Student Name: _____________________________________ Grade: __________ Score: __________
Division
M
1A
1B
Mathematical Olympiads
February 13nd, 2017
"
§
for Elementary and Middle Schools
If x ║ y = (x + y)2 for positive integers x and y,
what is the value of (1 ║ 2) ║ 3?
Ms. Spice tells her class that she is thinking of a positive common
fraction. The product of the numerator and denominator is 60. When
she adds 1 to the numerator and divides the denominator by 2, the
resulting fraction is equal to 1. What common fraction is Ms. Spice
thinking of ?
Let N be the greatest integer multiple of 8, no two of whose digits are
the same.
What is the remainder when N is divided by 1000?
A rectangular solid is 4 Cm by 6 Cm by 8 Cm. It is painted on all six
faces. Then, the solid is cut into cubes that measure 2 Cm. on each
side.
Please"fold"over"on"line."Write"answers"on"back.
1C
1D
Practice
Test-A
How many of these cubes have only 1 side painted?
1E
Triangle ABC has a right angle at B. AB=1, and BC=2. The bisector
of angle BAC meets BC at D. What is BD?
Chaboya Middle School, Math Olympiads, 2015-2016
1
Student Name: _____________________________________ Grade: __________ Score: __________
Division
Mathematical Olympiads
M
February 13nd, 2017
"
for Elementary and Middle Schools
2F
A regular Clock is now showing 8:24 am.
What is the degree between 2 hands?
2G
Define a “good word” as a sequence of letters that consists only of
the letters A, B and C - some of these letters may not appear in the
sequence - and in which A is never immediately followed by B,
B is never immediately followed by C, and
C is never immediately followed by A.
"
Practice
Test-B
How many seven-letter good words are there?
2H
The$sequence$
$
The$sequence$
$is$defined$by
$
$is$defined$by
"
$
Find$
2I
.
Let$ $and$ $be$two6digit$positive$integers$
with$mean$ .$What$is$the$maximum$
value$of$the$ratio$ ?
2J
A circle of radius 1 is surrounded by four
circles of radius r as shown.
What is r?
Chaboya Middle School, Math Olympiads, 2015-2016
2
Student Name: _____________________________________ Grade: __________ Score: __________
Division
M
Mathematical Olympiads
February 13nd, 2017
"
§
for Elementary and Middle Schools
A positive divisor of 1099 is chosen uniformly at random. What is the
probability that it is an integer multiple of 1088?
3B
How many different triangles can be formed by connecting three of the
points below?
3C
The fifth and eighth terms of a geometric sequence of real numbers are
7! and 8! respectively. What is the first term?
3D
Trapezoid$
$
and$
$
$
What$is$
?
3E
$has$$$
.$The$ratio$
,$$$$
,$$$
$is$
.$$
,$$
Please"fold"over"on"line."Write"answers"on"back.
3A
Practice
Test-C
In$
,$
,$
,$
and$
.$
Points$ $and$ $lie$
on$
$and$
,$respectively,$
with$
.$$
Points$ $and$ $are$on$
$so$
that$
$and$
$are$
perpendicular$to$
.$What$is$the$
area$of$pentagon$
?
Student Name: _____________________________________ Grade: __________ Score: __________
Chaboya Middle School, Math Olympiads, 2015-2016
3
Division
M
4F
Mathematical Olympiads
February 13nd, 2017
"
for Elementary and Middle Schools
"
Practice
Test-D
Rectangle ABCD has AB=8 and
BC=6. Point M is the midpoint of
diagonal AC, and E is on AB and
ME is perpendicular to AC.
What is the area of the triangle
AME?
In multiplying two positive integers a and b, Ron reversed the digits
of the two-digit number a. His erroneous product was 161. What is
the correct value of the product of a and b?
4H
A$square$has$sides$of$length$ ,$and$a$circle$centered$at$one$of$its$
vertices$has$radius$ .$What$is$the$area$of$the$union$of$the$regions$
enclosed$by$the$square$and$the$circle?
4I
In$the$expression$
,$the$values$
of$ ,$ ,$ ,$and$ $are$0,$1,$2,$and$3,$
although$not$necessarily$in$that$order.$
What$is$the$maximum$possible$value$of$
the$result?
4J
If$ $and$ $are$positive$integers$for$
which$
,$$
$
what$is$the$value$of$
?
"
4G
Chaboya Middle School, Math Olympiads, 2015-2016
4