SASMO 2018 Secondary 3 (Grade 9) Contest

Question 1

Evaluate -1+2-3+4—-5 +--+ 2016 — 2017 + 2018.

1. —1008
2. —1009
3. 1008
4. 1009
5. None of the above

Question 2

Given that —16 ‹ 2(y—7) ‹0 and -7 ‹ x ‹8, find the least possible value of
xy.

1. 0
2. 8
3. .12
4. 56
5. None of the above

Question 3

Given x ‹ 0, simplify the expression
—1? + fx? - Yani
AL tbe 2x24
B, 1-+x-8x2

1. 1+x— 2x4
2. 1+x—- 8x1?
3. -1—x + 2x74
4. -1-—x — 2x74
5. -1—x—- 8x"?

Question 4

Given 97 is equal to the 7-digit number a78296b, what is the value of a x b?

1. 32
2. 36
3. 45
4. 54
5. None of the above

Question 5

Tom writes all positive integers starting with the number 2 on the whiteboard.
He skips all perfect squares. What is the 2018" number he writes on the
whiteboard?

1. 1971
2. 1972
3. 1973
4. 1974
5. None of the above

Question 6

How many pairs of ordered integers (x,y) satisfy x? — y? = 2018?

1. 0
2. 2
3. 3
4. 5
5. None of the above

Question 7

Shannon, Jason and Robert can complete one round of the same track in 1
minute 15 seconds, 1 minute 30 seconds and 1 minute 45 seconds,
respectively. They start running at the same time from point A. After how many
seconds will they all be together again at point A?

1. 3150
2. 9140
3. 9450
4. 28350
5. None of the above

Question 8

The following calculations lead to the conclusion that x = 0. Which one of the
following transition steps is wrong?
Ne a a
V0 vn vt
i —=— 1 = — 2.
Wren nde
va
=a 3
Vav-1 a (3)
vav-Iv-1 = Vir (4)
vii (-1) = Va (5)
-viava =› 0=Vitvn (©)
vr=0 =› n=0 (7)

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

Question 9

Find the remainder when 252°8 — 25 is divided by 100.

1. 0
2. 25
3. 50
4. 75
5. None of the above

Question 10

The figure on the right is made of 5 cubes. The front ‹‹ = C› =
and side views of the figure are shown below. ™ › ›

Front View Side View
What is the largest number of cubes in a figure with the following front and
side view as follow:
Front View Side View

1. 30
2. 55
3. 62
4. 63
5. None of the above

Question 11

Suppose M is the minimum value of f(x) = x* + 6x + 19 and N is the
maximum value of g(x) = —3(x — 4) — 7. What is the value of M +N?

1. —36
2. -7
3. . 12
4. 17
5. None of the above

Question 12

Find the number of 4* on the left side of the equation to make the equality
correct.
Ax atx dt xx dt = gt
A, 28
Buz
Cc. 28
D2
Eg22*

1. 2°
2. 2° C2
3. See the source image for option C.
4. See the source image for option D.
5. See the source image for option E.

Question 13

The sum of some consecutive positive integers is 1000. Find the largest of
these integers.

1. 55
2. 70
3. 164
4. 169
5. None of the above

Question 14

There are four piles of cards: 10 cards, 12 cards, 8 cards, 11 cards. Each of the
five players must choose one pile and divide it into two smaller piles. Five
players take turns in order. The player who cannot divide a pile into smaller
piles will be the loser. Which player will be the loser?

1. 1% player
2. 2"4 player
3. 3" player
4. 4 player
5. 5% player

Question 15

In the diagram, 0 is the centre of the circle, OM
is a radius and OMNP is a square. Point L is on
the circle such that LK is perpendicular to MN
and K is a midpoint of MN. Find the value of
ZOLN. Pe

1. 105°
2. See the source image for option B.
3. 150° yy
4. 175°
5. None of the above

Question 16

Find the value of
a t 4 1 1 A
antese( oa aea* laa ee hae
Ses] See. «| fess peers | SSS eae, tenes aoe

ee ee SS SEE

Question 17

How many triangles are there in the diagram? Ly

Question 18

Three children have different ages. The sum of their ages is either 8, 9, or 10,
/ and the product of their ages is either 15, 16 or 17, What is the median of their
ages?

Question 19

Given x and y are positive integers such that x? — 12y? + 4xy — 148 = 0, what
is the value of x? + y??
————

Question 20

The sum of 6 different positive integers is 2018. Find the smallest possible
value of the largest of these 6 numbers.