SASMO 2016 Secondary 4 (Grade 10) Contest

Question 1

Calculate the value of
333 x 3333
A, 1110 999

1. 1110999
2. 1 109 889
3. 1109 999
4. 1110999
5. None of the above

Question 2

The numbers 1, 2,3,4,...,2015,2016 were written on a whiteboard. Tom chose
any two numbers a and b, erased them and then writes down their product ab.
He continued the same process until one number is left on the whiteboard. What
was the last digit of this number?

1. 0
2. . 2
3. 4
4. 6
5. 8

Question 3

A 10-sided dice with numbers from 1 to 10 on its faces is thrown once. Which of
the following events has the lowest probability of occurrence?

1. The number rolled is a prime number
2. The number rolled is an even number
3. The number rolled is a multiple of 3
4. The number rolled is one less than an even number
5. None of the above

Question 4

What is the missing number in the diagram below?
Ls

1. 493
2. 251
3. 364
4. 351
5. 122

Question 5

& =| Find the largest prime number which satisfies the following inequality.
: | 56 sF(e-3) ‹5 (x48)
= A. 7

1. 7
2. 13 Get7,
3. See the source image for option C.
4. 19
5. None of the above

Question 6

e = How many triangles are there in the diagram below?
E A. 24
i B. 40
SJ Cc. 48
f&S D. 50
f E. None of the above
Ee
.
E
iS
[Be]
—————— SSS

1. 24
2. 40
3. 48
4. 50
5. None of the above

Question 7

A leap year is a year that has the leap day Feb 29. The following criteria are
used to decide which year is a leap year.
(i) A leap year occurs once every 4 years (e.g. 2016 is a leap year),
with the following exception.
(ji) There is no leap year for every 100 years (e.g. 1900 is not a leap
year), with the following exception.
(iii) There is a leap year for every 400 years (e.g. 2000 is a leap year).
Which of the following statement is false?

1. 2056 is a leap year
2. 2600 is not a leap year
3. 4800 is a leap year
4. 7146 is not a leap year
5. 9000 is a leap year

Question 8

The year 2016 is an interesting number because it is divisible by 1, 2, 3, 4, 6, 7,
8 and 9. When is the next year that has the same properties as above?

1. 72.576
2. 4032
3. 3024
4. 2520
5. None of the above

Question 9

As shown in the diagram, ABC is a semi-circle, AC is its diameter and 2DAC =
90°. Point B is the midpoint of arc ABC. Given that AD = 25 cm and AC =
14 cm, what is the area of the shaded region? (take w
to be 3 round off the answer to one decimal place.) ;

1. 203 cm?
2. 100.5 cm? ‘i ¢
3. 100 cm?
4. 101.5 cm?
5. None of the above

Question 10

How many integers n satisfy the inequality?
1999 ‹ n(n +1) ‹ 2016

1. 14 Bie 15 G16
2. See the source image for option B.
3. See the source image for option C.
4. 17
5. None of the above

Question 11

The figure below shows the intersections of
3 chords in a circle. Those three chords
partition each other into nine smaller
segments as shown in the figure. What is X\
the greatest number of smaller segments
you can get with the intersections of 8 L
chords in a circle?

1. 49
2. 64
3. 81
4. 89
5. None of the above

Question 12

Determine the number of ordered pairs (a,b) if the 5-digit number 2a3b4 is
divisible by 12.

1. 5
2. 10
3. 14
4. 17
5. None of the above

Question 13

The diagram below shows a sequence of figures. Each figure consists of white
: squares and shaded squares of the same size (all squares are congruent). What
percentage of the Figure 9 is shaded? (The answer was rounded to the whole
: number of percentage)
[| nt | | i
Figure a ea iS
Figure 2
Figure 3

1. 19%
2. 20%
3. 21%
4. 22%
5. None of the above

Question 14

It is given that
ce
at =2
Find the positive value of a.
a x

1. A and — =
2. 22 and —22
3. 2-2 and 22
4. 00
5. None of the above

Question 15

Tel is rotated to te
As & is rotated to
° Y . "
SSS ee ES See RSS Sg
————

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. See the source image for option E.

Question 16

Find [V1 001 789] , where [x] is the greatest integer less than or equal to x. For
example, [7.45] = 7.

Question 17

There are 29 students in the classroom. 16 of them wear glasses. 13 of the 29
are girls. Only 5 boys don’t wear glasses. How many girls wear glasses?

Question 18

Find the 6-digit number beginning and ending with the digit 3 that is the
product of three consecutive odd integers.

Question 19

Simon was guessing the age of his maths professor. His maths professor gave
him three clues:
i) If my age is divisible by 6, then it is between 45 and 50.
ii) If my age is not divisible by 7, then my age is between 51 and 59.
f iii) If my age is not divisible by 12, then it is between 60 and 69.
How old is maths professor?
P

Question 20

The digits 1, 2, 3, 4 can form 24 four-digit numbers where every digit is used
exactly once. If these 24 numbers are arranged in ascending order, what is the
position of 3142?

1234,1243,...,4321

ist and 24th