calculator. — I am Mr. Quick. We are discovering interesting places and people around the world. What do you work in? — I have written a book about a language and environment for statistical computing and graphics — said John—. — What can we find in your book? —said Calculator— — You can find a series of data sets and examples, to take the beginning user through launching the environment, executing simple commands at the command-line, understanding objects and function calls, graphics, and some simple statistical modeling techniques —answer John—. — Have this language and environment got a name? — asked Mr. Quick— — Yes, they have one —said John—. If you want to know it, work out the next task and you will get the logo and the name in the center of it: You have to do two different tasks: 1. Represent the following points in the coordinate plane. Once you have represented them, draw a grey line to join them in the same order you have found in the bottom. You also have to join the last one with the first one: (-4,1), (-2,2), (2,2), (4,1), (4,-1), (2,-2), (-2,-2), (-4,-1) 2. Represent the following points in the coordinate plane. Once you have represented them, draw a blue line to join them in the same order you have found in the bottom: (-1,-4), (-1,1), (1,1), (2,0), (2,-1), (1,-2), (2,-4)
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-4Calculator 3000 and Mr. Quick were on their way to Sydney. Do you know which are the geographical coordinates of the two towns Santiago de Chile and Sydney?”, said Calculator 3000. “If you solve these calculations, you will find the answer”, said Mr. Quick:
Sydney
coordinates:
South latitude: the complement of the angle with the measure of 56° 5' is …. East longitude: the supplement of the angle with the measure of 28° 43' is ….. Santiago
coordinates:
South latitude: 7° 46' + 25° 40' = ….. West longitude: 23° 33'20'' * 3 = ……
All the sudden, the plane started to cough. It crashed to the land. Luckily, both of the experts made it out safely. They needed to find their way to Sydney, so they started their way by emergency compass. When they were on their way for like half an hour, they bumped into the kangaroo. ''What was that for?'' he asked. ''We're sorry, but we crashed on the land and we don't know how to get to Sydney,'' they said. ''Don't worry, I will help you out. I am Kenny,'' was his response. ''You must count all the kangaroos, multiply their number by all the dead shrubs, continue by dividing the result with the number of the acacia trees, take the result and add the result of multiplying the number of the scorpions, which are harmless, by the way, and the sum of creeper + snake, and you get the distance (in kms) to Sydney,'' he said.
Can you help them?
27
''Now that you found out how far Sydney is, you must calculate how long it will take us to get there. I can jump 6 meters, every leap takes me 3 seconds. How long will it take us to get there?''
Congratulations! You made it to Sydney safely! Your plane is shattered though…
“Sydney’s face is recognized around the world by its three major icons spectacular Sydney Harbour, Sydney Harbour
Bridge
Heritage
-
listed
and
the
World
Sydney
Opera
House. Admire the city’s natural beauty on a ferry ride or explore the harbour and its hidden coves on a yacht or cruise”. “I heard about a very famous park: Gorge Wildlife Park. Can you tell me some details about it?”, said Mr. Quick “Gorge Wildlife Park is not your average wildlife park; it’s a place where people and animals get together. Under shaded trees, paths meander amongst the animals offering many relaxing hours of wildlife enjoyment. See all of your favourite Australian animals including wombats, dingoes, echidnas and Tasmanian devils. Cuddle a koala and walk amongst the kangaroos and wallabies.” In Australia there are many species of kangaroo; kangaroo is the only mammal moving by leaps and its travel speed varies between 20 km/h to 70 km/h. Do you know that a famous Math contest is called Kangaroo? Try to solve a few of the problems in this contest:
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1. The number of kangaroo species is the result of the calculation: (a+2b)(3a+3b+2c) - 5, knowing that 4a+5b+2c=16 and 2a+b+2c=6 2. Two kangaroos leave at the same time: Kangourou 1 from Sydney City and Kangourou 2 from Newcastle City. Kangourou 1 moves with an average speed of 27 km/h and the other has a speed with 5 km/h higher. The distance between the two cities is of 118 km. How long and at what distance from the Sydney City will they meet? 3. The largest reptile is the saltwater crocodile. It is found in the region of Australia northern coast. The average length is of x dm, where x is the average of the numbers a and b, which are the solutions of the following riddles: a) I am thinking of a number “a”. If I increase it 11 times, I decrease the result with the product of the numbers 17 and 20, I double it and I decrease it again with the amount of the largest number of 2 digits and the smallest number of 3 digits, I will obtain 1. b) In the train that runs from Sydney to Wollongong there are 100 persons. In each station, a number of persons descends of the train and they climb with two persons less. The number of stops that the train makes until there will be no persons in the train is equals with “b”.
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Chapter 4 Asia -1- I know where we are flying today! Mr Quick shouted excitedly. - We are going to part of the world where, perhaps, human civilization was born! We will visit Asia! - Exactly! But did you know that Asia is the biggest continent on our planet?, - English Expert wondered. - No, I didn’t. And what is its area? - I don’t know. However, I know for sure that it is bigger than one of the celestial body!
Find out the area of which celestial body is less than the area of Asia! Make up its name from the points belonging to the plane β!
O M
β O1 N
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- But I know some Asian records, - said Calculator 300. - Do you know the longest river in Asia? It is 6300 km long! Let us find out! Make up the name of the river notation of parallel lines!
d i
z n r
c a j
k
- Wow! – English Expert and Mr. Quick said in unison - And yet, you know that Asia is divided into 5 parts? - asked Calculator 300 Can you locate the lines so that they divide the plane into 5 parts ! - Also, each part has its own traditions. For example in Southern Asia the oldest profession is „bede”. Do you know what they do?
31
Connect the points to find it out! 1
2
32
3
31 30
4 29
5
28 27
6 7
26
8 25
9
24
10 23
21
22
20
11 12 13
19 18
14 15
17
16
- Oh, I want to acquire these skills, too! – English Expert exclaimed. - We are flying to Asia. So, you will have enough time to do it!
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-2-
Mr. Quick was looking out of the airplane window – Is this such a big continent? “Yes, this is the biggest continent in the world?”, answered Maths expert. Now, make up the name of the continent, where Mr. Quick and Calculator 300 are flying, from the names of the rays.
“I know which is the biggest country on this continent”, says Calculator 300. This is ….. Do the test to find out which is the biggest country on this continent. 1) The straight line divides a plane into ….. half-planes K3
R 2
M 5
2) A line is the straight path connecting two points and … U infinite in both directions
I infinite in one direction O not extending beyond the points
3) How many points can be located on one line? S infinitely many
L 1000
N2
4) A segment is limited from ….. points. T0
D 1
S 2
5) If two lines cross, we have ........ angles. B
interior angles
supplementary angles
I
vertical angles and E takeout angles and
inscribed angles 6) Equel segments have equel ... E size
A length
Y angles
If you chose the correct letters, they will make up the name of the country Calculator 300 was talking about. ______
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Do you know what mountains we are flying over?, asked Maths Expert. Yes, these are the Gimalai!, Mr.Quick ecxlaimed. – And the highest point is Jomolungma or Everest. It is ....... ah.
1) How many croosspoints will have 4 parallel lines which are crossed by 2 perpindicular lines?
2) In how many parts 7 parallel lines divide a plane. 3) If one of supplementary angles is 174 how big is the second one? The answers will tell you the height of Everest. Clouds covered the view of the huge continent and Mr Quick was forced to look away. Don’t worry. We will become better acquainted with land!, promised Maths Expert.
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-3Our story goes on in India. Mr. Quick and I are going to visit some cities in the country to discover a very famous landmark and the city where a very important person was born, among other things. We arrive in Delhi —the capital of India—, a big city with 14 million inhabitants. It’s amazing and very beautiful! When we were exploring the city, Mr. Quick had the idea to go to Agra and visit a very important monument. — —
What is the monument? I asked Mr. Quick. It is a very big palace that many people considered the best example of Mongolian Architecture. If you want to know how it looks like, do the following.- Said Calculator.
Join every two consecutive points with a segment (1-2, 34…). After that, reflex the drawing obtained through the vertical line. Finally, you get the monument. Once we visited that important monument, we went to another major city in India, Calcutta. There, we visited the Museum of India where we saw a lot of things about the culture of India. We learnt a lot in that tour. After visiting Calcutta, I told Mr. Quick that I wanted to visit Erode. This is a not very well known city but important for Maths.
— Where is Erode? Asked me Mr. Quick. — It is in the south of the country. You can set it in the map with the next instructions. Starting with the line in the map, draw an angle of 47 degrees with vertex at Delhi. Another angle of 70 degree with vertex at Calcutta. The two lines drawn are crossing in Erode. — —
But, Why are we going to Erode? Told Mr. Quick. Erode is the city where a very important mathematician was born in 1887. That man was autodidact and made extraordinary contributions to mathematics. Do you want to discover his name? Solve this riddle.
Ra _ a _ _ ja _ First letter: draw two semicircunferences from 180º to 0º and put them together The second and fourth letters are the same: draw a semicircunference from 180º to 0º Third letter: draw a semicircunference from 180º to 360º
Chapter 5 Antarctica -1'So now we are going to Antarctica. You know that the name 'Antarctica' comes from a Greek word meaning 'opposite to the north'. The first people to reach the South Pole were from the Norwegian-led expedition of Roald Amundsen on December 14, 1911' − said Mr Quick 'Is there anything there besides snow as most of Antarctica is covered in ice over 1.6 kilometres thick?' − wondered Claculator 3000 'Do you know that there are no permanent human residents, nor indigenous inhabitants, but 1,000-5,000 researchers reside at research stations across the continent throughout the year' − Mr Quick said 'How do we get there?' − he asked after a while 'Of course on a boat!' − Mr Quick answered - 'We will be leaving from Hobart and head toward the Ross Sea side of the continent.' 'We can go there now because the Antarctic summer starts in December and runs through till about March. The skies are usually bright and the temperature is no colder than a crisp, sunny winter’s day. This is the best time to see Antarctica at its most beautiful. That doesn't mean it's balmy; we still have to wear a parka and bring extra layers' − explained Mr Quick The best place to witness this beauty at in a real paradise at the pristine place on the West side of Antarctica. If you want to know the name of that place solve the puzzle below.
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-2''Ok, we'll soon be there,'' said Mr. Quick. ''Thanks to Australian helicopter, we can finally continue our way around the world!'' As soon as he finished his sentence, the helicopter started to shake. ''Not again…'' Calculator 3000 slapped his face. The helicotper luckily allowed to land safely. ''We ran out of fuel!''. They needed to find some blue ice to power the helicopter. ''The best blue ice can be found at the South pole!'' shouted Mr. Quick. As that was a command, they started running towards the South pole. ''Hey! You there!'' said someone behind the iceberg floating in the sea. ''Can you help me? I'm kinda stuck here!'' Mr. Quick quickly (what an irony) flew to the iceberg. He grabbed the blue thing behind the hill and pulled it up. It was Pingu! ''Oh, thank God!'' were his first words after he got to the continent. ''How can I pay you back?''. ''We just need a couple blocks of blue ice to fuel our helicopter.'' Pingu scratched his head. ''Blue ice is really rare, but I'm sure you will get it! Over there, to get over the seal field, you need to solve this question: Seal number 1 can glide the ice faster than number 4, seal number 5 can glide faster than number 7, number 2 can glide faster than number 6, number 1 can glide faster than number 3, number 4 can glide faster than number 2, number 5 can glide faster than number 3. Which seal is the fastest?''
This is the tough one! Calculator 3000 and Mr. Quick guessed it right. The seals glided away and they had free way to blue ice. ''One more thing,'' said Pingu, ''You're gonna need this!'' He threw a funny looking gun. Calculator 3000 tested it. It shooted straight lines of laser that were able to cut ice. 3
''Hmmm…'' said Mr. Quick. ''We need 1m of blue ice. Every laser ray is 10cm x 10cm x 1cm. How many times do we need to shoot? We have enough energy for 500 shots. Will we have enough energy?'' Calculate!
''We got enough blue ice to continue your way around the world!''
-3-
Antarctica. The scenery was stunning... icebergs, glaciers, black sand. 'Next place we will visit is actually a caldera of a volcano and the prime site for going swimming in Antarctica. The reason this site is chosen is because the water is generally warmer due to the volcano and also because the world’s largest Chin Strap Penguin Colony lives on the island'- explained Calculator 2000 – 'There aren’t too many places in the world where you can be at arm’s length from thousands of penguins. They are very cute, but after a while they start seeming sort of stinky and loud. In addition to them which are the main attraction, you can also view many different types of birds, seals, and whales. If you want to know the name of some animals you can see in Antarctica solve the puzzle below.' Figure out the measure of the unknown angel in any exercise. Then find this measure in the code. Each time it appears, write the letter of that exercise above it.
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-4-
“Oh, don’t be said our journey through Australia finished! Maybe we will learn more things about penguins than about kangaroos. You have already bought some books about penguins and you promised me that you will suggest me a few problems in order to feel that time passes no hardly until there”, said Calculator 3000. Fifteen minutes later, Mr. Quick told to Calculator 3000 six problems with penguins: 1. The smallest of the penguins is the Little-Blue penguin at only about ten inches tall. This penguin has blue feathers, which is how it got its name. The Little-Blues live in Australia and New Zealand. The Macaroni penguin is about twenty-seven inches tall. How much smaller is the Little-Blue than the Macaroni? 2. Yellowed-eyed penguins live in New Zealand and are a little larger than most penguins. When they go on land to breed, they fear hungry predators like ferrets, stoats, or even dogs. If a female yellow-eyed penguin lays two eggs on September third, her chicks may hatch on October third. If she and her husband feed their chicks until February third, how many months did she and her husband feed their chicks? 3. Erect-crested penguins live on small islands not too far from Antarctica. They eat small fish and small crustaceans. There are approximately one hundred sixty-two thousand breeding pairs of the Erect-crested penguin. There are about three hundred twenty-two thousand breeding pairs of the Gentoo penguin. How many more Gentoo penguins are there than Erect-crested penguins? 4. Macaroni penguins live in the Antarctic region. They tend to eat fish and squid a lot. There are about 10 million pairs of this penguin. Their crests are bright orange and they have black faces. If a Macaroni penguin eats eight fish per day, how many fish will it eat in four days? 5. The Emperor penguin towers over the rest of the penguins at about forty-five inches tall. These penguins live only on the Antarctic continent. The Gentoo penguin is about thirty-three inches tall. How much taller is the Emperor penguin than the Gentoo? 6. There are about 320,000 pairs of the Gentoo penguin. Small fish and squid are a large part of this penguin's diet. They have to watch out for the leopard seal and the sea lion. They normally lay two eggs in the spring. If eight female Gentoo penguins lay their eggs, how many eggs will there be?
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Chapter 6 Africa -1''Finally!'' said Mr. Quick. ''After a long time, we safely made it to Africa!'' ''You're right,'' said Calculator 3000. He slowly made his way towards the rent-a-buggy shop. ''I borrowed it for five days. I think that should be enough to see the pyramids. We'll head to the desert and see nomadic people, then we''l go back to this airport. I already bought some tickets to Nigeria.'' They jumped into the buggy and started their trip. After 65 kilometers, Mr. Quick said: ''You forgot something again, didn't you?''. He was right. Calculator 3000 forgot to buy water. He only brought an empty water canteen. ''We need to find water now!'' was Calculator's response. ''Ow! Don't you look where you drive?''. Mr. Quick jumped out of the buggy. ''Sorry, are you okay?'' he asked. ''Yeah, but I need some water really badly right now,'' was an answer. A scorpion came to them. It was a really large one compared to the others. ''The oasis is behind these pyramids. You need to climb them to get the water,'' he said. ''Can't we just go around and fill up our canteens?'' Mr. Quick asked. ''Oh, it's not that easy. There is a bacteria colony all around the pyramids. We don't know when it'll start to spread, but it's pretty deadly. One of us stepped on the colony. He disappeared in five seconds,'' said the scorpion. '' Oh, and you need our sticky slime to climb them. I don't know if you have enough in this bucket, but you must smear it on at least two sides of the pyramids to make it safe for us,'' he said. ''If I remember correctly, the pyramid is 160 meters tall and 220 meters wide. You have enough of our slime to smear it on 120 000 square meters. I hope it's enough!'' 3 weeks later… ''We had a lot of fun smearing up all of this slime and we can finally go to Nigeria now!'' said Calculator 3000. They got on the coast and ran to the police officer. He was very tall, but he was looking scared. ''I'm in major trouble right now,'' he said. ''I need to find the robbers of the oilfield or I will get fired!''. ''We can help You, Sir,'' shouted Calculator 3000. If you don't know, they are both very tiny. ''Oh, I know you! Can you help me find the robbers? I would appreciate it!''. ''Of course, Sir,'' was Calculator's answer. They ran to the coast. There was a giant rock with coded door on it. There were 3 codes in total: A quadrilateral with four congruent sides. ___________________, ___________________ A quadrilateral with exactly one set of parallel sides. ___________________ Twenty minutes later… ''Thank you very much for saving my job, guys! I will never forget your help!''. ''You're welcome, Sir!'' said Mr. Quick. They were continuing their way towards the famous oilfields, when they saw another coded door. Name the geometrical shape whose interior angles add to 180 degrees. Code is _ _ _ _ _ _ _ _.
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-2Our next story takes place in Egypt. We arrived in this country by boat. Calculator was walking while a scary man was walking very near him. Calculator turned around and he met the man. Suddenly, Euclid — who was the man— said to him that we worked at the University of Alexandria. Calculator had never heard about that city and he asked Euclid to show Alexandria to him. — Calculator, wake up! Said Mr. Quick — OH! I was dreaming with Euclid. A mathematician that is supposed to have lived in Alexandria around 300 BC. Although some people said that he didn’t exist because there aren’t any pictures of him. — Do you know that Hero was another important mathematician from Alexandria? He discovered a formula to calculate the area of a triangle having the measure of its sides. We can use it to know the surface of Nile delta because it is a rhombus, — Explained Mr. Quick. Compute the area of these two triangles knowing: Alexandria-Baltim: 120 km Baltim-Port Said: 125 km Alexandria-Port Said: 228 km Alexandria-Cairo: 180 km Port Said-Cairo: 169 km Use this two steps process to compute the area of each triangle: Step 1: Calculate "s" (half of the triangles perimeter):
Step 2: Then calculate the Area: Add the two amounts you have obtained before. — Remember! We came to this country to decipher hieroglyphs, —Told Calculator. — True. It is well known that hieroglyphs means "sacred drawings" in Greek. They are basically drawings of familiar objects, simplified to make them easier to draw, to represent numbers in the ancient Egypt, —Reminded Mr. Quick to Calculator. — Some hieroglyphs were discovered in the pyramids of Giza. Let’s go there by boat along the Nile river. Mr. Quick do you know how long this river is? Decipher this hieroglyph!
Nile river length is:
Here you are the value that every picture represents:
Keep in mind that Egyptian number system is additive. Calculator was excited, but he was also wondering about where the pyramids were. When they arrived at Cairo, Calculator told him that the most famous landmarks are the pyramids at Giza named Kheops, Kefren and Mykerinos. They went to the pyramids and Calculator read a very interesting thing in the hieroglyphs; it was that if you climb to the highest point of the Kheops pyramid, you will receive a golden pot. Calculator and Mr. Quick climbed to the top of the pyramid but, to obtain the golden pot, they had to decipher the following riddle: Divide the perimeter of the base by the double of the height in this pyramid. What is the name of the number obtained? Height of Kheops pyramid: 146.528 m Base side of Kheops pyramid: 230.39 m One of the Egyptian pyramids VABCD (regular quadrilateral pyramid) has a height of 12 m and 10 m base side. 3
a) Knowing that a man which is essential 8m air, how many people can breathe the air from this pyramid? b) If I fill with water pyramid, how many liters would be needed? 2
c) How many pounds of paint should to paint the side surface of the pyramid, knowing that 1 m of surface we need 500 g paint? d) A scorpion moves on vertical surfaces A to C on the shortest path. You can tell if the road is less than 9m? - I can help you with this interesting problem, but first we have so solve a puzzle!- said Calculator 3000
Across 2. The sides of a rhombus are 3. Ancient mathematician who discovered a theorem of the same name used to calculate the hypotenuse of a right triangle 7. The diagonals of a parallelogram have the same 8. Quadrilateral with all sides equal 9. The branch of mathematics that studies geometrical figures and bodies Down 1. Rhombus with a right angle 3. The diagonals of a rhombus are 4. Quadrilateral with only two parallel sides 5. The quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane 6. Adjacent angles of a parallelogram are
It is… —they said the number— Then the golden pot appeared and they had a very good time in Egypt.
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-3Faster! Push down gas pedal! - Calculater 3000 screamed. look at the wild animals in Safari Park ...
Mr. Qiuck and Calculater 3000 decided to
I am not sure it was a good idea!, - English expert laughed when the car drove off at a safe distance from the wild beast. Do the task if you want to know which animal was chasing our heroes. 1) What is the sum of the angles of an isosceles triangle: H – 90 L- 180 R – 360 M-390 2) The longest side of a right-angled triangle is called: I - hypotenuse O- cathetus H- basis U – opposite side 3) rectangular perimeter - P= O- (a+b)*2 N - ab*2 A- a2+b 2
S- a+2*b+2
4) If you draw the diagonals of the rectangle, it would be allocated in 2 ... K- equilateral triangle
E - isosceles triangle
N- equal triangles
Now you know who feared Calculater 3000. Oh, what a beautiful continent! But do you know that the longest river in the world flows here? This is the Nile! It is ....... metres long. Do the task to know the lenght of the Nile. The result is 12 more than the sum of the angles of 38 triangles. - In Africa, there are many places which are worth visiting! – startled Maths expert. Fill in the table values. mm
2
cm
2
dm
2
m
2
a
ha
km
2
800 000 1.38 0.0000005895 500 000 000
The numbers obtained in the windows of a certain colour, put in the gaps in the sentences. You will know what famous places our heroes want to visit. 1) Lake Victoria - the largest lake in Africa, its depth ... .. meters. 2) Pyramid of Cheops - one of the wonders of the world, its height .... m. 3) Mount Kilimanjaro - the highest point on the continent, its height ... .. meters. 4) In Lake Malawi lives more species of fish than any other lake in the world - more ... ..
In Africa there is the world's largest desert. - Mr.Kvik said. Solve the crossword puzzle to find out the name of this desert.
1. A figure having four equal sides, angles and diagonals. 2. A figure the sum of the angles of which is 180 3. A rectangle having all equal sides. 4. A figure which has five angle. 5. A rectangle whose diagonals are equal. 6. A figure, whose two sides are parallel, but the other 2 are not. Also a big island belongs to Africa ... .. - said Mr. Quick. Solve a test to find out the name of the famous island.
1) What kind of triangles are displayed? M - isosceles
S - equilateral
2) The given triangle is: A - both right-angled and acute angled
I – right-angled
3) The median of this triangle is: S - also mid perpindicular
D – also height and bisector
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4) What kind of trapezoi is depicted? A – isosceles
I – right-angled
5) <= B L - 60
G - 30
6) What is BCMF drawings? E – square
A – rectangle
7) The legs of the given trapezoid are: N - BC & AD
S- BA & CD
8) What is the MN? C - mean line E - mid perpindicular 9) If MN = 12 and BC = 8, what is AD? K – 20
A - 16
10) If BC and AD = 12 = 42, what is MN? R - 27
X 30
If you selected the correct answers, the letters will make the island's name. Only on this island lemurs live! – shows off his knowledge Calculator 3000 - Let's go to see them! - With pleasure! - Said Mr. Quick. - And then let’s compose several new brainteasers to our friends mathematicians ...
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-4'Do you know that the world's largest land animal is the African elephant, the world's tallest animal, the giraffe. The fastest land animal in the world, the cheetah, and the gorilla, which can be found in the continents jungles, is the world's largest primate. All of them live in Africa.' - explained Mr. Quick After a while he said - 'Africa is a continent of extremes.' 'Why' - asked Calculator 3000. 'It’s extremely large, extremely dry, extremely poor, and extremely young.’ - clarified the English expert - 'Over 50% of Africans are under the age of 25' - he added. The travel went very smoothly. After few-hour flight and a good night’s sleep they started their tour in Africa. 'So what is our first destination' - asked Mr. Quick If you want to know where they go first write the word missing from each statement in the boxes next to the statement. Notice which letters are in numbered boxes. Write each of these letters in the matching numbered box at the bottom of the page.
When they get there they saw the highest freestanding mountain in the world. It is 5,895m high. Almost every kind of ecological system is found on the mountain: cultivated land, rain forest, heath, moorland, alpine desert and an arctic summit. 'It was an absolutely awesome experience climbing there' - said Mr. Quick.
Next days they went to next places. Undoubtedly the most breathtaking way to see first magnificent place is to take a helicopter. Nothing compares to seeing it for the first time from the air. 'Look there!' - sighed Mr. Quick - 'This is really outstanding.' 'If you want to know the name of this place solve the puzzle' - suggested Calculator 3000 Do each exercise and find your answer in the set of answers to the right. Write the letter of the answer in each box containing the number of the exercise. If the answer has a black circle , shade in each box containing that exercise number.
Â
49 Â
'What next?' - asked Calculator 3000 'Do you remember what my favourite animal from computer-animated comedy film is and the title of this movie?' - answered asking Mr. Quick. 'Yes, it is King Julien...' - replied the Maths expert. 'Don't say the title!' - the English expert interrupted him. If you want to know the our final destination cross out the box containing each correct answer. When you finish, write the letters from the remaining boxes in the spaces at the bottom of the page. You will find out where we are going next.
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50 Â
'Do you know Marco Polo was the first European explorer to reach the island? The Portuguese reached the island next in 1500 and it was later colonized by the French.' - explained Mr. Quick 'It was home to the largest bird in the world, the elephant bird, until it became extinct in the 17th century. The lemur is only found in the wild in the island. The unique ecology of this place has led some scientists to refer to the country as the "eighth continent" of the world. This place is home to the planet’s largest chameleon and smallest chameleon – Parson and Brookesia.' - he added. 'Africa has stolen my heart!' - Mr. Quick said to Maths expert when they were resting on an unspoilt and beautiful beach in Zanzibar and planning their last trip this time to Europe.
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Chapter 7 Europa -1Our next story takes place in Spain. We are in Granada an important city in Andalusia, a region in the South of Spain. —Why are we here Mr. Quick? —In this city, we are going to visit the Alhambra a palace and fortress complex built for the last Muslim emirs in Spain and the court of the Nasrid dynasty. Do you know when they live in this place? The following equation solutions are the centuries while they were living in Alhambra. 2
x -28x+195=0 —But, do you think this monument is important from the mathematic point of view? —Yes, it is —said Mr. Quick— An important mathematician named Marcus du Sautoy came to Granada, visited the Alhambra and told beautiful things about it. Do you know him? —Yes, I do. He is alive. Do you know the year he was born? These are the solutions of an equation: x=5 and x=13. a. Built up the equation. b. Change the sign to the x coefficient and add one to it. c. Put the number you got above in front of the equation independent term. d. Here you are the year you are looking for. —As you know, Marcus is a maths Professor at the University of Oxford. He writes for The Times and The Guardian, he has appeared several times on BBC Radio 4 and on TV and he also writes books using mathematics. One of these books is about the symmetry and it includes something about the Alhambra. Recently, he said “if I had to choose one building in the world to be cast out on a desert island, to live the rest of my life, being an addict of symmetry, I would probably choose the Alhambra in Granada. This is a palace celebrating symmetry”. They went into the Alhambra and Calculator was fascinated seeing symmetry everywhere in the building. —Oh! Here we can find every possible kind of mosaics. Do you know how many different kinds of mosaics exist in maths? Said Calculator to Mr. Quick. Work out this equation: —Another important visitor of the Alhambra was the Dutch painter and engraver Escher. He visited it several times and got inspiration. Escher has made amazing mosaics thanks to the understanding of the underlying geometry in them. Escher died shortly after du Sautoy’s birth. How old was Marcus when Escher died? Find the answer in the next riddle. Said Mr. Quick. Solve the following equation: 2x-3=4+x Then if you go to Granada you must visit the Alhambra!
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Where are we going next?- asked Calculator 3000 Mr.Quick. Mr. Quick checked with the list: Rome (3х*2)+х=6+6х 2 Paris (х+1)(х+1)+5х=10+х +2х+1 London ¼х=1,75+1,5 2 Madrid (x+1)(x+3)=x +7 Berlin 3х=24 -13,5 Warsaw 3х=7,1*9
Solve the equation to find out in what sequence the friends are going to visit the cities. Put the cities in order according to the result of this equation - from the smallest to the largest one. 1)
2)
3)
4)
5)
6)
-Do you know that there is the sea in Europe bordered by nine countries ? Choose the correct answer in each line: A) 0x>0 2 O) (1+x)(1+x)= 1+x 2 L) linear coeficient– x P)√-144 =- 12 2 I)√a =/a/ R)0x≤ -5
B) 0x≥0 2 A)(1+x)(1-x)= 1-x S) linear coeficient – 2x T) -√144= -12 2 O)√a = a C) 0x ≤ 5
Make up the name of the sea from the letters of the answers. The highest mountain in Europe is the Mont Blanc!-said Math Expert.- Its height is .... Solve the equation to find out the height of the mountain.
Mr. Quick, how much time will take our Europe tour?- asked Calculator 3000. 5 (-2 – 2 -2) *(- х) ≤ 2,5х –(3*2х)≤ 15 – 6х Now you know that our heroes should hurry up! And do you know what the largest lake in Europe?-asked English Expert. Solve the equations.
0,25х = 8,2 -х+7*4+8*2= 0
2
х – 15 *2=280: (
)
2
-9+0,01х+х = 0,47+ (х+3)(х-3)
The equations are divided into pairs (the pair of equations have the same answers), except one. This “lonely” answer will show you the area of Lake Ladoga, what English expert was talking about.
-3Hello, dear TV audience! Here is the super-quiz "Do you know?"! Today our guests are Mr. Quick, Mr. 300 Calculator and … English Expert! Storm of applause! Who will win - experienced travelers or amateurs? Dear players, today the questions will be on the theme " Unexplored Europe!" I remind you, that the winner of the show will walk away with € 1,000 in the pocket! Attention, the first question! In what city are you often above the water when walking on land? Let's find out! Write the letter of the correct answer in the box with the number of the question! 1. +/- infinity in the interval R. included [ H. not included (
2. а<b means A. b more а C. а more b
3. а more than o, but less than 4:
4. If х 0, then
M. 0
а
4
B. х
B. 0
а
4
M. х
5. If 4р=2, р= F. 2 U. 0,5
6. If 5-2х=-15, х= R. 10 N. -10
7. If -69н 23, then
1.
G. н -3 I. -3
2.
3.
4.
5.
6.
7.
н
Wow, Mr. Player! This is the correct answer, because this city has the highest number of bridges in the world! And the amateurs’ team takes the lead! Well, the second question is quite simple! How many capitals do you have to pass by, if you decide to visit every country in Europe? Let's find out! To do this, make up the name of the number of Europe countries from the letters of correct equalities and inequalities! 2 f. 4*5=20 b.-8<-9 i.-(-63)=63 h.78-15=15-78 f.(-5) >24 k.(-7)*(-9)=-63 r.98<0 u.1*1= 1+1 t.5:(-1)=(-5):1 y.0 0 d.1:69=-69 l.10782+4655>6895+8542 This is.... Wrong answer! Now is the experts’ turn! - We think that you have to pass by 36 capitals, because 14 countries in Europe are the islands!-said Calculator 300. - Quite correct! Travelers have equalized the score! And, now the final question! Pyrenees, Apennine Mountains - there are a lot of famous islands in Europe.... And what part of the area in Europe do they occupy? Let's find out! To do this, add the numbers of the correct statements! 1. If 4 х 9,5, то х 4 9,5 2. equation can be numeric and alphabetic. 3. 5 9 - false expression. 4. 1+3=5 – equality. 5. In the inequality 0х 0 – an infinite number of x variants 6. 25 25 – correct expression. 7. а b – unstrict inequality 8. а b means that а is more than b.
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The ideal answer! Well! The amateurs’ team didn’t lose with the score 2: 1! My congratulations! The award is waiting for you! Well, dear audience - thank you for your attention! See you soon at our intellectual meetings!
-4- What will be an interesting experience to walk on European lands where they lived most mathematicians – said Mr. Quick - So, we are arrived in Greece! Geometry in ancient Greece was introduced by Thales (b. About. 624 BC - d. About. 546 BC). He created theorems which are considered today as the cornerstones of mathematics. The most famous discoveries of his being: - A circle is divided into two equal parts by diameter; - Adjacent base angles of an isosceles triangle are equal; - Opposite angles to the peak are equal; - A triangle is determined when we know a side and its adjacent angles; - Angle inscribed in a semicircle is a right angle; - Basic Proportionality Theorem (Thales theorem): “If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio.” 1) In the given figure, PQ || MN. If KP/PM = 4/13 and KN = 20.4 cm, find KQ. Please, visit TwinSpce to see pictures!
2) In the figure given below, DE || BC. If AD = x cm, DB = x – 2 cm, AE = x + 2 cm, EC = x – 1 cm, then find the value of x. Please, visit TwinSpce to see pictures!
3) In the figure given, MN || BC. We know that AM = 4, BM = x – 1, AN = 6 and NC = x + 1. If AQ ∩ MN = {P}, Q ∈ (BC). Proof that AP = PQ. Please, visit TwinSpce to see pictures!
4) In the figure given, PQ || MN, OM = x +2 cm, ON = x cm, OP = 4 cm and OQ = 5 cm. Calculate x. Please, visit TwinSpce to see pictures!
- Do you know another famous mathematician from Greece? - Yes, we learned this year about Pythagoras, (born c. 570 BCE, Samon, Ionia [Greece]—died c. 500– 490BCE, Metapontum, Lucanium [Italy]), Greek philosopher, mathematician, and founder of the
Pythagorean brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy. We used a very famous theorem! Pythagorean theorem, proposition number 47 from Book I of Euclid’s Elements, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) - or, in familiar 2 2 2 algebraic notation, b + c =a .
- At Math test we have to solve some problems. Can we verify if I solved them correctly? 1) The lengths of the sides of a right triangle are consecutive integers. Calculate the area of the triangle. 2) The lengths of the sides of a right triangle are even numbers. Calculate the perimeter of the triangle. 3) Calculate x if b = 12, c= 5 cm and a = x +1 in this right triangle. 4) Calculate x if M(2; x), N(–1 ; 3) and MN = 5. 5) Calculate x if M(0; x), N(–4 ; 3) and OM = ON.
- Can you tell me some details about Francois Vieta? – asked Mr. Quick - Yes, I made a documentary about his like and his work – said Calculator 3000 Francois Vieta (1540 Fontenay-le-Comte -29.02.1603, Paris) was a French mathematician and lawyer who made an important contribution in the field of astronomy and trigonometry. He calculated the value of 2 2 2 “PI” (π) number with nine decimals. He introduced algebraic formulas such as (a + b) = a + 2ab + b and especially relations between coefficients and roots of an equation, named after him, "Relations of Vieta." If, 2 real numbers x1, x2 have their sum x1 + x2 = S and the product x1 · x2 = P, then they are the solutions of this equation: x² - Sx +P = 0. So, can you write the equations with their roots (solution): a) x1 = 10 and x2 = 20 b) x1 = –5 and x2 = –2 c) x1 = 1 and x2 = –8 d) x1 = –3 and x2 = 15
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