Download ISMTF Junior Mathematics Competition 2006 Team Event British

ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Trial Round
1.
2006 has 3 prime factors: p1 , p2 , p3
Calculate p1 + p2 + p3
2.
Find the perimeter of this quarter circle.
Write your answer in the form a  + b
4 cm
3.
How many terms are there in the simplified expansion of :
(a + b + c) (b + c + d)
Write one answer only in each of the boxes below.
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1
2
3
1
2
3
1
2
3
ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Round 1
1.
The sum of three consecutive prime numbers is 121.
Calculate the product of these three primes.
2.
Find the sum of:
1602 - 1502 + 1402 - 1302 + ……………………….. + 202 - 102
3.
A regular octagon of sides 2 cm is made by
cutting the corners of a square.
area of square
area of octagon
Calculate the ratio:
a  b
c
Express the answer in the form
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2
3
1
2
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ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Round 2
1.
The task is to reduce a given integer to the smallest integer possible using simple
calculations. As an example, to reduce 71:
71 - 1 = 70
Each of the single digits can be used only once.
70  7 = 10
Each simple calculation involves one operation ( + - x ) with
one single digit number.
10  5 = 2
2
- 2 = 0
Using this strategy (method), reduce 106 down to an integer less than 20
Show your steps in the table (the solution starts with….  8 )
operation
result
2.
8
125 000
What is the largest integer that may be reduced to 1 for the task described above ?
3.
A square based pyramid with all its edges of
length 4 cm is cut parallel to its base to give two
parts of equal volume.
How far down, measured vertically from the top
towards the horizontal base, is the cut made ?
Write your answer as a power of 2.
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ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Round 3
1.
5 x - 5 x  2 = 120
5 . Solve for x.
1
2.
If the pattern of 90o triangles
is
continued,
how
many
triangles are needed for the
hypotenuse to be greater than
10 ?
1
2
3
3.
Calculate the area of the largest equilateral triangle that fits inside a square of area
1 m2.
Write your answer in the form of
a b  c , where a, b and c are integers.
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ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Round 4
1.
A cube of volume 3 cm3 is placed on top of a cube of volume 15 cm3. Finally, a cube
of volume  cm3 is placed on top of the 3 cm3 cube.
What is the height of the stack of three cubes ?
4
2.
3
A rectangular card measuring 4 by 3 can be folded lengthways to form an open
cylinder and widthways to form a different open cylinder.
Find the difference in volume of the two cylinders.
3.
Find the sum of two numbers whose difference, sum and product are in the ratio
1 : 5 : 24
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ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Round 5
1.
A cube of volume 1 m3 sits tightly inside a sphere.
Calculate the volume of the sphere.
Give your answer as a multiple of .
2.
If n is the 2nd of 3 consecutive perfect squares, find in terms of n the difference
between the 1st and 3rd perfect squares.
3.
A STOP sign 0.5 metres high is fixed
to a lamp post such that the bottom
of the sign is 2 metres up from the
ground as shown.
lamp
lamp post
STOP sign
0.5m high
The lamp casts a shadow of the sign
on the ground that is 0.3 metres wide
and 0.5 metres from the bottom of
the lamp post.
2.0m
How high is the lamp post ?
ground
0.3m
0.5m
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ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Team
Number
score
Round 6
1.
Find the 4th root of the 3rd root of the square root of 4 to the power of factorial 3.
4 3
4 3!
2.
D
C
A
B
10m
H
G
15m
E
F
20m
A spider is in the top corner A of a rectangular room 20m long, 15m wide and 10m high.
It spots a tasty meal in the furthest corner of the room at G.
What is the shortest distance the spider could travel along the surface of the room
to claim its prize ?
3.
By completing the magic square, find the
product of the two numbers found in the
shaded cells.
3
20
14
1
9
21
13
16
8
25
24
11
18
10
17
12
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3
ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris
Answers
Trial Round
1.
78
2.
2 + 8
3.
8
Round 1
1.
65231
2.
13600
3.
1
2
2
Round 2
1.
17
2.
725 760
3.
2
3.
2 3 3
3.
20
3.
4 72
3.
506
7
6
Round 3
1.
3½
2.
7
Round 4
1.
4½
2.
32
Round 5
1.
3

2
2.
4 n
Round 6
1.
2
2.
5 41
ISMTF Junior Mathematics Competition 2006
Team Event
British School of Paris