SASMO 2015 Secondary 2 (Grade 8) Contest

Question 1

The diagram shows a big rectangle that is made up of 4 small
identical rectangles. If the smaller dimension of one of the small
rectangles is 9 cm, find the area of the big rectangle.

1. 108 cm?
2. 972 cm?
3. 2015 cm?
4. Not enough given information to find
5. None of the above

Question 2

Find the next term of the following sequence: 3, 2, 5, 9, 44, ...

1. 86
2. 87
3. 88
4. 395
5. 2015

Question 3

An operator ® acts on two numbers to give the following outcomes:
3@2= 94
5@3= 259
1@6= 136
4@9 = 1681
What is 5 © 7 equal to?

1. 2549
2. 3549
3. 4925
4. 4935
5. None of the above

Question 4

If the five-digit number 4567N is divisible by 12, find N.

1. 8
2. 6
3. 4 BD; 2 Evo
4. See the source image for option D.
5. See the source image for option E.

Question 5

The diagram shows a square, a regular hexagon and
: parts of a regular polygon. How many sides does the
latter polygon have?

1. 10 os
2. See the source image for option B.
3. 20
4. 24 BE. 30
5. 30

Question 6

A palindromic number is a whole number that reads the same forward and
backward. For example, 1221 is a palindromic number. How many 6-digit
palindromic numbers are there?

1. 190
2. 900
3. 1000
4. 90000
5. None of the above

Question 7

A farmer buys 36 metres of fence to build an enclosure to keep his livestock. He
decides to erect a 4-sided enclosure in such a way that it has the largest possible
area. Find the area of the enclosure.

1. 63 m2
2. 72 m?
3. 81 m*
4. 90 m?
5. None of the above

Question 8

A number gives a remainder of 5 when divided by 10. Another number gives a
remainder of 4 when divided by 10. The sum of these two numbers is multiplied
by 3 to give the third number. What is the remainder when this third number is
divided by 10?

1. 4
2. 5
3. 7
4. 9
5. None of the above

Question 9

A big cube is made up of 64 small cubes. All the faces of the big cube are then
painted. How many of the small cubes have exactly one painted face?

1. 6
2. 12
3. 24
4. 72
5. None of the above

Question 10

If both mand 2 are positive integers, how many possible values of 7 are there?
rf
Al

1. See the source image for option A.
2. 2
3. 3
4. 4
5. None of the above

Question 11

i The product of two numbers is 100 000. Neither of the two numbers has 10 as a
i] factor. Find the difference of these two numbers.

1. 465
2. 1170
3. 3093
4. 6234
5. Not enough given information to find

Question 12

The height of a man is 169 cm, correct to the nearest centimetre. What is the
upper bound of the man’s height?

1. 169.4 cm
2. 169.45 cm
3. 169.49 cm
4. 169.5 cm
5. 169.9 cm

Question 13

A circle and a rhombus are drawn on a flat surface. What is the biggest number
of regions that can be formed on the surface?

1. 6
2. 7
3. 8
4. 9
5. 10

Question 14

Find the smallest whole number 7 for which 5407 is a multiple of 168.

1. 2
2. 7
3. 14
4. 28
5. None of the above

Question 15

In AABC, AB = 10 cm, BC = 6 cm and AC = 8 cm. Find the value of _

1. 0.6
2. 0.75
3. 0.8
4. Cannot be found
5. None of the above

Question 16

] There are 15 rows of seats in a hall, each row having 20 seats. If there are 275
people seated in the hall, at least how many rows have an equal number of
people each?

Question 17

Tom drives 4000 km during a trip. He rotates the tyres (four tyres on the car and
one spare tyre) so that each tyre has been used for the same distance at the end
of the trip. How many kilometres are covered by each tyre?

Question 18

The diagram shows how an equilateral triangle can be cut into four pieces and
rearranged to form a square. This solution of the Haberdasher's Puzzle is
discovered by Henry Dudeney (1857 — 1930).
Tf the length of the square is 13 cm, find the length of the triangle, correct to
nearest whole number. (Note: a = 1.52, correct to three significant figures)
i
\
a

Question 19

Polite numbers are numbers that can be expressed as the sum of two or more
consecutive positive integers, e.g.
5=2+3;
9=24+344=445.
Find all the polite numbers that can be expressed as the sum of three
consecutive positive integers.

Question 20

Find the 2015" term of the following sequence: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4).