SASMO 2017 Secondary 2 (Grade 8) Contest

Question 1

Calculate the value of
39x 15+ 20x17 +20 x 18 +35 x 19.

1. 1560
2. 1600
3. 1950
4. 2000
5. None of the above

Question 2

If x is a positive number, then which of the following is NOT always true?
A x®=1
B, vx›0
Co xti#0

1. x®=1
2. vx>0
3. xt = #0
4. x6 >0
5. xt Sx?

Question 3

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

1. 1867
2. 1949
3. 1979
4. 2017
5. None of the above

Question 4

Find the next number in the sequence below.
1,5,21,57,121,.....

1. 185
2. 202
3. See the source image for option C.
4. 256
5. None of the above

Question 5

The “Fibonacci sequence” is a series of numbers where a number is obtained by
f adding up the two previous terms before it. Starting the series with two 1's, we
get the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, ....
i Which of the following terms is an even number?
I A. 55%"
: B; 56%
t Cc. 57th
f D. 58h
E E, 59h
E

1. 55%
2. 56%
3. 57%
4. 58%
5. 59"

Question 6

E It is given that n! = n x (n-1) x (n—2)x...x 3.x 2 1. For example, 4! =
i 4x 3x21. Find the remainder when 1! + 2! + 3! + +++ 10! is divided by 20.

1. 13
2. 14
3. 15
4. 16
5. None of the above

Question 7

The vertices A, B and C of the triangle below are on the circumference of the
circle. Point O is the centre of the circle and 2BCA = 30°. If the radius of circle
is 1 cm and BC = V3 cm, find the area of triangle ABC in cm?.
B
L ››
KS

1. v3
2. See the source image for option B.
3. See the source image for option C.
4. 2v3
5. Not enough information

Question 8

The operator «+ acts on two numbers to give the following results:
20 11 =30
3% 10 = 36
58 = 42
89 = 72
Find the value of 20 17.

1. 336
2. 342
3. 352
4. 378
5. None of the above

Question 9

Ben travels from his house to Sports Hall every Saturday. One Saturday, instead
of walking at his usual speed, he decided to walk slower at 1.2 m/s and arrived
at the destination 250 seconds later than his usual arrival time. The next
Saturday, he jogged at 3 m/s and arrived at the place 500 seconds earlier than
his usual arrival time. What is Ben’s usual walking speed?

1. 1.5 m/s
2. 1.8 m/s
3. 2.1 m/s
4. 2.4 m/s
5. None of the above

Question 10

Which of the following has the largest value?
E A. a
a
= Ga
Dp. &
‘¥
E E. 5

1. See the source image for option A.
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. 2

Question 11

‘ Given that a › b › c, which of the following is equal to
\@— 2a by? + fb —ay? + J(e—a)?2 + Ve b)??
A, 3c—4atb

1. 3c—4a+b
2. 4a—b—3c
3. c—b
4. 4a—3b-—c
5. 4a—b—3c

Question 12

How many numbers do appear in both sequences below?
9,14, 19, 24, ..., 494,499
9, 16, 23, 30, ..., 492, 499

1. 13
2. 14 €, 15
3. See the source image for option C.
4. 16 BE. 17
5. See the source image for option E.

Question 13

Of the 150 students, 120 have Facebook accounts, 75 have Instagram accounts
and 50 have Snapchat accounts. What is the maximum number of students
who have no accounts in these 3 social media websites?

1. 1
2. 5 Cy 15
3. 15
4. 30
5. See the source image for option E.

Question 14

Amy, Betty, Cathy, Denny and Eddy are confused about today’s day of the
week,

e Amy: “All I know is that yesterday was not Friday.”

e Betty: “Tomorrow is Tuesday.”

e Cathy: “No, today is Tuesday.”

e Denny: “The day after tomorrow is Tuesday.”

e Eddy: “Today is not Sunday, not Monday and not Tuesday.”
If only one of them is correct, which day is today?

1. Wednesday
2. Thursday
3. Tuesday
4. Sunday
5. Saturday

Question 15

Only 2 out of the 4 figures below will form a 3 by 3 cube
as shown on the right. Which 2 figures can form a 3 by 3
cube?
P. › Q wv
f : R. 2 S 7

i A. (P and Q)

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

Question 16

Find the smallest positive multiple of 15 which consists of the digits 1 and 0
E only?
=
al
el
SS ———

Question 17

How many zeros are there in the quotient of (10'°° — 1) + 11?

Question 18

The integers from 1 to 100 are written down on the whiteboard. Richard
underlined all numbers divisible by 3, then all numbers divisible by 5, and then
all numbers divisible by 9. How many numbers are underlined exactly twice?

Question 19

In the following, all the different letters stand for different digits.
YAY

x 5

PL A Y
What is the value of the four-digit number “PLAY”?
EE. ener › Pattee re cry. | (eae teenies e Sey
i
I
{ I
1 i
= | iF
BS
eee ee eee
&

Question 20

E The bar chart below shows the number of smartphones sold in Town A in the
ES second half of year 2016, For example, 1400 smartphones were sold in
=a September. Starting from August, the number of smartphones sold in each
i month is equal to the average number of smartphones sold in the previous
: month and in the following month. How many smartphones were sold in July,
S 2016?
& Number
Ress of smartphone
Ss (in Hundreds)
: Jul Aug Sep Oct Nov Dec
= | Month
=

SSI
/