SASMO 2017 Secondary 4 (Grade 10) Contest

Question 1

Calculate the value of
16 x 625 — 125 x 24 +. 96 x 25.

1. 9400
2. 9500
3. 9600
4. 9700
5. None of the above

Question 2

The number 2019 is the sum of two prime numbers. What is the product of
these prime numbers?

1. 2018
2. 4034
3. 6048
4. 10070
5. None of the above

Question 3

Ina3x 3x3 cube, made of 27 small cubes, 26 cubes are visible. How many
visible small cubes are in 4 x 4 x 4 cube?

1. 8
2. 27
3. 48
4. 56
5. 64

Question 4

Which one of the following has the greatest value?

1. 8
2. Qu
3. 177
4. 48 Ex Bi?
5. See the source image for option E.

Question 5

It is given that 1‹a‹4and-8‹b‹-4.
Find the least possible value of —2ab + a? + b?.
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1. 9
2. 16
3. 25
4. 36
5. 49

Question 6

If xy and oe are integers, how many possible values of (x — y) are there?
A 1

1. 1
2. 2 Gc. 3
3. See the source image for option C.
4. 4
5. None of the above

Question 7

What is the 408t" digit after the decimal point of the decimal form of “& i?
AA
B2.
G4
SS D.5
E. 8

1. 1 Bs 2
2. See the source image for option B.
3. 4 Bes
4. See the source image for option D.
5. 8

Question 8

ees It is given that n! = nx (n—1) x (n—- 2) x...x 3.x 2x 1. For example, 4! =
4X 3x2 1, Find the remainder when 1! + 2! +3! +--+ 10! is divided by 9.

See] A. 0

1. 0 Br i G2
2. 1
3. See the source image for option C.
4. 3
5. None of the above = Sey

Question 9

ES The circle below has radius 8 cm. PQ and RQ are both tangents to the circle,
E and the distance from the centre of the circle to point Q is ¥128 cm. Find the
area of the unshaded region PQR.
LIN P
LN
\ ia
GE
a

1. 64 — 641
2. 647
3. 64-167
4. 64m — 64
5. None of the above

Question 10

Find the largest integer value of m for which
1 el 1 4,
We oe ee
Vvi+V3 V34+V5 V5+V7 ¥23 +025

1. -1
2. 0
3. 4
4. 2
5. 3

Question 11

Paul, Queenie, Rosa and Samantha come from different countries: Philippines,
Qatar, Russia and Singapore. Each of them has different occupation:
Pharmacist, Quality Manager, Reporter and Scientist.
Below are some hints of the country and occupation for each person.
1. No person has a name or a country with the same first letter as their

occupation.
2. Rosa is from Philippines and her occupation has the most number of letters.
3. Paul and Samantha are friends with the Reporter who comes from

Singapore.

4, The Scientist is from Russia.
What is Paul’s occupation?

1. Reporter
2. Scientist
3. Quality Manager
4. Pharmacist
5. See the source image for option E.

Question 12

How many numbers appear in both sequences below?
6,11, 16, 21, ...,451,456
6,15, 24, 33, ..., 447,456

1. 10
2. 11 CanlZ DE 43
3. See the source image for option C.
4. 13 Es 14
5. 14

Question 13

Two darts are thrown at a 3-by-3 square on the right, each
lands in a different 1-by-1 square at random.
What is the probability that the 1-by-1 squares the darts land in
are next to each other, either horizontally or vertically?

1. 9 my
2. 10
3. See the source image for option C.
4. See the source image for option D.
5. None of the above

Question 14

How many integers «x satisfy the following inequality
(x= 3) + 7)(x — 8)(x +4) ‹ 07

1. 6
2. 7 GC. 8
3. See the source image for option C.
4. 9
5. 710

Question 15

Only 2 out of the 4 figures below can form the
rectangular solid as shown on the right. Which 2 figures
can form the rectangular solid?

P 1 Q 1:

R
Ss

1. (P and S)
2. (Rand P)
3. (Qand S)
4. (P and Q)
5. (Rand S)

Question 16

= Simplify the following expression: 1
=| 1 1 1 4 1 1
(1-33) @-a0) * G35) *~ * Go-2) “Gr )

E =|

Question 17

i Tf the four-digit number A69A is divisible by 36, find the value of A.
ES]

Question 18

The teacher asks Lisa to write integers starting from 1 on the whiteboard.
F However, Lisa skips all the integers that contain the digit 7. What is the 100"
integer that Lisa writes?

Question 19

“Double Factorial” n!! of a positive integer n is defined as
ee aE ae n=even
“tn x (n-2) XX 3X1, n=odd
For example,
SU=5x3x1,
6ll=6x4x2
Simplify
17! x 16! +16! x 15!!
1x2x3x..x 15x16"

Question 20

In the following, all the different letters stand for different digits.
G E T
#2 G 9 D
S A S M _O
What is the value of S+A+S+M+0?