Math Stars
®
Thursday, April 21st, 2016
F Regional Competition F
Power Round
Problems 1 – 30
Printed Full Name
School/Team Code (if known)
Grade
DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.
Number of Problems: 30
Time Allotted: 45 minutes
No calculators, books, or other aids are permitted
Answer in exact form (i.e. integer, common fraction...etc.) and round only when asked to do so. No
units need to be provided after your answers. Please record only final answers in the blanks in the
left-hand column of the competition paper. If you complete the problems before time is called, use
the remaining time to check your answers.
Form Code
Total Correct
A
B
C
D
E
F
G
H
I
J
0
1
2
3
4
5
6
7
8
9
Scorer’s Initials
CSSMA Major
Sponsors
University of Toronto
UBC Math Club
Canadian Mathematical Society
Expii.inc.
Various PAC committees
Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.
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Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.
1. ____________________ 1. Compute (and express your answer as a decimal):
0.1 + 0.2
2. ____________________ 2. A rectangle has length 10 and width 5. What’s its area?
3. ___________________
3. I flip a fair coin. What’s the probability that it doesn’t come up
heads? Assume that the coin can’t land on its side. Express your
answer as a common fraction.
4. ____________________ 4. How many diagonals does a square have?
5. ____________________ 5. An equilateral triangle has side length 6. What’s its perimeter?
6. ____________________ 6. How many of the following numbers are multiples of 3?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
2
x
7. ____________________ 7. Define $(x) = 4+x
, what is $(1)? Express your answer as a
common fraction.
8. ____________________ 8. What’s the circumference of a circle with radius
16
π?
Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.
9. ____________________ 9. A man has 4 daughters; each of his daughters has a brother. What
is the minimum number of children the man must have?
10. __________________
10. I want to paint every small square in the following grid with one
color so that no square shares a side with another square which is
painted the same color as itself. What is the minimum number of
colors I need?
11. __________________° 11. If the ratio of the angles in a triangle is 3:13:20, what is the degree
measure of the smallest angle?
12. ___________________ 12. Eric makes $10.50 an hour and works 8 hours a day, 5 days a
week. Eric wants to buy a car that cost $5,000. How many days
will he have to work? Round your answer up to a whole day.
13. __________________° 13. What’s the value of ∠β in the following diagram, in degrees?
Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.
14. ___________________ 14. What’s the value of
(1 × 23 + 0 × 22 + 1 × 21 + 1 × 20 ) + (1 × 22 + 1 × 21 + 0 × 20 )
15. ___________________ 15. Five friends met up last week. Amanda arrived before Jenny but
after Andrew. Emily arrived after Andrew. Derek arrived before
Jenny but was not the first to arrive. Who was the first to arrive?
16. ___________________ 16. The mean of 3 numbers is 10 and the mode of these numbers is
9. What is the median of these numbers?
17. ___________________ 17. What is the area of the largest circle that can fit inside a square
with side length 4? Express your answer in terms of π.
18. ___________________ 18. If x1 + y1 = 6 and x = 6, what’s the value of y? Express your
answer as a common fraction.
19. ___________________ 19. Two regular six sided dice, each numbered 1, 2, 3, 4, 5 and 6, are
rolled. What is the probability that the sum of the two numbers
on the top faces is a prime number? Express your answer as a
common fraction.
20. ___________________ 20. 25 kids share apples. Everyone gets 7 apples. Then came some
more kids and now everyone only gets 5 apples. How many more
kids came?
Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.
21. ___________________ 21. If a = 2 and b = 1, what’s the value of (a2 )3 × (b3 )5 ?
22. ___________________ 22. Alphonse, Beryl, and Catherine line up in a line. How many ways
are there to line them up if Beryl cannot be next to Catherine?
23. _________________km 23. A car travels on a straight highway at constant speed. It takes 6
hours for the car to travel from Town A to Town B, and 2 more
hours to travel from Town B to Town C. Town C is further from
Town A than Town B. The distance between Town A and Town B
is 240 km. What is the distance between Town A and Town C, in
km?
24. __________________% 24. Mr. A gave a test to his class. 5 students got 70%, 5 students got
80%, 5 students got 90%, and 5 students got 100%. What’s the
average percentage score of everyone in the class?
25. ___________________ 25. The sum of five consecutive positive integers is x. Five times the
largest of these numbers is y. What is the value of y − x?
Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.
26. ___________________ 26. A number of cubes completely fill up a rectangular prism with
dimensions 30 × 45 × 80. What’s the largest possible volume that
this cube can have?
27. ___________________ 27. If f (x) is a function such that f (x) = 2x + 1 for all numbers
x. What is the value of x for which f (x) is equal to the smallest
prime number? Express your answer as a common fraction.
28. ___________________ 28. 1 wibble is equal to 3 wobbles, 8 wobbles is equal to 5 weebles, 2
weebles is equal to 3 wabbles, and 9 wabbles is equal to 7 wubbles.
What is the minimum number of wubbles needed such that it is
equal to a whole number of wibbles?
29. ___________________ 29. Alphonse is thinking of a two digit number that is both a perfect
square and cube. What is the smallest possible number Alphonse
could be thinking of?
30. ___________________ 30. You have a string of length L. You use the string to make first a
circle, then a square, then a triangle of largest area possible. The
area of the circle is a times that of the square, and the area of the
square is b times that of the triangle.√ What is the value of a + b?
Express your answer in the form a+bdπ cπ for some positive integers
a, b, c, d such that gcd(a, b, d) = 1 and c is not divisible by any
perfect square.
Copyright Canadian Secondary School Mathematics Association (CSSMA). 2015-2016. All rights reserved.