HighFour Mathematics
Category B: Grades 6 – 8
Round 10
Tuesday, June 7, 2016
The use of calculator is required.
Question #1
In a certain month, three of the Sundays have dates that are even numbers.
What day is the tenth day of this month?
Question #2
A prime number is called a “super-prime” if doubling it, and then
subtracting 1, results in another prime number. What is the number of
super-primes less than 15?
Question #3
How many rectangles are in the figure shown?
Question #4
On the last day of school, Mrs. Kim brought a mega-pack of M&M’s for her
grade 8 class. The pack contained exactly 400 pieces. She gave each boy as
many M&M’s as there were boys in the class. She gave each girl as many
M&M’s as there were girls in the class. When she finished handing them
out, she had six pieces of M&M’s left. If there were two more boys than
girls in her class, how many students were in her class altogether?
Question #5
In a “Fibonacci” sequence of numbers, each term, beginning with the third,
is the sum of the previous two terms. The first number in such a sequence
is 2 and the third is 9. What is the eighth term in the sequence?
HighFour Mathematics
Category B: Grades 6 – 8
Round 10
Tuesday, June 7, 2016
The use of calculator is required.
Question #6
Ten points are spaced equally around a circle. How many different chords
can be formed by joining any 2 of these points? (A chord is a straight line
joining two points on the circumference of a circle.)
Question #7
The hundreds digit of a three-digit number is 2 more than the units digit.
The digits of the three-digit number are reversed, and the result is
subtracted from the original three-digit number. What is the units digit of
the result?
Question #8
The first 9 positive odd integers are placed in the magic square so that the
sum of the numbers in each row, column and diagonal are equal. Find the
value of A + E.
A
1
B
5
C
13
D
E
3
Question #9
A palindrome is a positive integer whose digits are the same when read
forwards or backwards. For example, 2002 is a palindrome. What is the
smallest number which can be added to 2002 to produce a larger
palindrome?
Question #10
Five people are in a room for a meeting. When the meeting ends, each
person shakes hands with each of the other people in the room exactly
once. What is the total number of handshakes that occurs after the
meeting ends?
HighFour Mathematics
Category B: Grades 6 – 8
Round 10
Tuesday, June 7, 2016
The use of calculator is required.
Question #11
Two congruent squares, ABCD and PQRS have side
length 15. They overlap to form the 15 by 25
rectangle AQRD, shown. What percent of the area
of rectangle AQRD is unshaded?
Question #12
A rectangular sign that has dimensions 9m by 16m has a square
advertisement painted on it. The border around the square is required to
be at least 1.5 m wide. What is the area of the largest square advertisement
that can be painted on the sign?
Question #13
By inserting parentheses, it is possible to give the expression
several values. How many different values can be obtained?
Question #14
A grocer makes a display of cans in which the top row has one can and each
lower row has two more cans than the row above it. If the display contains
100 cans, how many rows does it contain?
Question #15
Amelie has 6 daughters and no sons. Some of her daughters have 6
daughters, and the rest have none. Amelie has a total of 30 daughters and
granddaughters, and no great-granddaughters. How many of Amelie’s
daughters and grand-daughters have no daughters?
HighFour Mathematics
Category B: Grades 6 – 8
Round 10
Tuesday, June 7, 2016
The use of calculator is required.
Question #16
Quadrilateral ABCD is a trapezoid, AD = 15,
AB = 50, BC = 20, and the altitude is 12.
What is the area of the trapezoid?
Question #17
A palindrome, such as 83438, is a number that remains the same when its
digits are reversed. The numbers A and A+32 are three-digit and four-digit
palindromes, respectively. What is the sum of the digits of A?
Question #18
Distinct points A, B, C, and D lie on a line, with AB=BC=CD=1. Points E and F
lie on a second line, parallel to the first, with EF=1. A triangle with positive
area has three of the six points as its vertices. How many possible values
are there for the area of the triangle?
Question #19
Each of the small circles in the figure has radius one. The
innermost circle is tangent to the six circles that surround
it, and each of those circles is tangent to the large circle
and to its small-circle neighbors. Find the area of the
shaded region, using
.
Question #20
A solid cube has side length 3 inches. A 2-inch by 2-inch square hole is cut
into the center of each face. The edges of each cut are parallel to the edges
of the cube, and each hole goes all the way through the cube. What is the
volume, in cubic inches, of the remaining solid?