Download ISMTF Junior Mathematics Competition 2006 Individual Event British

ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Trial Round
1.
The average of four numbers is 85. If 80 is added to make a fifth number, what is the new
average ?
A.
80
B.
81
C.
82
D.
83
E.
84
Ans
2.
20 students at the BSP play football or rugby. 5 students do both. If 7 students play football
only, how many play rugby ?
A.
5
B.
8
C.
12
D.
13
E.
15
Ans
3.
If 102y = 25, then what is 10-y ?
A.
1
125
B.
1
625
C.
1
50
D.
1
25
E.
1
5
Ans
4.
The time shown on a 12-hour clock face is exactly 2:15. What is the angle between the hour
hand and the minute hand ?
A.
5o
B.
7½ o
C.
22½ o
D.
28 o
E.
30 o
Ans
5
A rectangle has an area of 24. The graph of the length as a function of its width is :
A.
a parabola that opens upward
B.
a parabola that opens downward
C.
a hyperbola
D.
one branch of a hyperbola
E.
not able to be determined from the given information
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 1
1.
29 2  19 2
14 2  22
A.
2
is equal to
B.
12
5
C.
3
D.
13
7
E.
10
3
Ans
2.
The smallest prime number which is a factor of 3 7  11 5 is
A.
11
B.
7
C.
5
D.
3
E.
2
Ans
3.
Two congruent equilateral triangles, each with an
area of 36 cm2, are placed on top of each other so
that they form a regular hexagon in the centre.
Find the area of the hexagon.
A.
30
B.
32
C.
27
D.
24
E.
28
Ans
4.
The series
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ……….. - 60 is equal to
A.
B.
-60
-30
C.
0
D.
36
E.
60
Ans
5.
What is the value of
A.
3
B.

6  6  6  6  .......
C.
10
D.
?
22
7
E.
6
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 2
1.
One quarter of the students in a maths class are girls. Of these girls, one fifth have green
eyes. If there are four green-eyed girls, how many boys are there ?
A.
8
B.
12
C.
20
D.
32
E.
60
Ans
2.
The reciprocal of
A.
12
B.
3x
1
is
. Calculate the value of x.
4
12
14
C.
16
D.
20
E.
8
Ans
3.
The number of square metres in the total
surface area of a right cylinder is equal to the
number of cubic metres of its volume. If the
radius r of its base is five times its height h,
what is its volume ?
A.
1728
5
B. 1728
C.
1128
5
D.
r
2126
5
E.
h
1528
5
Ans
4.
ABCD is a rectangle. How many circles, in the same plane as ABCD, have a diameter whose
endpoints are corners of the rectangle ?
A.
2
B.
5
C.
6
D.
4
E.
1
Ans
5.
The square shown has a side of length 2 units.
What is the radius of the circle ?
A.
1
B.
4
5
C.
5
4
D.
1
5
2
E.
2
5
5
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 3
1.
If 3a 3b 3c = 729, then the average of a, b and c is:
A.
6
B.
3
C.
2
D.
9
E.
81
Ans
2.
A new car is bought. The car decreases in value by 20% each year. After three years, it will be
worth x % of its original value. Calculate x.
A.
45.2%
B.
60%
C.
55.2%
D.
51.2%
E.
40%
Ans
3.
The area of a triangle bounded by the lines y = x , y = -x and y = 6 is:
A.
12
B.
12 2
C.
24
D.
24 2
E.
36
Ans
4.
John often drives to Paris from home. If he averages 42 km/h instead of 40 km/h, he can save
8 minutes on his journey. How many kilometres does he live from Paris ?
A.
105
B.
112
C.
116
D.
120
E.
125
Ans
5.
An isosceles triangle has sides 6cm, 12cm and 12cm. A circle passes through the three vertices
(corners) of the triangle.
The radius of the circle is :
A.
8 15
5
B.
4 3
C.
3 5
D.
6 3
E.
9
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 4
1.
Which one of the following is an odd number ?
A.
74 + 1
B.
34 + 2
C.
54 + 3
D.
114 + 7
E.
74 + 5
Ans
2.
In a school election, Susan received
2
3
of the ballots cast. Mary received
1
5
of the remaining
ballots and Bill received all of the other votes.
If Bill received 48 votes, how many votes did Susan receive ?
A.
75
B.
90
C.
120
D.
150
E.
180
Ans
3.
A pyramid consists of a square base of side 4cm and 4 equilateral
triangles as lateral faces.
Find the height of the pyramid.
A.
2
3
B.
C.
2
D.
6
E.
2 2
Ans
4.
How many positive, even three-digit numbers exist such that the sum of the hundreds digit and
the tens digit equals the units digit ?
A.
12
B.
14
C.
16
D.
18
E.
20
Ans
5.
a =
1
2
3
4
5
6
Which estimate is correct ?
A. 1  a  2
B. 2  a  3
C. 3  a  4
D. 4  a  5
E. 5  a  6
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 5
1.
My aunt has five children, who were born at three year intervals. Her oldest child is seven times
older than her youngest child. How old is her third child now ?
A.
15
B.
9
C.
12
D.
8
E.
5
Ans
2.
Find the sum of the series (-300) + (-297) + (-294) + …. + (306) + (309)
A.
918
B.
609
C.
603
D.
303
E.
0
Ans
3.
The square and the equilateral triangle have the same height.
The area of the square = k x the area of the triangle. Find k.
A.
2
B.
3
C.
2 2
D.
2 3
E.
3 2
Ans
4.
What is the largest power of 2 that divides into 632 - 1 ?
A.
21
B.
26
C.
27
D.
231
E.
263
Ans
5.
A straight line passes through A (-240,0) and B (0,300). The number of points on the straight
line between A and B (excluding these two points) that have both coordinates as integers is :
A.
239
B.
240
C.
60
D.
59
E.
58
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 6
1.
a and b are both odd numbers. The only even number is :
A. ab
B. a 2b
C. a + b + 1
D. 2a + 3b + 7
E. 2a + b
Ans
2.
The radius of a circle is decreased by 30%.
By what percentage is the area of the circle decreased ?
A.
30%
B.
49%
C.
51%
D.
60%
E.
70%
Ans
3.
What is the remainder when 1234 x 5678 x 4321 x 9 is divided by 5 ?
A.
0
B.
1
C.
2
D.
3
E.
4
Ans
P
4.
PQRS is a common diameter of three circles. The area of
the middle circle is the average of the areas of the other
Q
two. If PQ = 2 and RS = 1, the length of QR is :
A.
1+ 6
B.
6-1
C.
4
D.
3
R
E.
5
S
Ans
5.
If f(x) = ax 4 - bx 2 + x + 5 and
A.
-5
B.
-2
C.
1
f(-3) = 2 , then f(3) is :
D.
3
E.
8
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 7
1.
When n is a positive integer, which of the following is always divisible by 3 ?
A.
(n + 1)(n + 4)
B.
D.
n (n + 3)(n - 3)
E.
n (n + 2)(n + 6)
C. n (n + 2)(n + 4)
n (n + 3)(n + 6)
Ans
2.
A quadrilateral may have interior angles of 90 o. Here are some examples.
no 90o
angles
two 90o
angles
four 90o
angles
What is the maximum number of 90o angles in a 100 sided polygon ?
A.
100
B.
50
C.
98
D.
52
E.
96
Ans
3.
It is known that a =
A.
39
B.
3* * *
13
9 is a positive integer. a is therefore :
C.
29
D.
19
E.
23
Ans
4.
A rectangle measures 4 metres by 36 metres. A circle has the same area as this rectangle.
Find the circumference of the circle in terms of  .
A.
24
B.
2
C.
12
D.
144
E.
2
Ans
5.
Three vertices of a regular hexagon are chosen at random.
The probability that they form an equilateral triangle is :
A.
3
20
B.
1
10
C.
1
2
D.
1
5
E.
2
5
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Round 8
1.
If x = ¼, which of the following has the largest value ?
A.
x
B.
x2
x
2
C.
D.
1
x
E.
x
Ans
2.
When simplified, the units digit of 52006 + 62006 + 72006 is
A.
8
B.
2
C.
0
D.
9
E.
7
Ans
3.
Find the value of x , given that
A.
5
B.
-5
64
1  2x
2
C.

1
8x
1
D.
2
E.
-1
Ans
4.
Two concentric circles have a centre O. The radius of the smaller
circle is 4 and the difference between their circumferences is
10.
O
The radius of the larger circle is :
A.
14
B.
4  10

C.
14

D.
5 + 4
E.
4+
5

Ans
5.
The area and perimeter of this triangle are numerically equal.
Calculate the radius of the inscribed circle.
A.
1
B.
2
C.
3
D.
½ 3
E.
5
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Student
Number
score
Tie Breaker
1.
The sum of two numbers is 10. Their product is 20.
Calculate the sum of their reciprocals.
A.
1
10
1
2
B.
C.
1
D.
2
E.
4
Ans
2.
a is 40% of b.
A.
50%
Then b exceeds a by what percent of a ?
B.
100%
C.
140%
D.
150%
E.
250%
Ans
3.
Calculate
A.
-2
 14
3
B.
  13
4
-1
C.
0
D.
1
E.
2
Ans
4
Alan and Bob begin to jog round a 400 metre track, leaving at the exact same time from the
exact same starting point but in opposite directions. It takes Alan 2 minutes and Bob 3 minutes
to jog one lap.
If they both jog for 26 minutes at these constant rates, how many times will they cross after
starting off ?
A.
21
B.
19
C.
22
D.
20
E.
18
Ans
5.
If the following sum is evaluated, what are the last two digits in the result ?
2006
n!
n 1
A.
03
B.
13
C.
33
D.
53
E.
83
Ans
ISMTF Junior Mathematics Competition 2006
Individual Event
British School of Paris
Individual Event Answers
Trial Round
Round 1
Round 2
1.
E.
1.
B
1.
E
2.
D
2.
E
2.
C
3.
E
3.
D
3.
A
4.
C
4.
A
4.
B
5.
D
5.
A
5.
C
Round 3
Round 4
Round 5
1.
C
1.
B
1.
D
2.
D
2.
C
2.
A
3.
E
3.
E
3.
B
4.
B
4.
E
4.
C
5.
A
5.
A
5.
D
Round 6
Round 7
Round 8
1.
D
1.
C
1.
D
2.
C
2.
D
2.
C
3.
D
3.
D
3.
E
4.
B
4.
A
4.
E
5.
E
5.
B
5.
B
Tie Breaker
1.
B
2.
D
3.
E
4.
A
5.
B