SIMOC, Secondary 1 Contest
SIMOC SECONDARY 1 MOCK TEST
Section A
1.
It is given that a  b =
(a)
(b)
(c)
(d)
(e)
2.
𝑎×𝑏
𝑎−𝑏
. Find the value of 12  3  2  6.
1
7
14
24
None of the above
The following bar graph shows the favourite colour of a class of 40 students (each
student chooses exactly one colour). The tic marks on the vertical axis are equally
spaced. How many students’ favourite colour is blue?
No. of
students
0
(a)
(b)
(c)
(d)
(e)
3.
Favourite Colour
yellow
green
blue
red
colour
4
8
12
16
20
The diagram shows a square of length 7 cm and two quarter-circular arcs of radius 7 cm.
22
Find the area of the shaded region. (Take  to be 7 .)
(a)
(b)
(c)
(d)
(e)
14 m2
17 m2
28 cm2
30 m2
None of the above
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SIMOC, Secondary 1 Contest
4.
The figure shows the first three hexagonal numbers: 1, 6 and 15. Find T4.
T1 = 1
(a)
(b)
(c)
(d)
(e)
5.
24 [Possible mistake: easy to miscount if didn’t draw hexagonal accurately]
25
26
27
28
1953
1955
1957
1959
1961
Find the least value of n such that its LCM with 6 is 18.
(a)
(b)
(c)
(d)
(e)
7.
T3 = 15
The Southeast Asian (SEA) Games is held once every two years, except in 1963 (i.e. it
was held in 1961 and 1965, but not in 1963). Singapore hosted the 28th SEA Games in
2015. When was the first SEA Games held (although it was known as South East Asian
Peninsula Games at that time)?
(a)
(b)
(c)
(d)
(e)
6.
T2 = 6
3
6
9
12
15
The cost price of a pair of shoes was $15. Mr Lee sold the pair of shoes to a customer
for $30. The latter gave Mr Lee a $50 note, but Mr Lee did not have enough change.
So Mr Lee went to Mr Tan in the shop next door and exchanged the $50 note into
smaller notes. Then Mr Lee gave the customer a $20 change.
After the customer had left, Mr Tan discovered that the $50 note was a counterfeit. So
Mr Lee compensated Mr Tan $50. How much money did Mr Lee lose as compared to
if the $50 note was real?
(a)
(b)
(c)
(d)
(e)
$15
$20
$35
$50
$65
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SIMOC, Secondary 1 Contest
8.
If a and b are positive integers such that ab = 47, find the largest prime factor of a + b.
(a)
(b)
(c)
(d)
(e)
9.
A man walks for 5 metres in one direction, turns 45 to his right and walks for another
5 metres in that direction. Then he turns another 45 to his right and walks for another
5 metres in that direction. He continues walking in this pattern until he reaches his
original starting point. Find the total distance that the man has walked.
(a)
(b)
(c)
(d)
(e)
10.
2
3
17
47
None of the above
20 metres
30 metres
40 metres
50 metres
None of the above
The diagram shows two circles X and Y just touching each other. The radius of Circle
Y is 5 times the radius of Circle X. Circle X is rotated around Circle Y until Circle X
comes back to its starting point (both circles remain in contact with each other
throughout the rolling). How many rounds has Circle X rotated?
Y
X
(a)
(b)
(c)
(d)
(e)
11.
2.5
5
6
25
None of the above
If the four-digit number 19N6 is divisible by 14, find N.
(a)
(b)
(c)
(d)
(e)
0
1
2
3
4
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SIMOC, Secondary 1 Contest
12.
The outer walls of a rectangular house have dimensions 15 metres by 10 metres. A man
wants to build a garden around the house such that the garden is 7 metres from the outer
22
walls of the house. What is the area of the garden? (Take  to be 7 if necessary.)
(a)
(b)
(c)
(d)
(e)
13.
In a chess tournament, each player has to play one game with every other player. Seven
players, Albert, Ben, Charles, Dennis, Ethan, Francis and George, took part in the
tournament. So far, Albert has played 6 games, Ben has played 5 games, Charles has
played 4 games, Dennis has played 3 games, Ethan has played 2 games and Francis has
played 1 game. How many games has George played?
(a)
(b)
(c)
(d)
(e)
14.
220 m2
224 m2
504 m2
546 m2
None of the above
1
2
3
4
5
The decimal numeral system uses ten symbols 0 to 9 to form numbers, while the binary
numeral system uses only two symbols 0 and 1 to form numbers. The following table
shows the binary numbers for the decimal numbers 0 to 5.
Decimal Number
Binary Number
0
0
1
1
2
10
3
11
4
100
5
101
What is the binary number for the decimal number 33?
(a)
(b)
(c)
(d)
(e)
15.
11 110
11 111
100 000
100 001
100 010
There are ten stacks of coins. One of the stacks contains 10 identical counterfeit coins.
Each of the remaining nine stacks contains 10 genuine coins. All the genuine coins are
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SIMOC, Secondary 1 Contest
identical. The mass of a genuine coin is 5 g while the mass of a counterfeit coin is 4.6
g.
Jaime does not know which stack contains counterfeit coins. She takes 1 coin from the
first stack, 2 coins from the second stack, 3 coins from the third stack, and so on, until
she takes 10 coins from the tenth and last stack. Then she puts all the coins on a
weighing machine and finds that the mass of all the coins is 271.8 g.
So which stack contains the counterfeit coins?
(a)
(b)
(c)
(d)
(e)
Fifth stack
Six stack
Seventh stack
Eighth stack
None of the above
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SIMOC, Secondary 1 Contest
Section B
16.
The diagram shows parts of a city where the lines are roads. Alice walks from point A
to point B along the roads without ‘backtracking’ (i.e. she can only walk downwards or
to the right in the diagram below). How many ways can she walk from A to B?
A
B
17.
In a sequence, the nth term, Tn, is equal to the sum of the squares of the digits of the
previous term, Tn1, for all n > 1. If the sequence terminates at 1, the starting number is
called a happy number. Otherwise, it is called a sad number. Find all the happy years
in the decade 2011 to 2020.
18.
The diagram shows four cubes in which some of the corners have been removed. Two
of the cubes have exactly the same shape. Which are the two cubes?
A
19.
B
C
D
The following is a conversation between Charles and Denise who met on a bus.
Charles: I have three children. Assuming that their ages are whole numbers, the
product of their ages is 48, and the sum of their ages is the bus number of this
bus that we are on.
Denise: Of course I know the bus number, but I still don’t know their ages.
Charles: Oh, I forgot to tell you that two of my children have the same age.
Denise: Oh, now I know their ages.
So what are the ages of the three children?
20.
Find the next term of the following sequence: 1, 11, 21, 1211, 111221, …
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SIMOC, Secondary 1 Contest
21.
Five rectangular sheets of paper can be put up on a bulletin board by using a minimum
of 11 thumbtacks if the corners are overlapped as shown in the diagram, where the black
dots represent thumbtacks and the dotted lines represent the edges of the sheets of paper
that are covered by other sheets of paper.
What is the minimum number of thumbtacks required to put up n2 rectangular sheets of
paper, where n is a positive integer, on a very large bulletin board in the same way as
described above?
22.
Given that n! = n  (n  1)  (n  2)  …  3  2  1, find the remainder when
1! + 2! + 3! + … + 2015!
is divided by 8.
23.
There are 500 students, and 500 lockers numbered 1 to 500.
The first student opens all the 500 lockers.
The second student then closes every locker with an even number, i.e. 2, 4, 6, …
The third student then ‘reverses’ every third locker, i.e. if the locker is open, she will
close it; but if the locker is closed, she will open it.
The fourth student then ‘reverses’ every fourth locker, and so on until the 500th student
has ‘reversed’ the 500th locker.
What is the locker with the largest number that will remain open in the end?
24.
The following shows the top view and the front view of a structure. The structure does
not have any painted lines on it. Notice also that there are no dotted (or hidden) lines.
Draw the side view. (It does not matter whether you draw the left or right side view.
Both answers will be accepted.)
Top View
Front View
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SIMOC, Secondary 1 Contest
25.
In the following cryptarithm, all the different letters stand for different digits. Find the
five-digit sum SUSAN.
+
S
R
E
D
D
E
E
R
U
S
A
N
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