SASMO 2014 Round 1 Secondary 1
Problems
1.
Find ind the the next next term term of the the fol follo low wing ing sequ sequen ence ce:: 2, 1, 3, 4, 7, …
2.
Find Find the produ product ct of the the high highest est commo common n fac factor tor and the lowest lowest common common mu multi ltipl plee of of 8 and 12.
3.
Solve for x and y in the following equation
4.
The last The last day of 201 2013 3 was was a Tues Tuesday day.. Ther Theree are are 365 days days in in 2014 2014.. In In what what day of the week will 2014 end?
5.
What What is the the maxi maximu mum mn num umber ber of parts parts that that can can be obtain obtained ed from from cuttin cutting g a circu circular lar disc disc using 3 straight cuts?
6.
A man man boug bought ht two two pai paint ntin ings gs and and then then sol sold d them them for for $300 $300 eac each. h. He made made a prof profit it of 20% for the first painting, but a loss of 20% for the second painting. Overall, did he make a profit, a loss or break even? If he did not break even, state the amount of profit or loss.
7.
Solve
8.
Given that xyz = 2014, and x, y and z are positive integers such that x < y < z , how many possible triples ( x x, y, z ) are there?
9.
At a wor worksh kshop op,, ther theree are are 27 parti particip cipant ants. s. Each Each of them them shake shakess hand hand once once with with one another. How many handshakes are there?
10.
A perfe perfect ct numb number er is a posit positive ive inte integer ger that that is equal equal to to the sum sum of of its prop proper er posi positiv tivee factors. Proper positive factors of a number are positive factors that are less than the number. For example, 6 = 1 + 2 + 3 is a perfect number because 1, 2 and 3 are the only proper positive factors of 6. Find the next perfect number. numb er.
11. 11.
The dime dimens nsio ions ns of a rect rectan angl glee are are x cm by y cm, where x and y are integers, such that the area and perimeter of the rectangle are numerically equal. Find all the possible values of x and y.
12.
If a and b are positive integers such that a < b and ab = ba, find a possible value for a and for b.
13.
Find the value of
.
= 2.
1
1 1 2 1 2
1
1
.
14 .
Find the last digit of 20142014.
15.
The diagram diagram shows shows 9 points. points. Draw Draw 4 consecut consecutive ive line segments segments (i.e. (i.e. the start start point point of the next segment must coincide with the endpoint of the previous segment) to pass through all the 9 points.
16.
What are the last 5 digits of the sum 1 + 11 + 111 + … + 111…111? 2014 digits
17.
What is the least number of cuts required to cut 10 identical sausages so that they can be shared equally among 18 people?
18.
Divide the following shape into 4 identical parts.
19.
Solve the following equation: x5 + 2 x3 x2 2 = 0.
20.
Find the value of
21.
In the following cryptarithm, all the letters stand for different digits. Find the values of A, B, C and D.
22.
A
8
B
C
3
D
9
8
2
0
1
4
.
Find the sum of the terms in the nth pair of brackets: (1, 2), (3, 4), (5, 6), (7, 8), …
23.
In the diagram, PQ is parallel to RS , PA = PB and RB = RC . Given that BCA = 60, find BAC . A
P
Q
B
60 R
C
S
24.
Find the remainder when 22014 is divided by 7.
25.
The diagram shows a triangle ABC where AB = AC , BC = AD and BAC = 20. Find ADB. A
20
D
B
C
