SASMO 2018 Secondary 4 (Grade 10) Contest

Question 1

= 24+4464--420
A 3
- B. 4
(c é
aa
= E. None of the above
=

1. None of the above
2. See the source image for option B.
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 2

=| The following calculations lead to the conclusion that 2018 = 0. Which one of
the following transition steps is wrong?
V=2018 = V-2018 =› = = = (65)
v=2018 _V2018 _ ¥2018
. ayer PS @
2018
v2018 x v-1 = et (3)
V2018 x V-1 x V-1 = 2018 (4)
V2018 x (-1) = V2018 (6)

— 2018 = V2018 == 0=~¥2018 + ¥2018 (6)
V2i8=0 = 2018=0 ”)

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

Question 3

Find the remainder when the 10-digit number 1234567890 is divided by 9.
A 0

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

Question 4

Which of the following is always true about a basic trigonometric function?

1. The sine function gives any integer value.
2. The cosine of 90 degrees is 1.
3. The tangent of 0 degrees is undefined.
4. The minimum value of the cosine function is -1.
5. The tangent function is always positive.

Question 5

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

1. —60
2. —49
3. 0
4. 48
5. None of the above

Question 6

Ifa= (), find the value of a~*.

1. 3v3
2. a
3. V9 V9
4. a5
5. None of the above

Question 7

If x ‹ 0, which of the following choices is equal to
Vet
-12 + (=x) -~
@)
ot

1. 14+x- a
2. 1-x+ a
3. -1-x- a
4. -1+x4+ -
5. None of the above

Question 8

A rectangular cuboid with dimensions 126 x 162 x 180 centimetres was cut into
an exact number of identical cubes. What is the least possible number of cubes.

1. 560
2. 630
3. 5040
4. 459270
5. None of the above

Question 9

The median of X consecutive integers is 60, where X is an odd number. Find
the largest of these integers.

1. **+ 60
2. +59
3. +60
4. =~
5. 22 "2

Question 10

Consider a deck of 52 cards. If these cards are labelled using different integers,
what is the probability that the cards are arranged in increasing order of the
integers?
AS
Biss
"a
Gs
Dot
E. None of the above
Seiwa], fasennpeeeee es = 5 a Sa a See i: SA Saae Soe
i
faa
——S—————_———eeeeeeeeeee

1. 2
2. See the source image for option B.
3. 4 Ds
4. See the source image for option D.
5. None of the above

Question 11

: Amadeus finds the arithmetic series 7, 14, 21, 28, ... in his puzzle book. The book
: says that 7! = 1x 2 x...x 7 is part of the arithmetic series. He wants to know
in what term will 7! appear. What is the correct answer to his question?

1. 110%
2. 120%
3. 114%
4. 140
5. None of the above

Question 12

a
a SNe
The centre of the circle in the diagram is point
/ O. All the vertices of the two triangles are on So
the circumference of the circle. The diameter is A›
equal to 25 cm and EF = 20 cm. If ZEDF = 37° 5
and 2BCA = 53°, find the area of AABC.

1. 100 cm?
2. 150 cm? n a
3. 250 cm?
4. 300 cm?
5. None of the above

Question 13

The figure on the right is made of 5 cubes. The front go. ‹C›.
and side views of the figure are shown below. ny P‹
Front View Side View
What is the largest number of cubes in a figure with the following front and
side views:
Front View Side View

1. 25
2. 30 iG. 155
3. See the source image for option C.
4. 225
5. None of the above

Question 14

Ss] Find the remainder when 767°? — 76 is divided by 100.
AO

1. 0
2. 4 G32
3. See the source image for option C.
4. 76
5. None of the above

Question 15

i: How many triples of ordered integers (x, y, z) satisfy x x y x z = 2018?

1. 3
2. 6 (ogee
3. See the source image for option C.
4. 18
5. None of the above.

Question 16

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

Question 17

How many triangles are there in the diagram? fy

Question 18

Find the sum of all real roots of the following equation.

(x-2)t +x4 = 82
Rae} GS a ie See f ees + } Sea

\
a
EEE

Question 19

Find the integer n such that 1 + 2 +3 +--+ 7 is equal to a 3-digit number AAA
where A is a digit.
i
==

Question 20

The four-digit number ABCD is divisible by the product of two 2-digit numbers
= AB x CD. Find the 4-digit number ABCD.