!
YOU MAY USE THIS PAGE FOR ROUGH WORKINGS
1. Given !, ! and ! are three consecutive
4. Find the value of 12345! − 12344! .
!
even numbers and ! = 1728.
Find the value of !".
(A)
1
(B)
10 000
(A)
80
(C)
12 345
(B)
120
(D)
24 689
(C)
140
(E)
None of the above
(D)
192
(E)
None of the above
5.
2. Find the simplest expression for
(A)
(B)
!!"
!!"
Given !!"" is a square number, find the
value of (! + !).
.
(A)
8
(B)
9
!
(C)
10
!
(D)
11
!
(E)
None of the above
!
(C)
1
(D)
2
(E)
None of the above
6. !"# is an equilateral triangle of side 6 !". It
first rotates about !, then !! , without sliding.
As a result, Vertex A travels from ! to !! ,
3. Find the possible value(s) of ! in
!
!!!
+
!
!!!
then comes to rest at !! . Find the length, in
!", of the path travelled by vertex A, in terms
!
−!=0.
of !.
(A)
0, 5
(B)
1, 4
(C)
2, 3
(D)
3
(A)
8!
(E)
6
(B)
10!
(C)
12!
(D)
14π
(E)
None of the above
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SEAMO 2016 Paper E © TCIMO
7. The figure shows a can of height 8 !". The
9. ! and ! are midpoints of !" and !" ,
circumference of its base is 44 !". Find
respectively, in rectangle !"#$ . Lines !"
the shortest distance from ! to !, without
and !" intersect at point ! . Find ∠!"# ,
cutting through the can.
(A)
18
(B)
20
(C)
22
(D)
24
(E)
26
given that ∠!"# = ∠!"# + 31°.
8. In triangle !"# , ∠!"# = 90° , !" = 7!"
(A)
23°
(B)
31°
(C)
38°
(D)
42°
(E)
None of the above
10. Suppose !! + 1 = 3! , !! + 1 = 3! , then
and !" = 24!" . ! is a point inside the
the value of
triangle such that its shortest distance to
!
!!
!
+ !! is ____.
each side of the triangle is the same. What
is this distance?
(A)
5
(B)
6
(C)
7
(D)
8
(E)
9
11. Find the value of
(A)
1
(B)
2
(C)
3
(D)
6
(E)
8
SEAMO 2016 Paper E © TCIMO
!
!!! 3!!
4
(A)
0
(B)
1
(C)
14
(D)
16
(E)
18
−
!
!! !
2!! − 3 .
12. In the figure below, !" and !" are tangents
15. The area of rectangle !"#$ is is 35!!! .
to the circle with centre ! . Suppose
Points ! and ! divide side !" into 3 equal
!" = 3 !", !" = 2 !", find !" in !".
segments. ! is the midpoint of side !". Find
the area of green triangle !"# in !!! .
(A)
2
(B)
3
(C)
4
(D)
5
(E)
6
(A)
1.5
(B)
2
(C)
2.5
(D)
3
(E)
None of the above
13. Find the remainder when 55!"#$ + 17 is
16. Given that m +
divided by 8.
(A)
0
(B)
1
(C)
3
(D)
5
(E)
7
1
= 4, find the value of
m
m4+
1
m4
(A)
169
(B)
181
14. The sum of a positive integer and 100 is a
(C)
194
square number. The sum of same positive
(D)
196
integer and 168 is also a square number.
(E)
None of the above
.
Find the integer.
(A)
100
(B)
121
(C)
144
(D)
156
(E)
None of the above
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SEAMO 2016 Paper E © TCIMO
17. Find the integer part of
20. The circumference of a circular lake is
1
1
1
1
1
1
1
1
+
+
+
+
+
+
2010 2011 2012 2013 2014 2015 2016
30 !". Paul and Mary cycles around the lake
in opposite directions, both starting from the
same point.
(A)
270
(B)
271
(C)
287
(D)
288
(E)
None of the above
18. An integer is chosen from the set {1, 2,
3, … , 499, 500}. The probability that this
integer is divisible by 9 or 11 is
!
!
, in its
Paul’s speed is 250 !/!"#, but he rests for
lowest terms. Find the value of ! + !.
5 minutes after every 55 minutes of cycling.
Mary’s speed is 200 !/!"#, but she rests for
(A)
110
(B)
111
(C)
117
(D)
118
(E)
119
10 minutes after every 1h of cycling. Find the
time taken, in hours, for them to meet for the
first time.
19. It is given ! ! + 2! = 3, find the value of
! ! + 7! ! + 8! ! − 13! + 12
(A)
12
(B)
13
(C)
14
(D)
15
(E)
16
SEAMO 2016 Paper E © TCIMO
6
!
(A)
1 !"
(B)
1 !"
(C)
2 !"
(D)
2 !"
(E)
2 !"
!
!
!
!
QUESTIONS 21 - 25 ARE FREE RESPONSE
24. The radius of the 2 identical circles is 3 !".
Write your answer in the free response section of
the ANSWER SHEET provided.
They are inscribed in a larger circle of radius
9 !", as shown in the figure below. Find the
area of blue shaded region, in terms of !.
21. Fill in each circle with one number from 1
to 10 such that the sum of any five
adjacent numbers is the minimum.
25. How many ways are there to colour a
10×10 grid using two colours, such that
22. Suppose ! and n are two positive integers
each 2×2 grid contains exactly 2 squares of
such that ! > ! . Given ! + ! = 28 and
each colour?
!! + !! = 400, find the value of !! − !! .
23.
Evaluate the following
1 1
1
2 2
2
+ + ⋯+
+ + + ⋯+
+
2 3
30
3 4
30
3 3
3
28 28
29
+ + ⋯+
+ ⋯+
+
+
4 5
30
29 30
30
END OF PAPER
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SEAMO 2016 Paper E © TCIMO