SASMO 2018 Secondary 1 (Grade 7) Contest

Question 1

Find the value of the following
(1996 + 2497 + 3507) +16

1. 500
2. 800
3. 5000
4. 8000
5. None of the above

Question 2

Which of the following is NOT a rational number?

1. 1? Be 0:333 wa
2. 0:333 5.
3. . (V7)
4. See the source image for option D.
5. None of the above

Question 3

Which steps have mathematical errors in the following sequence of reasoning?
0x7=0and0x8=0 (1)
0x7=0x8 (2)
ox7=2x8 (3)
Since ; Sr (4)
1x7=1%x8, therefore 7=8.

1. (1) and (3)
2. (1) and (4)
3. (2) and (3)
4. (3) and (4)
5. (1), (2), (3) and (4)

Question 4

If p is a prime number, then which of the following is NOT ALWAYS true?

1. The number 2 x p is an even number.
2. The number 2 x p + 3 is an odd number.
3. The number p x p is not a prime number.
4. The number 3 x p + p is not a prime number.
5. The number p + 1 is an even number.

Question 5

Ronald rolls two 6-sided standard dice and calculates the sum of the two
numbers shown on them. What is the most likely to occur among the choices
below?

1. The sum is 4.
2. The sum is an even number.
3. The sum is 15.
4. The sum is 12.
5. The sum is an odd number less than 5.

Question 6

You received 4 gift vouchers from ‘Forever Chic’ store. Which option will save
you the most money if you want to buy 2 items of the same price?

1. “Buy 1, get 1 free”.
2. “1%t item: 80% sale. 24 item: 20% of the 1‘ item’s sale price”.
3. “15 item: 60% sale. 2"4 item: 60% of the 1* item’s sale price”.
4. “1 item: 70% sale. 24 item: 30% of the 1% item’s sale price”.
5. All of the above options have the same price.

Question 7

Goofy started running at 12 m/s (meters per second) at 4:00 pm. His dog,
Pluto, started following him at 4:03 pm and ran at 18 m/s. At what time would
Pluto catch up to Goofy?

1. 4.08 pm
2. 4.09 pm
3. 4.10 pm
4. 4.11 pm
5. None of the above

Question 8

‘ What is the smallest possible value of n such that the sum
/ Lt 2434+--4n
is divisible by 5 and 9?
A5
Bo
Cc. 10

1. 5
2. 9
3. 10
4. 45
5. None of the above

Question 9

\ Integers starting from 1 are arranged in the following way:
1 Row 1
2 3 Row 2
4 5 6 Row 3
ra 8 9 10 Row 4
i 12 13 14 15 Row 5
In what row can you find 2018?

1. 46
2. 63
3. 64
4. 66
5. None of the above

Question 10

Machine A can produce 450 cheese blocks in m hours. If machine A and
machine B work together at their respective rates, their combined production in
n hours is 450 cheese blocks altogether. If machine B works alone, how long, in
hours, would it take to produce 450 cheese blocks?
m=n
A Fou
mxn
ey
n
Oa
nom
De xn
mxn
aa

1. —— mxn
2. n
3. —— n-m Dice
4. See the source image for option D.
5. a

Question 11

Letn!=1x2x3x...xn. For example, 4!=1x2x3x4and3!=1x2x3.
Find the last digit of 9! + 99! + 999! + 9999! + 99999! ,
Al

1. 1
2. 4
3. 6
4. 9
5. None of the above

Question 12

The least common multiple (LCM) of two positive integers is 216. If the ratio of
the two positive integers is 2:9, find their highest common factor (HCF).

1. 12
2. 18
3. 24
4. 108
5. None of the above

Question 13

Find the sum of the shaded angles in the figure.
= | A. 360°
B, 540°
S Cc. 720°
D. 900°
=| E. None of the above
=
BS

1. 360°
2. 540°
3. 720°
4. 900°
5. None of the above

Question 14

The figure on the right is made of 5 cubes. The front ‹›‹
and side views of the figure are shown below. a i
1 a co

a Front View Side View
; What is the largest number of cubes in a figure with the following front and
side views:
{
AES
Front View Side View
s A. 20
B35
G32
i D. 30
E. None of the above.
sa
oa
&
i
a

1. 20
2. 35
3. 32
4. 30
5. None of the above.

Question 15

Danica, Jessica, Marina, Neo and Samantha went to a popular pet store at
different times and bought different pets. Marina was the second person who
went inside the store. Danica went in before the person who bought a cat but
went inside after the person who bought a hamster. Jessica went inside after
Neo. The last person who went inside bought a rabbit. Marina did not buy a cat,
and Samantha bought a dog. Who bought a fish?

1. Danica
2. Jessica
3. Marina
4. Neo
5. Samantha

Question 16

How many triangles are there in the figure?
. (Soe, | Rane | Pocmescno me ores fies achqanaemanse :
i
:

—
i
} | :
[ee
1 of —— | =
:
hel =
a @
I | oc \
ieee SS
‘Cia ss == i | 2 1
ees a
= |

Question 17

The bar chart below shows the production growth of cars in a factory for the first
i half of the year. The average number of cars manufactured in the first half of the
! year is 20% less than the average number of cars manufactured in the second
half of the year. What is the average number of cars manufactured in the entire
Sl year?
SS] | 4900 -— —— Se eee
aS 4800
SS] 4700
KS 2 4600
x 8 4500
i 8
SS zum
2 03 —
4200 i
4100
aS
so @ 2 EE
Sl January Feburary ‘March April May June
Month
E

i}
=

Question 18

Find the smallest positive integer n for which 250n is a multiple of 900.
Ss
E
a s
ee
‘S
SS Sl

Question 19

An operator A acts on two numbers to give the following results:

7TA2=94

3A3=66

5A4=98

1149 = 2018
What is 4 A 7 equal to?

Question 20

Given a,b,c and d are positive integers such that a* + b* + c+ + d* = 2018,
find the value of a? + b? + c? + d?.