SASMO 2017 Secondary 3 (Grade 9) Contest

Question 1

E Calculate the value of
ee 23 x 51 +39 x 24 + 25 x 39 — 49 x 16.
s A. 2070
: B. 2300
i Cc. 3084
eal D. 3868
i E. None of the above
C
E

1. 2070
2. 2300
3. 3084
4. 3868
5. None of the above

Question 2

eS What is the last digit of the product 32°17 x 720177
is 1
md
: B2
: G3
& D.7
S| E. 9
SS

1. 1
2. 2 Gs D7
3. See the source image for option C.
4. See the source image for option D.
5. 9

Question 3

i It can be shown that 5 = 4 by the following steps:
: (1) —20 = ~20
i (2) 25-45 = 16 — 36
: (3) 5?-5x9=42-4x9
eS (4) St-sx94S=4-4x945
{ 2 2
©) (342) (4-3)
©) s-3=4-2
(7) 5=4
Which transition step is wrong?
' A. (2) to (3)

1. (2) to (3)
2. (3) to (4)
3. (4) to (5)
4. (5) to (6)
5. (6) to (7)

Question 4

Fifteen students took an exam. The exam scores are 84, 85, 87, 88 and 90. Five
of them got 84 and two of them got 85. If the most common score is 87, what is
the average score of the fifteen students?

1. 85.5
2. 86
3. 86.5
4. 87 Es 87.5
5. 87.5

Question 5

2_42

Given that —6 ‹ a ‹7 and —3 ‹b ‹5, find the greatest possible value of

1. 6
2. 8 €.9
3. See the source image for option C.
4. 10 Ee 42
5. 12

Question 6

Find the value of X in the following sequence.

[a [8 [3 [2 fo
(7 [s [8 [9 [x ]

1. 5
2. 6
3. 7
4. 8
5. 9

Question 7

Which of the following has the greatest value?

1. 204
2. 45 GC. 8+
3. See the source image for option C.
4. 173
5. See the source image for option E.

Question 8

It is given that a,b,c are non-zero real numbers. What is the sum of all possible
values of the expression
Cara,
Ja] © |b] lel”

1. 0 Biot.
2. jal i"
3. See the source image for option C.
4. See the source image for option D.
5. None of the above

Question 9

Calculate the value of
12-3? +5? — 72 +92 —...— 19? + 21?

1. 0
2. . 121
3. 241
4. 362
5. None of the above

Question 10

Determine the smallest positive integer m which satisfies the conditions:
e 2mis a perfect cube
e 3misa perfect square

1. 36
2. 72
3. 108
4. 144
5. 216

Question 11

Let n be an integer. Which of the following is ALWAYS divisible by 6?

1. n+6
2. n?—n
3. n?+n
4. ne-n
5. n?—n?

Question 12

The sum of the 3-digit numbers 346 and 2B8 is a multiple of 9. What is the
smallest value of A + B?
Ai

1. 2
2. 2 G4
3. See the source image for option C.
4. 8
5. None of the above = i f sie: k = : ms =

Question 13

In the diagram, the line segment AB passes through the B
centre 0 of the circle. Point A is on the circumference of
the circle. Line BD intersects the circle at two points C and
D such that BC = AO. It is given that ZABD = 26°. Find
: ZBAD. Ic

1. 26°
2. 372
3. See the source image for option C.
4. 76° A
5. 104°

Question 14

Amy, Betty, Cathy, Denny and Eddy are confused about today’s day of the
week.
Amy: “Tomorrow is Wednesday.”
Betty: “No, today is Wednesday.”
Cathy: “The day after tomorrow is Saturday.”
Denny: “All I know is that yesterday was not Thursday.”
Eddy: “Today is not Tuesday, not Wednesday and not Thursday.”
If only one of them is correct, which day is today?

1. Monday
2. Tuesday
3. Wednesday
4. Thursday
5. Friday

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?

“i ie. Q eo

R
s

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

Question 16

What is the 5" digit from the left in the product of 77777 and 99999?

Question 17

If the four-digit number A514 is divisible by 36, find the value of A.

Question 18

A club has 15 members. In how many ways can Chairperson, Secretary and
Treasurer be selected, if no member can hold more than one position?
eS SS SS SSS

Question 19

What is the remainder when 2017° is divided by 9?

Question 20

IXYZ5 and 2XYZ1 are two 5-digit numbers. Given that 1XYZ5:2XYZ1 = 5:9,
what is the value of X +¥ +Z?