Gauss Contest: Grade 7

The CENTRE for EDUCATION
in MATHEMATICS and COMPUTING

cemc.uwaterloo.ca
Gauss Contest
Grade 7
(The Grade 8 Contest is on the reverse side)
Wednesday, May 14, 2014
(in North America and South America)
Thursday, May 15, 2014
(outside of North America and South America)
Time: 1 hour ©2013 University of Waterloo

Calculators are permitted.
Instructions
1. Do not open the contest booklet until you are told to do so.
2. You may use rulers, compasses and paper for rough work.
3. Be sure that you understand the coding system for your answer sheet. If you are not sure,
ask your teacher to explain it.
4. This is a multiple-choice test. Each question is followed by five possible answers marked
A, B, C, D, and E. Only one of these is correct. When you have made your choice, enter
the appropriate letter for that question on your answer sheet.
5. Scoring: Each correct answer is worth 5 in Part A, 6 in Part B, and 8 in Part C.
There is no penalty for an incorrect answer.
Each unanswered question is worth 2, to a maximum of 10 unanswered questions.
6. Diagrams are not drawn to scale. They are intended as aids only.
7. When your supervisor instructs you to start, you will have sixty minutes of working time.
The name, school and location of some top-scoring students will be published on the Web site,
http://www.cemc.uwaterloo.ca. You will also be able to find copies of past Contests and excellent
resources for enrichment, problem solving and contest preparation.
Grade 7
Scoring: There is no penalty for an incorrect answer.
Part A: Each correct answer is worth 5.
1. The value of (4 × 3) + 2 is
(A) 33 (B) 10 (C) 14 (D) 24 (E) 11
2. Which of the following numbers is closest to 100 on the number line?
(A) 98 (B) 95 (C) 103 (D) 107 (E) 110
3. Five times a number equals one hundred. The number is
(A) 50 (B) 10 (C) 15 (D) 25 (E) 20
4. The spinner shown is divided into 6 sections of equal
size. What is the probability of landing on a section that
P R
contains the letter P using this spinner?
3 4 5
Q P
(A) (B) (C)
6
2
6
1
6
R Q
(D) 6 (E) 6
5. One scoop of fish food can feed 8 goldfish. How many goldfish can 4 scoops of fish
food feed?
(A) 12 (B) 16 (C) 8 (D) 64 (E) 32
15
6. Which of these fractions is equivalent to 25 ?
3 2 3 1 5
(A) 4 (B) 3 (C) 5 (D) 2 (E) 7
7. How many positive two-digit whole numbers are divisible by 7?

(A) 11 (B) 9 (C) 15 (D) 12 (E) 13
8. If 9210 − 9124 = 210 − , the value represented by the is

(A) 296 (B) 210 (C) 186 (D) 124 (E) 24
9. A clockwise rotation around point Z (that is, a rotation
in the direction of the arrow) transforms the shaded
quadrilateral to the unshaded quadrilateral. The angle
of rotation is approximately
(A) 180◦ (B) 270◦ (C) 360◦
(D) 45◦ (E) 135◦ Z
10. Which one of the following is equal to 17?
(A) 3 − 4 × 5 + 6 (B) 3 × 4 + 5 ÷ 6 (C) 3 + 4 × 5 − 6
(D) 3 ÷ 4 + 5 − 6 (E) 3 × 4 ÷ 5 + 6
Part B: Each correct answer is worth 6.
11. Consider the set {0.34, 0.304, 0.034, 0.43}. The sum of the smallest and largest numbers
in the set is
(A) 0.77 (B) 0.734 (C) 0.077 (D) 0.464 (E) 0.338
Grade 7
12. The diagonals have been drawn in the square shown. The
area of the shaded region of the square is
(A) 4 cm2 (B) 8 cm2 (C) 16 cm2
(D) 56 cm2 (E) 64 cm2
13. In the special square shown, the sum of the three numbers
in each column equals the sum of the three numbers in 13 8
each row. The value of x is
14 x 10
(A) 3 (B) 4 (C) 5
(D) 6 (E) 12 9
14. In the diagram shown, the number of rectangles of all

sizes is
(A) 11 (B) 15 (C) 7
(D) 13 (E) 9
15. The diagram shows Lori’s house located at (6, 3). If

Alex’s house is located at (−2, −4), what translation is y
needed to get from Lori’s house to Alex’s house?
Lori’s House
(A) 4 units left, 1 unit up (6, 3)
(B) 8 units right, 7 units up
x
(C) 4 units left, 1 unit down
(D) 8 units left, 7 units down
(E) 7 units right, 8 units down
16. The graph shows points scored by Riley-Ann in her first

Riley-Ann’s Points
five basketball games. The difference between the mean 22
and the median of the number of points that she scored is 20
18
(A) 1 (B) 2 (C) 3 16
14
12
(D) 4 (E) 5 Points
10
8
6
4
2
0
1 2 3 4 5
17. In the diagram shown, P QR is a straight line segment. Game
S
The measure of ∠QSR is
(A) 25◦ (B) 30◦ (C) 35◦
(D) 40◦ (E) 45◦
75° 30°
P Q R
18. In the figure shown, the outer square has an area of

9 cm2 , the inner square has an area of 1 cm2 , and the
Lori’s
four rectangles are identical. What is the perimeter of House
one of the four identical rectangles?
(A) 6 cm (B) 8 cm (C) 10 cm
(D) 9 cm (E) 7 cm
Grade 7
19. Sarah’s hand length is 20 cm. She measures the dimensions of her rectangular floor
to be 18 by 22 hand lengths. Which of the following is the closest to the area of the
floor?
(A) 160 000 cm2 (B) 80 000 cm2 (C) 200 000 cm2
(D) 16 000 cm2 (E) 20 000 cm2
20. The product of three consecutive odd numbers is 9177. What is the sum of the
numbers?
(A) 51 (B) 57 (C) 60 (D) 63 (E) 69
Part C: Each correct answer is worth 8.

21. A bicycle at Store P costs $200. The regular price of the same bicycle at Store Q is
15% more than it is at Store P. The bicycle is on sale at Store Q for 10% off of the
regular price. What is the sale price of the bicycle at Store Q?
(A) $230.00 (B) $201.50 (C) $199.00 (D) $207.00 (E) $210.00
22. Each face of a cube is painted with exactly one colour. What is the smallest number
of colours needed to paint a cube so that no two faces that share an edge are the
same colour?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
23. Two standard six-sided dice are tossed. One die is red and the other die is blue.
What is the probability that the number appearing on the red die is greater than the
number appearing on the blue die?
(A) 18
36
25
(B) 36 (C) 15
36 (D) 12
36 (E) 1736
24. In the diagram shown,
• ST U V is a square, S Q T
• Q and P are the midpoints of ST and U V ,

• P R = QR, and
R
• V Q is parallel to P R.
What is the ratio of the shaded area to the unshaded

area? V P U
(A) 2 : 3 (B) 3 : 5 (C) 1 : 1

(D) 7 : 9 (E) 5 : 7
25. On a coordinate grid, Paul draws a line segment of

length 1 from the origin to the right, stopping at (1, 0). y
He then draws a line segment of length 2 up from this
point, stopping at (1, 2). He continues to draw line 4
segments to the right and up, increasing the length of 3
the line segment he draws by 1 each time. One of his 2
x
line segments stops at the point (529, 506). What is the 1
endpoint of the next line segment that he draws?
(A) (529, 552) (B) (576, 506) (C) (575, 506)
(D) (529, 576) (E) (576, 552)
www.cemc.uwaterloo.ca
Gauss Contest
Grade 7
Time: 1 hour ©2012 University of Waterloo

Instructions
The name, school and location of some top-scoring students will be published on the Web site,
http://www.cemc.uwaterloo.ca. You will also be able to find copies of past Contests and excellent
Grade 7
1. The value of (5 × 3) − 2 is
(A) 5 (B) 9 (C) 6 (D) 8 (E) 13
2. Which of the following numbers is a multiple of 9?
(A) 50 (B) 40 (C) 35 (D) 45 (E) 55
3. Thirty-six hundredths is equal to

(A) 0.36 (B) 360 (C) 3.6 (D) 0.036 (E) 0.0036
4. The value of 1 + 1 − 2 + 3 + 5 − 8 + 13 + 21 − 34 is
(A) −32 (B) 1 (C) 88 (D) 0 (E) −34
5. If P Q is a straight line segment, then the value of x is

(A) 160 (B) 70 (C) 110 x
(D) 20 (E) 80 20
P Q
6. Nick has six nickels (5¢ coins), two dimes (10¢ coins) and one quarter (25¢ coin). In
cents (¢), how much money does Nick have?
(A) 65 (B) 75 (C) 35 (D) 15 (E) 55
1 2 1 5 7
7. The smallest number in the set 2 , 3 , 4 , 6 , 12 is
1 2 1 5 7
(A) 2 (B) 3 (C) 4 (D) 6 (E) 12
8. Ahmed is going to the store. One quarter of the way to

the store, he stops to talk with Kee. He then continues Start Kee Store
for 12 km and reaches the store. How many kilometres
12 km
does he travel altogether?
(A) 15 (B) 16 (C) 24
(D) 48 (E) 20
9. An expression that produces the values in the second row
of the table shown, given the values of n in the first row, is
(A) 3n − 2 (B) 2(n − 1) (C) n + 4
n 1 2 3 4 5
(D) 2n (E) 2n − 1
value 1 3 5 7 9
10. U V W and XY Z are each 3-digit integers. U, V, W, X, Y, and Z are different digits
chosen from the integers 1 to 9. What is the largest possible value for U V W −XY Z?
(A) 678 (B) 864 (C) 885 (D) 888 (E) 975
11. The length of each edge of a cube is 1 cm. The surface area of the cube, in cm2 , is
(A) 24 (B) 1 (C) 4 (D) 12 (E) 6
Grade 7
12. Which of the following pairs of numbers has a greatest common factor of 20?
(A) 200 and 2000 (B) 40 and 50 (C) 20 and 40
(D) 20 and 25 (E) 40 and 80
13. Jack, Kelly, Lan, Mihai, and Nate are sitting in the 5 chairs around a circular table.
Lan and Mihai are sitting beside each other. Jack and Kelly are not sitting beside
each other. The 2 people who are seated on either side of Nate are
(A) Jack and Lan (B) Jack and Kelly (C) Kelly and Mihai
(D) Lan and Mihai (E) Mihai and Jack
14. If x = 4 and 3x + 2y = 30, what is the value of y?

(A) 18 (B) 6 (C) 3 (D) 4 (E) 9
15. Daniel begins with 64 coins in his coin jar. Each time he reaches into the jar, he
removes half of the coins that are in the jar. How many times must he reach in and
remove coins from his jar so that exactly 1 coin remains in the jar?
(A) 5 (B) 32 (C) 6 (D) 7 (E) 63
16. The mean (average) of five consecutive even numbers is 12. The mean of the smallest
and largest of these numbers is
(A) 12 (B) 10 (C) 14 (D) 8 (E) 16
17. For every 3 chocolates that Claire buys at the regular price, she buys a fourth
chocolate for 25 cents. Claire buys 12 chocolates in total for $6.15. What is the
regular price of one chocolate, in cents?
(A) 180 (B) 45 (C) 60 (D) 54 (E) 57
18. JKLM is a square and P QRS is a rectangle. If JK is

parallel to P Q, JK = 8 and P S = 2, then the total area P J K Q
of the shaded regions is R
S
(A) 32 (B) 16 (C) 56 M L
(D) 48 (E) 62
19. A special six-sided die is rolled. The probability of rolling a number that is a multiple
of three is 12 . The probability of rolling an even number is 31 . A possibility for the
numbers on the die is
(A) 1, 2, 3, 5, 5, 6 (B) 1, 2, 3, 3, 5, 6 (C) 1, 2, 3, 4, 6, 6
(D) 1, 2, 3, 3, 4, 6 (E) 2, 3, 3, 3, 5, 6
20. Toothpicks are used to make rectangular grids, as shown.

Note that a total of 31 identical toothpicks are used in the 1 x 10
1 × 10 grid. How many toothpicks are used in a 43 × 10
grid?
(A) 913 (B) 860 (C) 871 2 x 10
(D) 903 (E) 946
3 x 10
Grade 7

21. In the addition shown, P and Q each represent single 7 7P
digits, and the sum is 1P P 7. What is P + Q? 6 QP
(A) 9 (B) 12 (C) 14 + QQP
1PP 7
(D) 15 (E) 13
22. An arithmetic sequence is a sequence in which each term

after the first is obtained by adding a constant to the 1
previous term. For example, 2, 4, 6, 8 and 1, 4, 7, 10 are
arithmetic sequences. 4 25
In the grid shown, the numbers in each row must form 7 x
an arithmetic sequence and the numbers in each column
must form an arithmetic sequence. The value of x is 10 36
(A) 37 (B) 28 (C) 36
(D) 43.75 (E) 46
P
23. In the right-angled triangle P QR, P Q = QR. The
segments QS, T U and V W are perpendicular to P R, and
the segments ST and U V are perpendicular to QR, as S
shown. What fraction of 4P QR is shaded?
(A) 3
(B) 3
(C) 5 U
16 8 16 W
5 7
(D) 32 (E) 32
Q T V R
24. One face of a cube contains a circle, as shown. This cube rolls without sliding on a
four by four checkerboard. The cube always begins a path on the bottom left square
in the position shown and completes the path on the top right square. During each
move, an edge of the cube remains in contact with the board. Each move of the cube
is either to the right or up. For each path, a face of the cube contacts seven different
squares on the checkerboard, including the bottom left and top right squares. The
number of different squares that will not be contacted by the face with the circle on
any path is
(A) 9 (B) 11 (C) 8 (D) 12 (E) 10
up
right
25. A box contains a total of 400 tickets that come in five colours: blue, green, red, yellow
and orange. The ratio of blue to green to red tickets is 1 : 2 : 4. The ratio of green to
yellow to orange tickets is 1 : 3 : 6. What is the smallest number of tickets that must
be drawn to ensure that at least 50 tickets of one colour have been selected?
(A) 50 (B) 246 (C) 148 (D) 196 (E) 115
Gauss Contest
Grade 7
Time: 1 hour ©2011 Centre for Education in Mathematics and Computing

Instructions
Please see our Web site: http://www.cemc.uwaterloo.ca. The Gauss Report will list the names
of some top-scoring students. You will also be able to find copies of past Contests and excellent
Grade 7
1. The value of 202 − 101 + 9 is equal to

(A) 120 (B) 110 (C) 111 (D) 109 (E) 92
2. Which of the following numbers is equal to 33 million?

(A) 3 300 000 (B) 330 000 (C) 33 000 (D) 33 000 000 (E) 330 000 000
3. A six-sided die has the numbers one to six on its sides. What is the probability of
rolling a five?
2 1 5 3 4
(A) 6 (B) 6 (C) 6 (D) 6 (E) 6
1 1 1 1 1

4. The largest fraction in the set 2 , 3 , 4 , 5 , 10 is
1 1
(A) 2 (B) 3 (C) 14 (D) 1
5 (E) 1
10
5. Two straight lines intersect as shown.

The measure of the angle marked is 120 o
(A) 60◦ (B) 120◦ (C) 30◦ 60 o
(D) 300◦ (E) 180◦
6. Fifteen times a number equals three hundred. The number is
(A) 20 (B) 10 (C) 60 (D) 30 (E) 25
7. Which of the following statements is true?

1
(A) 0 is less than −5 (B) 7 is less than −1 (C) 10 is less than 4
(D) −1 is less than −3 (E) −8 is less than −2
8. Bailey scores on six of her eight shots. The percentage of shots that she does not
score on is
(A) 2 (B) 40 (C) 10 (D) 20 (E) 25
9. Ben recorded the number of visits to his website from

Visits to Ben s Website
Monday to Friday as shown in the bar graph. The mean
Number of Visits
(average) number of visits per day to his website over the 400
5 days is 300
(A) less than 100 200
(B) between 100 and 200 100
(C) between 200 and 300
(D) between 300 and 400 M Tu W Th F
(E) more than 400 Days of the Week
Grade 7
10. Using the graph, the number of seconds required Vehicle s Speed vs. Time Graph
for a vehicle to travel a total distance of 100 m is
Speed (m/s)
(A) 2.5 (B) 20 (C) 8 30
(D) 10 (E) 5 20
10
1 2 3 4 5 6
Time (s)
11. The perimeter of a square is 36 cm. The area of the square, in cm2 , is
(A) 24 (B) 81 (C) 36 (D) 1296 (E) 324
15
12. Which of the following is not equal to 4 ?
14+1 3 5 3 21 5 1
(A) 3.75 (B) 3+1 (C) 4 +3 (D) 4 × 4 (E) 4 − 4 − 4
13. On the spinner shown, P Q passes through centre O. If P

areas labelled R and S are equal, then what percentage
of the time will a spin stop on the shaded region? R
S
(A) 50% (B) 22.5% (C) 25% O
(D) 45% (E) 12.5%
14. The digits 2, 4, 6 and 8 are each used once to create two 2-digit numbers. What is
the largest possible difference between the two 2-digit numbers?
(A) 66 (B) 62 (C) 58 (D) 44 (E) 36
15. If snow falls at a rate of 1 mm every 6 minutes, then how many hours will it take for
1 m of snow to fall?
(A) 33 (B) 60 (C) 26 (D) 10 (E) 100
16. The number 503 is a prime number. How many positive integers are factors of 2012?
(A) 2 (B) 3 (C) 7 (D) 6 (E) 8
17. The ratio of boys to girls at Gauss Public School is 8 : 5. If there are 128 boys at the
school, then how many students are there at the school?
(A) 218 (B) 253 (C) 208 (D) 133 (E) 198
18. All four scales shown are balanced.

One possible replacement for the ? is
(A) (B) (C)
(D) (E)
Grade 7
19. A set of five different positive integers has a mean (average) of 20 and a median of 18.
What is the greatest possible integer in the set?
(A) 60 (B) 26 (C) 46 (D) 12 (E) 61
20. Chris lies on Fridays, Saturdays and Sundays, but he tells the truth on all other days.
Mark lies on Tuesdays, Wednesdays and Thursdays, but he tells the truth on all other
days. On what day of the week would they both say: “Tomorrow, I will lie.”?
(A) Monday (B) Thursday (C) Friday (D) Sunday (E) Tuesday

21. A triangular prism has a volume of 120 cm3 . Two edges 3
4
of the triangular faces measure 3 cm and 4 cm, as shown.
The height of the prism, in cm, is
(A) 12 (B) 20 (C) 10
(D) 16 (E) 8
22. A quiz has three questions, with each question worth one mark. If 20% of the students
got 0 questions correct, 5% got 1 question correct, 40% got 2 questions correct, and
35% got all 3 questions correct, then the overall class mean (average) mark was
(A) 1.8 (B) 1.9 (C) 2 (D) 2.1 (E) 2.35
23. The number N is the product of all positive odd integers from 1 to 99 that do not end
in the digit 5. That is, N = 1 × 3 × 7 × 9 × 11 × 13 × 17 × 19 × · · · × 91 × 93 × 97 × 99.
The units digit of N is
(A) 1 (B) 3 (C) 5 (D) 7 (E) 9
24. P QRS is a parallelogram with area 40. If T and V are

Q R
the midpoints of sides P S and RS respectively, then the
area of P RV T is
(A) 10 (B) 12 (C) 15 V
(D) 16 (E) 18
P T S
25. The positive integers are arranged in rows and columns as shown below.
Row 1 1
Row 2 2 3
Row 3 4 5 6
Row 4 7 8 9 10
Row 5 11 12 13 14 15
Row 6 16 17 18 19 20 21
..
.
More rows continue to list the positive integers in order, with each new row containing
one more integer than the previous row. How many integers less than 2000 are in the
column that contains the number 2000?
(A) 15 (B) 19 (C) 17 (D) 16 (E) 18
Gauss Contest
(Grade 7)

Instructions
4. This is a multiple-choice test. Each question is followed by five possible answers marked A,
B, C, D, and E. Only one of these is correct. When you have made your choice, enter the
appropriate letter for that question on your answer sheet.
Grade 7

1. The value of 5 + 4 − 3 + 2 − 1 is
(A) 0 (B) −5 (C) 3 (D) −3 (E) 7
√
2. The value of 9 + 16 is
(A) 5.2 (B) 7 (C) 5.7 (D) 25 (E) 5
3. Students were surveyed about their favourite season. The

results are shown in the bar graph. What percentage of Favourite Season
Number of Students
the 10 students surveyed chose Spring? 5
(A) 50 (B) 10 (C) 25 4
(D) 250 (E) 5 3
2
1
0
Winter
Spring
Fall
Summer
4. Ground beef sells for $5.00 per kg. How much does 12 kg of ground beef cost?
(A) $5.00 (B) $12.00 (C) $60.00 (D) $17.00 (E) $2.40
5. The smallest number in the list {1.0101, 1.0011, 1.0110, 1.1001, 1.1100} is
(A) 1.0101 (B) 1.0011 (C) 1.0110 (D) 1.1001 (E) 1.1100
6. You are writing a multiple choice test and on one question you guess and pick
an answer at random. If there are five possible choices (A,B,C,D,E), what is the
probability that you guessed correctly?
(A) 51 (B) 55 (C) 45 (D) 25 (E) 35
1 1 1 1 1 1 1
7. 3 + 3 + 3 + 3 + 3 + 3 + 3 equals
(A) 3 31 (B) 7 + 1
3 (C) 3
7 (D) 7 + 3 (E) 7 × 1
3
8. Keegan paddled the first 12 km of his 36 km kayak trip before lunch. What fraction
of his overall trip remains to be completed after lunch?
(A) 12 (B) 65 (C) 34 (D) 23 (E) 35
9. If the point (3, 4) is reflected in the x-axis, what are the y

coordinates of its image? (3, 4)
(A) (−4, 3) (B) (−3, 4) (C) (4, 3)
(D) (3, −4) (E) (−3, −4)
x
Grade 7
10. I bought a new plant for my garden. Anika said it was a red rose, Bill said it was a
purple daisy, and Cathy said it was a red dahlia. Each person was correct in stating
either the colour or the type of plant. What was the plant that I bought?
(A) purple dahlia (B) purple rose (C) red dahlia
(D) yellow rose (E) red daisy
11. In the diagram, the value of x is

(A) 15 (B) 20 (C) 22
2x
(D) 18 (E) 36
3x
12. A square has a perimeter of 28 cm. The area of the square, in cm2 , is
(A) 196 (B) 784 (C) 64 (D) 49 (E) 56
13. Five children had dinner. Chris ate more than Max. Brandon ate less than Kayla.
Kayla ate less than Max but more than Tanya. Which child ate the second most?
(A) Brandon (B) Chris (C) Kayla (D) Max (E) Tanya
14. A palindrome is a positive integer that is the same when read forwards or backwards.
For example, 545 and 1331 are both palindromes. The difference between the smallest
three-digit palindrome and the largest three-digit palindrome is
(A) 909 (B) 898 (C) 888 (D) 979 (E) 878
15. A ski lift carries a skier at a rate of 12 km per hour. How many kilometres does the
ski lift carry the skier in 10 minutes?
(A) 120 (B) 1.2 (C) 2 (D) 2.4 (E) 1.67
16. A 51 cm rod is built from 5 cm rods and 2 cm rods. All of the 5 cm rods must come
first, and are followed by the 2 cm rods. For example, the rod could be made from
seven 5 cm rods followed by eight 2 cm rods. How many ways are there to build the
51 cm rod?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
17. In Braydon’s cafeteria, the meats available are beef and chicken. The fruits available
are apple, pear and banana. Braydon is randomly given a lunch with one meat and
one fruit. What is the probability that the lunch will include a banana?
1 2 1 1 3
(A) 3 (B) 3 (C) 2 (D) 5 (E) 5
18. Three pumpkins are weighed two at a time in all possible ways. The weights of the
pairs of pumpkins are 12 kg, 13 kg and 15 kg. How much does the lightest pumpkin
weigh?
(A) 4 kg (B) 5 kg (C) 6 kg (D) 7 kg (E) 8 kg
Grade 7
19. The sum of four numbers is T . Suppose that each of the four numbers is now increased
by 1. These four new numbers are added together and then the sum is tripled. What
is the value of this final result?
(A) 3T + 3 (B) 3T + 4 (C) 3T + 12 (D) T + 12 (E) 12T
20. A triangular prism is placed on a rectangular prism, as

shown. The volume of the combined structure, in cm3 ,
is 3 cm
(A) 76 (B) 78 (C) 72 5 cm 2 cm

(D) 84 (E) 66
4 cm
6 cm
21. Steve begins at 7 and counts forward by 3, obtaining the list 7, 10, 13, and so on.
Dave begins at 2011 and counts backwards by 5, obtaining the list 2011, 2006, 2001,
and so on. Which of the following numbers appear in each of their lists?
(A) 1009 (B) 1006 (C) 1003 (D) 1001 (E) 1011
22. A pool has a volume of 4000 L. Sheila starts filling the empty pool with water at a
rate of 20 L/min. The pool springs a leak after 20 minutes and water leaks out at
2 L/min. Beginning from the time when Sheila starts filling the empty pool, how
long does it take until the pool is completely full?
(A) 3 hours (B) 3 hours 40 minutes (C) 4 hours
(D) 4 hours 20 minutes (E) 3 hours 20 minutes
23. In the addition of the three-digit numbers shown, the letters A, B, C, D, and E each
represent a single digit.
A B E
A C E
+ A D E
2 0 1 1
The value of A + B + C + D + E is
(A) 34 (B) 21 (C) 32 (D) 27 (E) 24
24. From the figure shown, three of the nine squares are to be
selected. Each of the three selected squares must share a
side with at least one of the other two selected squares.
In how many ways can this be done?
(A) 19 (B) 22 (C) 15
(D) 16 (E) 20
25. Ten circles are all the same size. Each pair of these circles overlap but no circle
is exactly on top of another circle. What is the greatest possible total number of
intersection points of these ten circles?
(A) 40 (B) 70 (C) 80 (D) 90 (E) 110
Canadian
Mathematics
Competition
An activity of the Centre for Education
in Mathematics and Computing,
University of Waterloo, Waterloo, Ontario
Gauss Contest (Grade 7)


Instructions
Grade 7

60 Favourite Pet
Number of Students
1. The grade 7 students at Gauss Public School were 50
asked, “What is your favourite pet?” The number
40
of students who chose fish is
30
(A) 10 (B) 20 (C) 30
20
(D) 40 (E) 50 10
0
fish
dog
cat
bird
rabbit
2. Tanya scored 20 out of 25 on her math quiz. What percent did she score?
(A) 75 (B) 95 (C) 80 (D) 20 (E) 45
3. The value of 4 × 5 + 5 × 4 is
(A) 160 (B) 400 (C) 100 (D) 18 (E) 40
4. In the diagram, the point with coordinates (−2, −3) is

located at E
B A
(A) A (B) B (C) C
x
(D) D (E) E
C
D
5. Chaz gets on the elevator on the eleventh floor. The elevator goes down two floors,
then stops. Then the elevator goes down four more floors and Chaz gets off the
elevator. On what floor does Chaz get off the elevator?
(A) 7th floor (B) 9th floor (C) 4th floor (D) 5th floor (E) 6th floor
6. If 10.0003 × = 10000.3, the number that should replace the is

(A) 100 (B) 1000 (C) 10000 (D) 0.001 (E) 0.0001
7. In the diagram, the value of x is

150
(A) 40 (B) 35 (C) 150
(D) 30 (E) 25
x
8. How many 1 cm × 1 cm × 1 cm blocks are needed to

build the solid rectangular prism shown?
(A) 10 (B) 12 (C) 33 3 cm
(D) 66 (E) 36
3 cm
4 cm
Grade 7
9. The time on a digital clock reads 3:33. What is the shortest length of time, in minutes,
until all of the digits are again equal to each other?
(A) 71 (B) 60 (C) 142 (D) 222 (E) 111
10. Each number below the top row is the product of the 7 5 x
number to the right and the number to the left in the
row immediately above it. What is the value of x?
35 y
(A) 8 (B) 4 (C) 7
(D) 5 (E) 6
700
Part B: Each correct answer is worth 6. 2

11. The area of the figure, in square units, is 3
(A) 36 (B) 64 (C) 46 6
(D) 58 (E) 32
5
3
12. Recycling 1 tonne of paper will save 24 trees. If 4 schools each recycle 4 of a tonne
of paper, then the total number of trees this will save is
(A) 24 (B) 72 (C) 18 (D) 126 (E) 80
13. If the mean (average) of five consecutive integers is 21, the smallest of the five
integers is
(A) 17 (B) 21 (C) 1 (D) 18 (E) 19
14. A bag contains green mints and red mints only. If 75% of the mints are green, what
is the ratio of the number of green mints to the number of red mints?
(A) 3 : 4 (B) 3 : 1 (C) 4 : 3 (D) 1 : 3 (E) 3 : 7
15. Square M has an area of 100 cm2 . The area of square N is four times the area of
square M . The perimeter of square N is
(A) 160 cm (B) 400 cm (C) 80 cm (D) 40 cm (E) 200 cm
16. In a magic square, all rows, columns, and diagonals have

the same sum. The magic square shown uses each of the +1 Y
integers from −6 to +2. What is the value of Y ?
(A) −1 (B) 0 (C) −6 4
(D) +2 (E) −2
3 5
17. How many three-digit integers are exactly 17 more than a two-digit integer?
(A) 17 (B) 16 (C) 10 (D) 18 (E) 5
Grade 7
18. Distinct points are placed on a circle. Each pair of points
is joined with a line segment. An example with 4 points
and 6 line segments is shown. If 6 distinct points are
placed on a circle, how many line segments would there
be?
(A) 13 (B) 16 (C) 30
(D) 15 (E) 14
19. If each of the four numbers 3, 4, 6, and 7 replaces a ,
what is the largest possible sum of the fractions shown?
+
19 13 5
(A) 12 (B) 7 (C) 2
15 23
(D) 4 (E) 6
20. Andy, Jen, Sally, Mike, and Tom are sitting in a row of five seats. Andy is not beside
Jen. Sally is beside Mike. Who cannot be sitting in the middle seat?
(A) Andy (B) Jen (C) Sally (D) Mike (E) Tom
21. A bicycle travels at a constant speed of 15 km/h. A bus starts 195 km behind the
bicycle and catches up to the bicycle in 3 hours. What is the average speed of the
bus in km/h?
(A) 65 (B) 80 (C) 70 (D) 60 (E) 50
22. In the Coin Game, you toss three coins at the same time. You win only if the 3 coins
are all showing heads, or if the 3 coins are all showing tails. If you play the game
once only, what is the probability of winning?
(A) 61 (B) 41 (C) 272
(D) 23 (E) 13
23. Molly assigns every letter of the alphabet a different

whole number value. She finds the value of a word Word Value
by multiplying the values of its letters together. For TOTE 18
example, if D has a value of 10, and I has a value of 8, TEAM 168
then the word DID has a value of 10 × 8 × 10 = 800. The MOM 49
table shows the value of some words. What is the value HOME 70
of the word MATH? MATH ?
(A) 19 (B) 840 (C) 420
(D) 190 (E) 84
24. How many different pairs (m, n) can be formed using numbers from the list of integers
{1, 2, 3, . . . , 20} such that m < n and m + n is even?
(A) 55 (B) 90 (C) 140 (D) 110 (E) 50
25. Tanner wants to fill his swimming pool using two hoses, each of which sprays water
at a constant rate. Hose A fills the pool in a hours when used by itself, where a is
a positive integer. Hose B fills the pool in b hours when used by itself, where b is a
positive integer. When used together, Hose A and Hose B fill the pool in 6 hours.
How many different possible values are there for a?
(A) 5 (B) 6 (C) 9 (D) 10 (E) 12
Canadian
Mathematics
Competition

C.M.C. Sponsors C.M.C. Supporter
Chartered
Accountants

Instructions
Grade 7
1. 4.1 + 1.05 + 2.005 equals

(A) 7.155 (B) 7.2 (C) 8.1 (D) 7.605 (E) 8.63
2. In the diagram, the equilateral triangle has a base of 8 m.

The perimeter of the equilateral triangle is
(A) 4 m (B) 16 m (C) 24 m
(D) 32 m (E) 64 m
8m
3. How many numbers in the list 11, 12, 13, 14, 15, 16, 17 are prime numbers?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
4. The smallest number in the list {0.40, 0.25, 0.37, 0.05, 0.81} is
(A) 0.40 (B) 0.25 (C) 0.37 (D) 0.05 (E) 0.81
5. In the diagram, the coordinates of point P could be y

(A) (1, 3) (B) (1, −3) (C) (−3, 1)
(D) (3, −1) (E) (−1, 3) 4
P
2
x
4 2 2 4
2
6. The temperature in Vancouver is 22◦ C. The temperature in Calgary is 19◦ C colder

than the temperature in Vancouver. The temperature in Quebec City is 11◦ C colder
than the temperature in Calgary. What is the temperature in Quebec City?
(A) 14◦ C (B) 3◦ C (C) −8◦ C (D) 8◦ C (E) −13◦ C
7. On a map of Nunavut, a length of 1 centimetre measured on the map represents a

real distance of 60 kilometres. What length on the map represents a real distance of
540 kilometres?
(A) 9 cm (B) 90 cm (C) 0.09 cm (D) 0.11 cm (E) 5.4 cm
8. In 4P QR, the sum of ∠P and ∠Q is 60◦ . The measure of ∠R is

(A) 60◦ (B) 300◦ (C) 120◦ (D) 30◦ (E) 40◦
9. In a class of 30 students, exactly 7 have been to Mexico and exactly 11 have been to
England. Of these students, 4 have been to both Mexico and England. How many
students in this class have not been to Mexico or England?
(A) 23 (B) 16 (C) 20 (D) 12 (E) 18
Grade 7
10. If the figure is rotated 180◦ about point F , the result could be
F
(A) (B) (C) F (D) F (E) F
F F

11. Scott challenges Chris to a 100 m race. Scott runs 4 m for every 5 m that Chris runs.
How far will Scott have run when Chris crosses the finish line?
(A) 75 m (B) 96 m (C) 20 m (D) 76 m (E) 80 m
12. 4P QR has an area of 27 cm2 and a base measuring 6 cm. P

What is the height, h, of 4P QR?
(A) 9 cm (B) 18 cm (C) 4.5 cm
h
(D) 2.25 cm (E) 7 cm
Q R
13. The product 60 × 60 × 24 × 7 equals 6 cm
(A) the number of minutes in seven weeks

(B) the number of hours in sixty days
(C) the number of seconds in seven hours
(D) the number of seconds in one week
(E) the number of minutes in twenty-four weeks
14. Which of the points positioned on the number line best

represents the value of S ÷ T ?
(A) P (B) Q (C) R 0 1 2
P Q R S T U
(D) T (E) U
15. The product of three different positive integers is 144. What is the maximum possible
sum of these three integers?
(A) 20 (B) 75 (C) 146 (D) 52 (E) 29
16. A square has an area of 25. A rectangle has the same width as the square. The length
of the rectangle is double its width. What is the area of the rectangle?
(A) 25 (B) 12.5 (C) 100 (D) 50 (E) 30
17. Vanessa set a school record for most points in a single basketball game when her team
scored 48 points. The six other players on her team averaged 3.5 points each. How
many points did Vanessa score to set her school record?
(A) 21 (B) 25 (C) 32 (D) 17 (E) 27
18. If x, y and z are positive integers with xy = 18, xz = 3 and yz = 6, what is the value
of x + y + z?
(A) 6 (B) 10 (C) 25 (D) 11 (E) 8
Grade 7
19. A jar contains quarters (worth $0.25 each), nickels (worth $0.05 each) and pennies
(worth $0.01 each). The value of the quarters is $10.00. The value of the nickels is
$10.00. The value of the pennies is $10.00. If Judith randomly chooses one coin from
the jar, what is the probability that it is a quarter?
(A) 25
31 (B) 311
(C) 13 5
(D) 248 1
(E) 30
20. Each of 4P QR and 4ST U has an area of 1. In 4P QR, P U Q

U , W and V are the midpoints of the sides, as shown.
In 4ST U , R, V and W are the midpoints of the sides.
What is the area of parallelogram U V RW ?
1 1
V W
(A) 1 (B) 2 (C) 3
1 2
(D) 4 (E) 3
T R S

21. Lara ate 14 of a pie and Ryan ate 10
3
of the same pie. The next day Cassie ate 2
3 of
the pie that was left. What fraction of the original pie was not eaten?
9 3 7 3 1
(A) 10 (B) 10 (C) 60 (D) 20 (E) 20
22. In the diagram, a 4 × 4 grid is to be filled so that each

of the digits 1, 2, 3, and 4 appears in each row and each 1 3
column. The 4 × 4 grid is divided into four smaller 2 × 2
squares. Each of these 2 × 2 squares is also to contain 2
each of the digits 1, 2, 3 and 4. What digit replaces P ? P
(A) 1 (B) 2 (C) 3
4
(D) 4 (E) The digit cannot be determined
23. Each time Kim pours water from a jug into a glass, exactly 10% of the water remaining
in the jug is used. What is the minimum number of times that she must pour water
into a glass so that less than half the water remains in the jug?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
24. In square ABCD, P is the midpoint of DC and Q is the A B

midpoint of AD. If the area of the quadrilateral QBCP
is 15, what is the area of square ABCD?
Q
(A) 27.5 (B) 25 (C) 30
(D) 20 (E) 24
D P C
25. Kira can draw a connected path from M to N by drawing N

arrows along only the diagonals of the nine squares
shown. One such possible path is shown. A path cannot
pass through the interior of the same square twice. In
total, how many different paths can she draw from M to
N?
(A) 5 (B) 6 (C) 7 M
(D) 8 (E) 9
Canadian
Mathematics
Competition

Chartered
Accountants
Time: 1 hour 2008

c Waterloo Mathematics Foundation
Instructions
Grade 7
1. The value of 6 × 2 − 3 is
(A) 9 (B) −6 (C) 12 (D) 15 (E) 10
2. The value of 1 + 0.01 + 0.0001 is

(A) 1.0011 (B) 1.0110 (C) 1.1001 (D) 1.1010 (E) 1.0101
1 1 1
3. 2 + 4 + 8 is equal to
1 3 7 3
(A) 1 (B) 64 (C) 14 (D) 8 (E) 8
4. A regular polygon has perimeter 108 cm and each side has length 12 cm. How many
sides does this polygon have?
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10
5. The smallest number in the set { 3.2, 2.3, 3, 2.23, 3.22 } is

(A) 3.2 (B) 2.3 (C) 3 (D) 2.23 (E) 3.22
6. If P Q is a straight line, then the value of x is

(A) 36 (B) 72 (C) 18
(D) 20 (E) 45
x x x
P x x Q
7. Which of the following is a prime number?

(A) 20 (B) 21 (C) 23 (D) 25 (E) 27
8. Kayla went for a walk every day last week. Each day, she walked half as far as she did
the day before. If she walked 8 kilometres on Monday last week, how many kilometres
did she walk on Friday last week?
(A) 0.25 (B) 4 (C) 1 (D) 2 (E) 0.5
9. The circle graph shows the favourite ice cream

15%
flavours of those surveyed. What fraction Mint 10%
of people surveyed selected either chocolate Strawberry
or strawberry as their favourite flavour of ice 50%
Chocolate
cream? 25%
(A) 3
(B) 1
(C) 2 Vanilla
5 3 3
3 5
(D) 4 (E) 8
10. Max sold glasses of lemonade for 25 cents each. He sold 41 glasses on Saturday and
53 glasses on Sunday. What were his total sales for these two days?
(A) $23.50 (B) $10.25 (C) $13.25 (D) $21.50 (E) $24.25
Grade 7
11. Chris bought two hockey sticks at the same price. He also bought a helmet for $25.
If Chris spent $68 in total, how much did one hockey stick cost?
(A) $9.00 (B) $18.00 (C) $21.50 (D) $43.00 (E) $41.50
12. In the chart, each number below the top row is

the positive difference of the two numbers to the 8 9 17 6 4
right and left in the row immediately above it. 1 8 2
What is the value of x? 7
(A) 1 (B) 2 (C) 3
x
(D) 4 (E) 0
P
13. In the diagram, 4P QR is isosceles. The value of x is
(A) 40 (B) 70 (C) 60 40
(D) 30 (E) 110
Q
R x
14. Wesley is 15 and his sister Breenah is 7. The sum of their ages is 22. In how many
years will the sum of their ages be double what it is now?
(A) 7 (B) 8 (C) 15 (D) 14 (E) 11
R R
15. Using two transformations, the letter R is changed as shown: R → → .
L L
Using the same two transformations, the letter L is changed as shown: L → → .
Using the same two transformations, the letter G is changed to
G G
(A) G (B) G (C) (D) (E)
G
16. In the diagram, each small square in the grid is the same
size. What percent of the grid is shaded?
(A) 84 (B) 80 (C) 90
(D) 75 (E) 66
17. The length of a rectangle is 6 more than twice its width. If the perimeter of the
rectangle is 120, what is its width?
(A) 8 (B) 18 (C) 27 (D) 38 (E) 22
18. Rishi got the following marks on four math tests: 71, 77, 80, and 87. He will write
one more math test. Each test is worth the same amount and all marks are between
0 and 100. Which of the following is a possible average for his five math tests?
(A) 88 (B) 62 (C) 82 (D) 84 (E) 86
Grade 7
19. A 4 × 4 square grid can be entirely covered by three non-overlapping pieces made
from 1 × 1 squares. If the first two pieces are and , the third piece is
(A) (B) (C) (D) (E)
20. The product of three different positive integers is 72. What is the smallest possible
sum of these integers?
(A) 13 (B) 14 (C) 15 (D) 17 (E) 12
21. Andrea has finished the third day of a six day canoe trip. If she has completed 37 of
the trip’s total distance of 168 km, how many km per day must she average for the
remainder of her trip?
(A) 29 (B) 24 (C) 27 (D) 32 (E) 26
22. In the diagram, P QRS is a trapezoid with an area of 12.

RS is twice the length of P Q. The area of 4P QS is P Q
(A) 3 (B) 4 (C) 5
(D) 6 (E) 8
S R
23. There are 24 ways in which Beverly, Dianne, Ethan, and Jamaal can arrange them-
selves to sit in a row of four seats. In how many ways can Beverly, Dianne, Ethan,
and Jamaal arrange themselves in a row of four seats so that Ethan does not sit
beside Dianne?
(A) 18 (B) 12 (C) 21 (D) 6 (E) 15
24. A star is made by overlapping two identical equilateral

triangles, as shown. The entire star has an area of 36.
What is the area of the shaded region?
(A) 24 (B) 18 (C) 27
(D) 33 (E) 30
25. The sum of all the digits of the integers from 98 to 101 is
9 + 8 + 9 + 9 + 1 + 0 + 0 + 1 + 0 + 1 = 38
The sum of all of the digits of the integers from 1 to 2008 is

(A) 30 054 (B) 27 018 (C) 28 036 (D) 30 036 (E) 28 054
Canadian
Mathematics
Competition

Sybase
iAnywhere Solutions
Chartered
Accountants Maplesoft
Time: 1 hour 2006

Instructions
The names of some top-scoring students will be published in the Gauss Report on our Web site,
http://www.cemc.uwaterloo.ca.
Please see our Web site http://www.cemc.uwaterloo.ca for copies of past Contests and for
information on publications which are excellent resources for enrichment, problem solving and
contest preparation.
Grade 7

1. The value of (4 − 3) × 2 is
(A) −2 (B) 2 (C) 1 (D) 3 (E) 5
2. Which number represents ten thousand?

(A) 10 (B) 10 000 000 (C) 10 000 (D) 100 (E) 1 000
3. What integer should be placed in the to make the statement − 5 = 2 true?

(A) 7 (B) 4 (C) 3 (D) 1 (E) 8
4. If Mukesh got 80% on a test which has a total of 50 marks, how many marks did he
get?
(A) 40 (B) 62.5 (C) 10 (D) 45 (E) 35
7 3 9
5. The sum 10 + 100+ 1000 is equal to
(A) 0.937 (B) 0.9037 (C) 0.7309 (D) 0.739 (E) 0.0739
6. Mark has 43 of a dollar and Carolyn has 10

3
of a dollar. Together they have
(A) $0.90 (B) $0.95 (C) $1.00 (D) $1.10 (E) $1.05
7. Six students have an apple eating contest. The

graph shows the number of apples eaten by each
student. Lorenzo ate the most apples and Jo ate 6
the fewest. How many more apples did Lorenzo Apples
eat than Jo? Eaten 4
(A) 2 (B) 5 (C) 4 2
(D) 3 (E) 6
Students
8. In the diagram, what is the value of x?
(A) 110 (B) 50 (C) 10
50
(D) 60 (E) 70
60
x
9. The word BANK is painted exactly as shown on the outside of a clear glass window.
Looking out through the window from the inside of the building, the word appears
as
(A) BANK (B) KNAB (C) BANK (D) KNAB (E) KNAB
10. A large box of chocolates and a small box of chocolates together cost $15. If the
large box costs $3 more than the small box, what is the price of the small box of
chocolates?
(A) $3 (B) $4 (C) $5 (D) $6 (E) $9
Grade 7

11. In the Fibonacci sequence 1, 1, 2, 3, 5, . . . , each number beginning with the 2 is the
sum of the two numbers before it. For example, the next number in the sequence is
3 + 5 = 8. Which of the following numbers is in the sequence?
(A) 20 (B) 21 (C) 22 (D) 23 (E) 24
12. The Grade 7 class at Gauss Public School has sold 120 tickets for a lottery. One
winning ticket will be drawn. If the probability of one of Mary’s tickets being drawn
1
is 15 , how many tickets did she buy?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
13. What is the largest amount of postage in cents that cannot be made using only 3 cent
and 5 cent stamps?
(A) 7 (B) 13 (C) 4 (D) 8 (E) 9
14. Harry, Ron and Neville are having a race on their broomsticks. If there are no ties,
in how many different possible orders can they finish?
(A) 7 (B) 6 (C) 5 (D) 4 (E) 3
15. How many positive whole numbers, including 1, divide exactly into both 40 and 72?
(A) 9 (B) 12 (C) 4 (D) 2 (E) 5
16. In the diagram, each scale shows the total

mass (weight) of the shapes on that scale.
What is the mass (weight) of a ? 8 11 15
(A) 3 (B) 5 (C) 12
(D) 6 (E) 5.5
17. To rent a kayak and a paddle, there is a fixed fee to use the paddle, plus a charge of
$5 per hour to use the kayak. For a three hour rental, the total cost is $30. What is
the total cost for a six hour rental?
(A) $50 (B) $15 (C) $45 (D) $60 (E) $90
18. Fred’s birthday was on a Monday and was exactly 37 days after Pat’s birthday.
Julie’s birthday was 67 days before Pat’s birthday. On what day of the week was
Julie’s birthday?
(A) Saturday (B) Sunday (C) Monday (D) Tuesday (E) Wednesday
19. The whole numbers from 1 to 1000 are written. How many of these numbers have at
least two 7’s appearing side-by-side?
(A) 10 (B) 11 (C) 21 (D) 30 (E) 19
20. In the diagram, the square has a perimeter of 48 and the

triangle has a height of 48. If the square and the triangle
have the same area, what is the value of x?
48
(A) 1.5 (B) 12 (C) 6
(D) 3 (E) 24
x
Grade 7
21. In the diagram, how many paths can be taken to spell

“KARL”? K
(A) 4 (B) 16 (C) 6 A A
(D) 8 (E) 14 R R R
L L L L
22. The average of four different positive whole numbers is 4. If the difference between
the largest and smallest of these numbers is as large as possible, what is the average
of the other two numbers?
(A) 1 21 (B) 2 12 (C) 4 (D) 5 (E) 2
23. A square is divided, as shown. What fraction of the area

of the square is shaded?
1 1 3
(A) 4 (B) 8 (C) 16
1 3
(D) 6 (E) 32
24. In the multiplication shown, P , Q and R are all different digits so that
PPQ
× Q
RQ 5 Q
What is the value of P + Q + R?

(A) 20 (B) 13 (C) 15 (D) 16 (E) 17
25. The CMC reception desk has a tray in which to stack letters as they arrive. Starting
at 12:00, the following process repeats every five minutes:
• Step 1 – Three letters arrive at the reception desk and are stacked on top of the
letters already in the stack. The first of the three is placed on the stack first,
the second letter next, and the third letter on top.
• Step 2 – The top two letters in the stack are removed.
This process repeats until 36 letters have arrived (and the top two letters have been
immediately removed). Once all 36 letters have arrived (and the top two letters have
been immediately removed), no more letters arrive and the top two letters in the stack
continue to be removed every five minutes until all 36 letters have been removed. At
what time was the 13th letter to arrive removed?
(A) 1:15 (B) 1:20 (C) 1:10 (D) 1:05 (E) 1:25
Canadian
Mathematics
Competition

C.M.C. Sponsors: Sybase

Chartered
Accountants Great West Life iAnywhere Solutions
and London Life
C.M.C. Supporter:
Canadian Institute
of Actuaries
Time: 1 hour 2005

Instructions
Please see our website http://www.cemc.uwaterloo.ca for copies of past Contests and for
information on publications which are excellent resources for enrichment, problem solving and
contest preparation.
Grade 7
1. The value of (8 × 4) + 3 is
(A) 96 (B) 15 (C) 56 (D) 35 (E) 28
2. In the diagram, ABC is a straight line. The value of x is

(A) 100 (B) 140 (C) 50
(D) 120 (E) 320
x 40
A C
B
3. Mikhail has $10 000 in $50 bills. How many $50 bills does he have?
(A) 1000 (B) 200 (C) 1250 (D) 500 (E) 2000
4. What is the perimeter of the figure shown?

(A) 16 (B) 10 (C) 8
(D) 14 (E) 18
2
2 1
5. The value of 5 + 3 is
3 2 11 13 3
(A) 8 (B) 15 (C) 15 (D) 15 (E) 15
6. The value of 6 × 100 000 + 8 × 1000 + 6 × 100 + 7 × 1 is

(A) 6867 (B) 608 067 (C) 608 607 (D) 6 008 607 (E) 600 000 867
7. If 3 + 5x = 28, the value of x is

(A) 20 (B) 3.5 (C) 5 (D) 6.2 (E) 125
√
8. The value of 92 − 9 is
(A) 0 (B) 6 (C) 15 (D) 72 (E) 78
9. There are 2 red, 5 yellow and 4 blue balls in a bag. If a ball is chosen at random from
the bag, without looking, the probability of choosing a yellow ball is
2 5 4 6 7
(A) 11 (B) 11 (C) 11 (D) 11 (E) 11
10. A small block is placed along a 10 cm ruler. Which of

the following is closest to the length of the block?
(A) 0.24 cm (B) 4.4 cm (C) 2.4 cm 1 2 3 4 5 6 7 8 9
(D) 3 cm (E) 24 cm
Grade 7
11. The cost, before taxes, of the latest CD released by The Magic Squares is $14.99.
If the sales tax is 15%, how much does it cost to buy this CD, including tax?
(A) $17.24 (B) $15.14 (C) $2.25 (D) $16.49 (E) $16.50
12. A rectangular pool is 6 m wide, 12 m long and 4 m deep. If the pool is half full of
water, what is the volume of water in the pool?
(A) 100 m3 (B) 288 m3 (C) 36 m3 (D) 22 m3 (E) 144 m3
13. What number must be added to 8 to give the result −5?

(A) 3 (B) −3 (C) 13 (D) −13 (E) −10
14. In the diagram, O is the centre of the circle, AOB is a

diameter, and the circle graph illustrates the favourite
season of 600 students. How many of the students Summer
surveyed chose Fall as their favourite season? O
A B
(A) 100 (B) 50 (C) 360 60
Winter Spring
(D) 150 (E) 75
Fall
15. Harry charges $4 to babysit for the first hour. For each additional hour, he charges
50% more than he did for the previous hour. How much money in total would Harry
earn for 4 hours of babysitting?
(A) $16.00 (B) $19.00 (C) $32.50 (D) $13.50 (E) $28.00
16. A fraction is equivalent to 58 . Its denominator and numerator add up to 91. What is
the difference between the denominator and numerator of this fraction?
(A) 21 (B) 3 (C) 33 (D) 13 (E) 19
17. Bogdan needs to measure the area of a rectangular carpet. However, he does not
have a ruler, so he uses a shoe instead. He finds that the shoe fits exactly 15 times
along one edge of the carpet and 10 times along another. He later measures the shoe
and finds that it is 28 cm long. What is the area of the carpet?
(A) 150 cm2 (B) 4200 cm2 (C) 22 500 cm2
(D) 630 000 cm2 (E) 117 600 cm2
18. Keiko and Leah run on a track that is 150 m around. It takes Keiko 120 seconds to
run 3 times around the track, and it takes Leah 160 seconds to run 5 times around
the track. Who is the faster runner and at approximately what speed does she run?
(A) Keiko, 3.75 m/s (B) Keiko, 2.4 m/s (C) Leah, 3.3 m/s
(D) Leah, 4.69 m/s (E) Leah, 3.75 m/s
19. Which of the following is closest to one million (106 ) seconds?

(A) 1 day (B) 10 days (C) 100 days (D) 1 year (E) 10 years
Grade 7
20. The letter P is written in a 2 × 2 grid of squares as shown:
A combination of rotations about the centre of the grid and reflections in the two
lines through the centre achieves the result:
When the same combination of rotations and reflections is applied to , the
result is
(A) (B) (C) (D) (E)

21. Gail is a server at a restaurant. On Saturday, Gail gets up at 6:30 a.m., starts work
at x a.m. and finishes at x p.m. How long does Gail work on Saturday?
(A) 24 − 2x hours (B) 12 − x hours (C) 2x hours
(D) 0 hours (E) 12 hours
22. In the diagram, a shape is formed using unit squares, P

with B the midpoint of AC and D the midpoint of CE.
The line which passes through P and cuts the area of the
shape into two pieces of equal area also passes through
E
the point
(A) A (B) B (C) C D
(D) D (E) E A B C
23. In the addition of two 2-digit numbers, each blank space,

including those in the answer, is to be filled with one of
the digits 0, 1, 2, 3, 4, 5, 6, each used exactly once. The
units digit of the sum is +
(A) 2 (B) 3 (C) 4 ?
(D) 5 (E) 6
24. A triangle can be formed having side lengths 4, 5 and 8. It is impossible, however,
to construct a triangle with side lengths 4, 5 and 10. Using the side lengths 2, 3, 5,
7 and 11, how many different triangles with exactly two equal sides can be formed?
(A) 8 (B) 5 (C) 20 (D) 10 (E) 14
25. Five students wrote a quiz with a maximum score of 50. The scores of four of
the students were 42, 43, 46, and 49. The score of the fifth student was N . The
average (mean) of the five students’ scores was the same as the median of the five
students’ scores. The number of values of N which are possible is
(A) 3 (B) 4 (C) 1 (D) 0 (E) 2
Canadian
Mathematics
Competition

(Grade 8 Contest is on the reverse side)
C.M.C. Sponsors: C.M.C. Supporters:
Canadian Institute
Chartered Accountants of Actuaries
Great West Life

and London Life
Sybase
iAnywhere Solutions
Time: 1 hour 2004

Instructions
3. Be sure that you understand the coding system for your answer sheet. If you are not sure, ask your
teacher to explain it.
4. This is a multiple-choice test. Each question is followed by five possible answers marked A, B, C,
D, and E. Only one of these is correct. When you have made your choice, enter the appropriate letter
on your answer sheet for that question.
Please see our website http://www.cemc.uwaterloo.ca for copies of past Contests and for information
on publications which are excellent resources for enrichment, problem solving and contest preparation.
Grade 7

3×4
1. The value of is
6
(A) 1 (B) 2 (C) 3 (D) 4 (E) 6
2. 0.8 − 0.07 equals

(A) 0.1 (B) 0.71 (C) 0.793 (D) 0.01 (E) 0.73
3. Contestants on “Gauss Reality TV” are rated by an 9

9.2
applause metre. In the diagram, the arrow for one of the con- 9.4
testants is pointing to a rating that is closest to 9.6
(A) 9.4 (B) 9.3 (C) 9.7 9.8
(D) 9.9 (E) 9.5 10
4. Twelve million added to twelve thousand equals

(A) 12 012 000 (B) 12 120 000 (C) 120 120 000
(D) 12 000 012 000 (E) 12 012 000 000
5. The largest number in the set {0.109, 0.2, 0.111, 0.114, 0.19} is
(A) 0.109 (B) 0.2 (C) 0.11 (D) 0.114 (E) 0.19
6. At a class party, each student randomly selects a wrapped prize from a bag. The prizes
include books and calculators. There are 27 prizes in the bag. Meghan is the first to choose a
prize. If the probability of Meghan choosing a book for her prize is 23 , how many books are
in the bag?
(A) 15 (B) 9 (C) 21 (D) 7 (E) 18
7. Karen has just been chosen the new “Math Idol”. A total of 1 480 000 votes were cast and
Karen received 83% of them. How many people voted for her?
(A) 830 000 (B) 1 228 400 (C) 1 100 000 (D) 251 600 (E) 1 783 132
8. In the diagram, the size of ∠ACB is A

(A) 57◦ (B) 37◦ (C) 47◦ 93o
(D) 60◦ (E) 17◦
130o
D B C
9. A movie theatre has eleven rows of seats. The rows are numbered from 1 to 11. Odd-
numbered rows have 15 seats and even-numbered rows have 16 seats. How many seats are
there in the theatre?
(A) 176 (B) 186 (C) 165 (D) 170 (E) 171
Grade 7
10. In relation to Smiths Falls, Ontario, the local time in St. John’s, Newfoundland, is 90 minutes
ahead, and the local time in Whitehorse, Yukon, is 3 hours behind. When the local time in
St. John’s is 5:36 p.m., the local time in Whitehorse is
(A) 1:06 p.m. (B) 2:36 p.m. (C) 4:06 p.m. (D) 12:06 p.m. (E) 10:06 p.m.
Fri.
Mon.
Thurs.
Wed.
8
Tues.
11. The temperature range on a given day is the difference
6
between the daily high and the daily low temperatures.
Temperature (oC )
4
On the graph shown, which day has the greatest 2
temperature range? 0
(A) Monday (B) Tuesday (C) Wednesday -2
-4
(D) Thursday (E) Friday
-6 Daily High
-8 Daily Low
12. A bamboo plant grows at a rate of 105 cm per day. On May 1st at noon it was 2 m tall.
Approximately how tall, in metres, was it on May 8th at noon?
(A) 10.40 (B) 8.30 (C) 3.05 (D) 7.35 (E) 9.35
13. In the diagram, the length of DC is twice the length of BD. A

The area of the triangle ABC is
(A) 24 (B) 72 (C) 12 4
(D) 18 (E) 36 3
B D C
14. The numbers on opposite sides of a die total 7. What is

the sum of the numbers on the unseen faces of the two dice
shown?
(A) 14 (B) 20 (C) 21
(D) 24 (E) 30
15. In the diagram, the area of rectangle P QRS is 24. P Q
If T Q = T R, the area of quadrilateral P T RS is
(A) 18 (B) 20 (C) 16 T
(D) 6 (E) 15 S R
16. Nicholas is counting the sheep in a flock as they cross a road. The sheep begin to cross the
road at 2:00 p.m. and cross at a constant rate of three sheep per minute. After counting 42
sheep, Nicholas falls asleep. He wakes up an hour and a half later, at which point exactly
half of the total flock has crossed the road since 2:00 p.m. How many sheep are there in the
entire flock?
(A) 630 (B) 621 (C) 582 (D) 624 (E) 618
3 4 2 6
17. The symbol is evaluated as 3 × 6 + 4 × 5 = 38. If is evaluated as 16,
5 6 1
then the number that should be placed in the empty space is
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
Grade 7
18. A game is said to be fair if your chance of winning is equal to your chance of losing.
How many of the following games, involving tossing a regular six-sided die, are fair?
• You win if you roll a 2
• You win if you roll an even number
• You win if you roll a number less than 4
• You win if you roll a number divisible by 3
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
19. Chris and Pat are playing catch. Standing 1 m apart, Pat first throws the ball to Chris and
then Chris throws the ball back to Pat. Next, standing 2 m apart, Pat throws to Chris and
Chris throws back to Pat. After each pair of throws, Chris moves 1 m farther away from Pat.
They stop playing when one of them misses the ball. If the game ends when the 29th throw
is missed, how far apart are they standing and who misses catching the ball?
(A) 15 m, Chris (B) 15 m, Pat (C) 14m, Chris (D) 14 m, Pat (E) 16 m, Pat
20. While driving at 80 km/h, Sally’s car passes a hydro pole every four seconds. Which of the
following is closest to the distance between two neighbouring hydro poles?
(A) 50 m (B) 60 m (C) 70 m (D) 80 m (E) 90 m

21. Emily was at a garage sale where the price of every item was reduced by 10% of its current
price every 15 minutes. At 9:00 a.m., the price of a carpet was $10.00. At 9:15 a.m., the price
was reduced to $9.00. As soon as the price of the carpet fell below $8.00, Emily bought it.
At what time did Emily buy the carpet?
(A) 9:45 a.m. (B) 9:15 a.m. (C) 9:30 a.m. (D) 10:15 a.m. (E) 10:00 a.m.
22. In a bin at the Gauss Grocery, the ratio of the number of apples to the number of oranges
is 1 : 4, and the ratio of the number of oranges to the number of lemons is 5 : 2. What is the
ratio of the number of apples to the number of lemons?
(A) 1 : 2 (B) 4 : 5 (C) 5 : 8 (D) 20 : 8 (E) 2 : 1
23. Using an equal-armed balance, if balances and balances , which of the

following would not balance ?
(A) (B) (C) (D) (E)
24. On a circular track, Alphonse is at point A and Beryl is A

diametrically opposite at point B. Alphonse runs
counterclockwise and Beryl runs clockwise. They run at
constant, but different, speeds. After running for a while they
notice that when they pass each other it is always at the same
three places on the track. What is the ratio of their speeds?
(A) 3 : 2 (B) 3 : 1 (C) 4 : 1 B
(D) 2 : 1 (E) 5 : 2
25. How many different combinations of pennies, nickels, dimes and quarters use 48 coins to
total $1.00?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 8
Canadian
Mathematics
Competition
An activity of The Centre for Education

C.M.C. Sponsors: C.M.C. Supporters:
Canadian Institute
of Actuaries
Chartered Accountants
Great West Life
and London Life
Sybase
Inc. (Waterloo)
iAnywhere Solutions
Time: 1 hour © 2004 Waterloo Mathematics Foundation

Instructions
1. Do not open the examination booklet until you are told to do so.
3. Be certain that you understand the coding system for your answer sheet. If you are not sure, ask
your teacher to explain it.
4. This is a multiple-choice test. Each question is followed by five possible answers marked A, B,
C, D, and E. Only one of these is correct. When you have decided on your choice, enter the
appropriate letter on your answer sheet for that question.
5. Scoring:
Each correct answer is worth 5 in Part A, 6 in Part B, and 8 in Part C.
7. When your supervisor tells you to start, you will have sixty minutes of working time.
Grade 7


10 + 20 + 30 + 40
1. The value of is
10
(A) 90 (B) 91 (C) 10 (D) 64 (E) 9
1 1
2. The value of 2
– 8 is
3 1 5 1 1
(A) 8
(B) – 6 (C) 8
(D) 16
(E) 4
3. Seven thousand twenty-two can be written as

(A) 70 022 (B) 722 (C) 7202 (D) 7022 (E) 7220
4. In the diagram, the value of x is 23°

(A) 77 (B) 113 (C) 67 x°
(D) 103 (E) 90
5. Five years ago today, Sally was 7 years old. In two more years, Sally will be
(A) 12 (B) 14 (C) 9 (D) 13 (E) 10
6. At the Gauss Store, you earn 5 “reward points” for each $25 you spend. When Stuart spends $200 at
the Gauss Store, the number of reward points that he earns is
(A) 5 (B) 8 (C) 40 (D) 125 (E) 1000
7. Which of the following fractions has the largest value?

8 7 66 55 4
(A) 9
(B) 8
(C) 77
(D) 66
(E) 5
8. A box contains 1 grey ball, 2 white balls and 3 black balls. Without looking, John reaches in and
chooses one ball at random. What is the probability that the ball is not grey?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
6 6 6 6
9. In the diagram, all rows, columns and diagonals have the same sum.
14 19
What is the value of x?
(A) 12 (B) 13 (C) 16 15
(D) 17 (E) 18 x 11
10. The perimeter of the figure, in cm, is 3 cm
(A) 30 (B) 28 (C) 25
(D) 24 (E) 22
6 cm
5 cm
Grade 7
11. What is the median quiz score of the 25 scores FREQUENCY OF QUIZ SCORES
Number of Students
shown on the bar graph? 10
(A) 8 (B) 9 (C) 10 8
(D) 11 (E) 12 6
4
2
8 9 10 11 12
Quiz score
12. The elevation of Lake Ontario is 75.00 m and the elevation of Lake Erie is 174.28 m. A ship
travels between the two lakes, passing through the locks of the Welland Canal. If the ship takes
8 hours to travel between the lakes, the average (mean) change in elevation per hour is
(A) 12.41 m (B) 21.79 m (C) 5.25 m (D) 4.14 m (E) 7.80 m
13. Two positive integers have a sum of 11. The greatest possible product of these two positive
integers is
(A) 11 (B) 18 (C) 28 (D) 35 (E) 30
2 3
14. How many even whole numbers lie between 3 and 3 ?
(A) 9 (B) 4 (C) 6 (D) 10 (E) 17
15. If P = 1000 and Q = 0.01, which of the following calculations gives the largest result?
P Q
(A) P + Q (B) P × Q (C) (D) (E) P – Q
Q P
16. What is the maximum number of rectangular wooden
blocks with dimensions 20 cm × 30 cm × 40 cm that
could fit into a rectangular box with inner dimensions
40 cm × 60 cm × 80 cm ? 40 cm
(A) 2 (B) 4 (C) 10
80 cm
(D) 8 (E) 6
60 cm
17. Kalyn is trying out a new recipe that calls for 5 cups of flour and 1 cup shortening. She only has
2
3
cup of shortening, and uses all of it. How much flour should she use to keep the ingredients in
the same ratio as called for in the recipe?
1 1 2 1
(A) 2 3 (B) 3 3 (C) 1 3 (D) 1 3 (E) 2
18. A rectangular wooden prism is made up of three pieces,

each consisting of four cubes of wood glued together.
Which of the pieces below has the same shape as the
black piece?
(A) (B) (C) (D) (E)

Grade 7
19. A two-digit number is divisible by 8, 12 and 18. The number is between
(A) 10 and 19 (B) 20 and 39 (C) 40 and 59 (D) 60 and 79 (E) 80 and 99
20. The area of square ABCD is 64 and AX = BW = CZ = DY = 2. A W B

What is the area of square WXYZ? X
(A) 58 (B) 52 (C) 48
(D) 40 (E) 36
Z
D Y C
21. In the diagram, the rectangular floor plan of the first floor Dining
Living
of a house is shown. The living room and the laundry room Room Room
are both square. The areas of three of the rooms are shown 16 m2 24 m2
on the diagram. The area of the kitchen, in m2 , is Laundry
(A) 12 (B) 16 (C) 18 4 m2 Kitchen
(D) 24 (E) 36
22. The entire contents of a jug can exactly fill 9 small glasses and 4 large glasses of juice. The entire
contents of the jug could instead fill 6 small glasses and 6 large glasses. If the entire contents of
the jug is used to fill only large glasses, the maximum number of large glasses that can be filled is
(A) 8 (B) 9 (C) 10 (D) 11 (E) 12
23. It takes Sharon one hour to drive the 59 km from her home to her office. Her drive includes 20
minutes on a highway and 40 minutes on city roads. If her average speed when she is on city roads
is 45 km/h, the average speed, in km/h, at which she drives on the highway is
(A) 42 (B) 59 (C) 87 (D) 90 (E) 100
24. In the Gauss 2004 Olympics, there are six competitors and eight events. The top three competitors
in each event receive gold, silver and bronze medals respectively. (There are no ties at the Gauss
Olympics, and no competitor can win more than one medal on the same event.) Each competitor
scores 5 points for each gold medal, 3 points for each silver medal, and 1 point for each bronze
medal. If one of the competitors had a total of 27 points, what is the maximum number of silver
medals she could have won?
(A) 6 (B) 2 (C) 3 (D) 4 (E) 5
25. A grid with 10 rows and some number of columns is made . ?. .

up of unit squares, as shown. A domino ( ) can be
placed horizontally or vertically to exactly cover two unit
squares. There are 2004 positions in which the domino
could be placed. The number of columns in the grid is 10
(A) 105 (B) 106 (C) 107
(D) 108 (E) 109
...

PUBLICATIONS
Please see our website http://www.cemc.uwaterloo.ca for information on publications which are excellent resources for enrichment,
problem solving and contest preparation.
Canadian
Mathematics
Competition

C.M.C. Sponsors: C.M.C. Supporters: C.M.C. Contributors:
Manulife
Financial
Canadian Institute
of Actuaries
Great West Life
and London Life
Sybase
Inc. (Waterloo)
iAnywhere Solutions

Instructions
5. Scoring:
Grade 7

1. 3.26 × 1.5 equals

(A) 0.489 (B) 4.89 (C) 48.9 (D) 489 (E) 4890
2. The value of ( 9 – 2 ) – ( 4 – 1) is
(A) 2 (B) 3 (C) 4 (D) 6 (E) 10
3. The value of 30 + 80 000 + 700 + 60 is

(A) 87 090 (B) 807 090 (C) 800 790 (D) 80 790 (E) 87 630
1+ 2 + 3
4. equals
4+5+6
1 1 2 4 1
(A) (B) (C) (D) (E)
9 3 5 11 10
5. In a survey, 90 people were asked “What is your 40

favourite pet?” Their responses were recorded and
35
then graphed. In the graph, the bar representing
Number of People
“favourite pet is dog” has been omitted. How many 30
people selected a dog as their favourite pet? 25
(A) 20 (B) 55 (C) 40 20
(D) 45 (E) 35 15
10
5
0
?
Cat Dog Fish Bird Other
Favourite Pet
6. Travis spikes his hair using gel. If he uses 4 mL of gel every day, how many days will it take him to
empty a 128 mL tube of gel?
(A) 32 (B) 33 (C) 40 (D) 30 (E) 28
3× 6 × 9
7. An expression that can be placed in the box to make the equation = true is
3 2
(A) 2 × 4 × 6 (B) 3 × 4 × 6 (C) 2 × 6 × 9 (D) 2 × 4 × 8 (E) 2 × 12 × 18
8. The words “PUNK CD FOR SALE” are painted on a clear window. How many of the letters in the
sign look the same from both sides of the window?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
1000
9. Spencer was walking home from school when he
Distance from Home (m)
realized he had forgotten his homework. He walked 800

back to the school, picked up his homework and then 600
walked home. The graph shows his distance from
400
home at different times. In total, how far did he walk?
(A) 2800 m (B) 1000 m (C) 800 m 200
(D) 1200 m (E) 1400 m

10 20
time (minutes)
Grade 7
10. In the diagram, three lines meet at the points A, B and C. If

∠ABC = 50o and ∠ACB = 30o , the value of x is C
(A) 80 (B) 30 (C) 100 A x° 30°
(D) 60 (E) 50
50°
B
1 2
11. If of of the twelve small squares in the given figure are removed, how many squares remain?
2 3
(A) 2 (B) 3 (C) 4 (D) 8 (E) 9
12. The perimeter of a rectangular field is 3 times its length. If the perimeter is 240 m, the width of the
field is
(A) 80 m (B) 40 m (C) 20 m (D) 30 m (E) 120 m
1
13. Chris and Pat go on a 30 km run. They both usually run at 10 km/h. If Chris runs at 2
his usual
running speed, and Pat runs at 1 12 times her usual speed, how many more hours does it take Chris to
complete the run than it takes Pat to complete the run?
(A) 1 (B) 1.5 (C) 2 (D) 4 (E) 6
14. A box contains 14 disks, each coloured red, blue or green. There are twice as many red disks as green
disks, and half as many blue as green. How many disks are green?
(A) 2 (B) 4 (C) 6 (D) 8 (E) 10
15. A bottle of children’s vitamins contains tablets in three different shapes. Among the vitamins, there
are 60 squares, 60 triangles and 60 stars. Each shape comes in an equal number of three different
flavours – strawberry, grape and orange. A tablet is randomly chosen from a newly opened bottle.
What is the probability that this tablet is a grape star?
1 1 1 1 1
(A) (B) (C) (D) (E)
9 60 20 3 180
16. Triangle ABC has its vertices at A(2, 0) , B(6, 0) and C (6, 3) . The area of the triangle, in square
units, is
(A) 3 (B) 4 (C) 6 (D) 7 (E) 12
17. Genna rents a car for a business trip. The rental company charges a fee of $45 plus 12 cents per
kilometre driven. If Genna’s bill before taxes is $74.16, how many kilometres did she travel in
the car?
(A) 993 (B) 375 (C) 243 (D) 288 (E) 618
18. Two squares, each with side length 5 cm, overlap as shown.
The shape of their overlap is a square, which has an area 5
of 4 cm 2 . What is the perimeter, in centimetres, of the shaded
figure?
5
(A) 24 (B) 32 (C) 40
(D) 42 (E) 50
Grade 7
19. Abraham’s mathematics exam had 30 algebra questions and 50 geometry questions, each worth 1
mark. He got 70% of the algebra questions correct, and his overall exam mark was 80%. How many
geometry questions did he answer correctly?
(A) 43 (B) 45 (C) 39 (D) 41 (E) 35
20. Six points A, B, C, D, E, and F are placed on a square grid, as shown. How
many triangles that are not right-angled can be drawn by using 3 of these A B C
6 points as vertices?
(A) 2 (B) 1 (C) 6 D E F
(D) 0 (E) 4
21. In a large hospital with several operating rooms, ten people are each waiting for a 45 minute operation.
The first operation starts at 8:00 a.m., the second at 8:15 a.m., and each of the other operations starts
at 15 minute intervals thereafter. When does the last operation end?
(A) 10:15 a.m. (B) 10:30 a.m. (C) 10:45 a.m. (D) 11:00 a.m. (E) 11:15 a.m.
22. Luke has played 20 games and has a 95% winning percentage. Without losing any more games, how
many more games in a row must he win to reach exactly a 96% winning percentage?
(A) 1 (B) 3 (C) 4 (D) 5 (E) 10
23. A different letter is painted on each face of a cube. This cube is shown below in 3 different positions:
X
What letter belongs on the shaded face of this cube in the following diagram?
(A) T (B) P (C) X
(D) E (E) V
24. In the pattern of numbers shown, every row begins with a 1 and 1 2
ends with a 2. Each of the numbers, not on the end of a row, is the 1 3 2
sum of the two numbers located immediately above and to the right, 1 4 5 2
and immediately above and to the left. For example, in the fourth
1 5 9 7 2
row the 9 is the sum of the 4 and the 5 in the third row. If this
N M O
pattern continues, the sum of all of the numbers in the thirteenth
row is
(A) 12 270 (B) 12 276 (C) 12 282
(D) 12 288 (E) 12 294
25. The digits 1, 2, 3, 4, 5, and 6 are each placed in one of the boxes so
that the resulting product is correct. If each of the six digits is used
exactly once, the digit represented by “?” is × ?
(A) 2 (B) 3 (C) 4
(D) 5 (E) 6

PUBLICATIONS
Canadian
Mathematics
Competition

Great West Life

and London Life
Canadian Institute
of Actuaries Manulife
Financial
Equitable Life
of Canada
Sybase
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Instructions
5. Scoring:
Grade 7

1. When the numbers 8, 3, 5, 0, 1 are arranged from smallest to largest, the middle number is
(A) 5 (B) 8 (C) 3 (D) 0 (E) 1
2. The value of 0.9 + 0.99 is

(A) 0.999 (B) 1.89 (C) 1.08 (D) 1.98 (E) 0.89
2 +1
3. equals
7+6
3 21 1 2 1
(A) (B) (C) (D) (E)
13 76 21 13 14
4. 20% of 20 is equal to
(A) 400 (B) 100 (C) 5 (D) 2 (E) 4
5. Tyesha earns $5 per hour babysitting, and babysits for 7 hours in a particular week. If she starts the
week with $20 in her bank account, deposits all she earns into her account, and does not withdraw
any money, the amount she has in her account at the end of the week is
(A) $35 (B) $20 (C) $45 (D) $55 (E) $65
6. Five rats competed in a 25 metre race. The graph

shows the time that each rat took to complete the
Allan
race. Which rat won the race?
Betsy
(A) Allan (B) Betsy (C) Caelin
(D) Devon (E) Ella Caelin
Devon
Ella
1 2 3 4 5 6 7 8 9 10
Time (seconds)
7. The mean (average) of the numbers 12, 14, 16, and 18, is
(A) 30 (B) 60 (C) 17 (D) 13 (E) 15
8. If P = 1 and Q = 2 , which of the following expressions is not equal to an integer?

P Q
(A) P + Q (B) P × Q (C) (D) (E) PQ
Q P
3
9. Four friends equally shared of a pizza, which was left over after a party. What fraction of a whole
4
pizza did each friend get?
3 3 1 1 1
(A) (B) (C) (D) (E)
8 16 12 16 8
10. Two squares, each with an area of 25 cm 2 , are placed side by side to form a rectangle. What is the
perimeter of this rectangle?
(A) 30 cm (B) 25 cm (C) 50 cm (D) 20 cm (E) 15 cm
Grade 7
11. After running 25% of a race, Giselle had run 50 metres. How long was the race, in metres?
(A) 100 (B) 1250 (C) 200 (D) 12.5 (E) 400
12. Qaddama is 6 years older than Jack. Jack is 3 years younger than Doug. If Qaddama is 19 years old,
how old is Doug?
(A) 17 (B) 16 (C) 10 (D) 18 (E) 15
13. 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?
(A) 11 (B) 110 (C) 108 (D) 18 (E) 1001
14. The first six letters of the alphabet are assigned values A = 1, B = 2, C = 3, D = 4, E = 5, and F = 6.
The value of a word equals the sum of the values of its letters. For example, the value of BEEF is
2 + 5 + 5 + 6 = 18. Which of the following words has the greatest value?
(A) BEEF (B) FADE (C) FEED (D) FACE (E) DEAF
15. In the diagram, AC = 4, BC = 3, and BD = 10. The A

area of the shaded triangle is
(A) 14 (B) 20 (C) 28
4
(D) 25 (E) 12
B 3 D
C
10
16. In the following equations, the letters a, b and c represent different numbers.
13 = 1
a3 = 1 + 7
33 = 1 + 7 + b
43 = 1+ 7 + c
The numerical value of a + b + c is
(A) 58 (B) 110 (C) 75 (D) 77 (E) 79
17. In the diagram, the value of z is

(A) 150 (B) 180 (C) 60 2x°
(D) 90 (E) 120
3x° x° z°
18. A perfect number is an integer that is equal to the sum of all of its positive divisors, except itself. For
example, 28 is a perfect number because 28 = 1 + 2 + 4 + 7 + 14 . Which of the following is a perfect
number?
(A) 10 (B) 13 (C) 6 (D) 8 (E) 9
19. Subesha wrote down Davina’s phone number in her math binder. Later that day, while correcting her
homework, Subesha accidentally erased the last two digits of the phone number, leaving 893-44_ _.
Subesha tries to call Davina by dialing phone numbers starting with 893-44. What is the least number
of phone calls that she has to make to be guaranteed to reach Davina’s house?
(A) 100 (B) 90 (C) 10 (D) 1000 (E) 20
Grade 7
20. The word “stop” starts in the position shown in the diagram y
to the right. It is then rotated 180° clockwise about the
origin, O, and this result is then reflected in the x-axis.
Which of the following represents the final image? O
x
stop
(A) y (B) y (C) y (D) y (E) y
pots
O O O O
x x x x x
O
stop pots stop pots
21. 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. The total number of handshakes that occurs is
(A) 5 (B) 10 (C) 12 (D) 15 (E) 25
22. The figure shown can be folded along the lines to form a
rectangular prism. The surface area of the rectangular prism, 5cm
in cm 2 , is
6 cm
(A) 312 (B) 300 (C) 280
(D) 84 (E) 600
10 cm
23. Mark has a bag that contains 3 black marbles, 6 gold marbles, 2 purple marbles, and 6 red marbles.
Mark adds a number of white marbles to the bag and tells Susan that if she now draws a marble at
3
random from the bag, the probability of it being black or gold is 7
. The number of white marbles
that Mark adds to the bag is
(A) 5 (B) 2 (C) 6 (D) 4 (E) 3
24. PQRS is a square with side length 8. X is the midpoint of P X Q

side PQ , and Y and Z are the midpoints of XS and XR,
respectively, as shown. The area of trapezoid YZRS is
(A) 24 (B) 16 (C) 20
(D) 28 (E) 32 Y Z
S R
25. Each of the integers 226 and 318 have digits whose product is 24. How many three-digit positive
integers have digits whose product is 24?
(A) 4 (B) 18 (C) 24 (D) 12 (E) 21
❋❋❋❋❋
PUBLICATIONS
Canadian
Mathematics
Competition

Great West Life

and London Life
Canadian Institute
of Actuaries Manulife
Financial
Equitable Life
of Canada
Chartered Accountants Sybase

Inc. (Waterloo)

Instructions
3. Be certain that you understand the coding system for your answer sheet. If you are not sure, ask your
4. This is a multiple-choice test. Each question is followed by five possible answers marked A, B, C, D, and
E. Only one of these is correct. When you have decided on your choice, enter the appropriate letter on
your answer sheet for that question.
5. Scoring:
Each unanswered question is worth 2, to a maximum of 20.
Grade 7

1. The largest number in the set _0.01, 0.2, 0.03, 0.02, 0.1a is
(A) 0.01 (B) 0.2 (C) 0.03 (D) 0.02 (E) 0.1
2. In 1998, the population of Canada was 30.3 million. Which number is the same as 30.3 million?
(A) 30 300 000 (B) 303 000 000 (C) 30 300 (D) 303 000 (E) 30 300 000 000
3. The value of 0.001 1.01 0.11 is

(A) 1.111 (B) 1.101 (C) 1.013 (D) 0.113 (E) 1.121
4. When the number 16 is doubled and the answer is then halved, the result is
(A) 21 (B) 2 2 (C) 23 (D) 2 4 (E) 28
5. The value of 3 v 4 2 – 8 z 2 is
(A) 44 (B) 12 (C) 20 (D) 8 (E) 140
6. In the diagram, ABCD is a rhombus. The size of BCD is A B

(A) 60r (B) 90r (C) 120r
(D) 45r (E) 160r
D C
7. A number line has 40 consecutive integers marked on it. If the smallest of these integers is –11, what
is the largest?
(A) 29 (B) 30 (C) 28 (D) 51 (E) 50
8. The area of the entire figure shown is 4

(A) 16 (B) 32 (C) 20
(D) 24 (E) 64
9. The bar graph shows the hair colours of the Campers’ Hair Colour
campers at Camp Gauss. The bar corresponding 25
to redheads has been accidentally removed. If
50% of the campers have brown hair, how many 20
of the campers have red hair? Number
of 15
(A) 5 (B) 10 (C) 25
(D) 50 (E) 60 People
10
5
?
Green Black Brown Red
Hair Colour
Grade 7
1
10. Henri scored a total of 20 points in his basketball team’s first three games. He scored of these
2
1
points in the first game and of these points in the second game. How many points did he score in
10
the third game?
(A) 2 (B) 10 (C) 11 (D) 12 (E) 8
11. A fair die is constructed by labelling the faces of a wooden cube with the numbers 1, 1, 1, 2, 3, and 3.
If this die is rolled once, the probability of rolling an odd number is
5 4 3 2 1
(A) (B) (C) (D) (E)
6 6 6 6 6
12. The ratio of the number of big dogs to the number of small dogs at a pet show is 3:17. There are 80
dogs, in total, at this pet show. How many big dogs are there?
(A) 12 (B) 68 (C) 20 (D) 24 (E) 6
13. The product of two whole numbers is 24. The smallest possible sum of these two numbers is
(A) 9 (B) 10 (C) 11 (D) 14 (E) 25
14. In the square shown, the numbers in each row, column, and
diagonal multiply to give the same result. The sum of the 12 1 18
two missing numbers is
9 6 4
(A) 28 (B) 15 (C) 30
(D) 38 (E) 72 3
15. A prime number is called a “Superprime” if doubling it, and then subtracting 1, results in another
prime number. The number of Superprimes less than 15 is
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
16. BC is a diameter of the circle with centre O and radius 5, as A

shown. If A lies on the circle and AO is perpendicular to
BC, the area of triangle ABC is
(A) 6.25 (B) 12.5 (C) 25
(D) 37.5 (E) 50 B C
O 5
17. A rectangular sign that has dimensions 9 m by 16 m has a square advertisement painted on it. The
border around the square is required to be at least 1.5 m wide. The area of the largest square
advertisement that can be painted on the sign is
(A) 78 m 2 (B) 144 m 2 (C) 36 m 2 (D) 9 m 2 (E) 56.25 m 2
18. Felix converted $924.00 to francs before his trip to France. At that time, each franc was worth thirty
cents. If he returned from his trip with 21 francs, how many francs did he spend?
(A) 3080 (B) 3101 (C) 256.2 (D) 3059 (E) 298.2
19. Rectangular tiles, which measure 6 by 4, are arranged without overlapping, to create a square. The
minimum number of these tiles needed to make a square is
(A) 8 (B) 24 (C) 4 (D) 12 (E) 6
20. Anne, Beth and Chris have 10 candies to divide amongst themselves. Anne gets at least 3 candies,
while Beth and Chris each get at least 2. If Chris gets at most 3, the number of candies that Beth
could get is
(A) 2 (B) 2 or 3 (C) 3 or 4 (D) 2, 3 or 5 (E) 2, 3, 4, or 5
Grade 7
21. Naoki wrote nine tests, each out of 100. His average on these nine tests is 68%. If his lowest mark is
omitted, what is his highest possible resulting average?
(A) 76.5% (B) 70% (C) 60.4% (D) 77% (E) 76%
22. A regular hexagon is inscribed in an equilateral triangle, as

shown. If the hexagon has an area of 12, the area of this
triangle is
(A) 20 (B) 16 (C) 15
(D) 18 (E) 24
23. Catrina runs 100 m in 10 seconds. Sedra runs 400 m in 44 seconds. Maintaining these constant
speeds, they participate in a 1 km race. How far ahead, to the nearest metre, is the winner as she
crosses the finish line?
(A) 100 m (B) 110 m (C) 95 m (D) 90 m (E) 91 m
24. Enzo has fish in two aquariums. In one aquarium, the ratio of the number of guppies to the number
of goldfish is 2:3. In the other, this ratio is 3:5. If Enzo has 20 guppies in total, the least number of
goldfish that he could have is
(A) 29 (B) 30 (C) 31 (D) 32 (E) 33
25. A triangle can be formed having side lengths 4, 5 and 8. It is impossible, however, to construct a
triangle with side lengths 4, 5 and 9. Ron has eight sticks, each having an integer length. He observes
that he cannot form a triangle using any three of these sticks as side lengths. The shortest possible
length of the longest of the eight sticks is
(A) 20 (B) 21 (C) 22 (D) 23 (E) 24
✿✿✿✿✿✿✿✿✿
PUBLICATIONS
Students and parents who enjoy solving problems for fun and recreation may find the following publications of interest. They are an
excellent resource for enrichment, problem solving, and contest preparation.
COPIES OF PREVIOUS CONTESTS (WITH FULL SOLUTIONS)
Copies of previous contests, together with solutions, are available as described below. Each item in the package has two numbers. Numbers
prefixed with E are English language supplies - numbers prefixed with F are French language supplies. Each package is considered as one
title. Included is one copy of any one contest, together with solutions, for each of the past three years. Recommended for individuals.
Gauss Contests (Grades 7,8) E 213, F 213 $10.00 Pascal/Cayley/Fermat Contests (Grades 9,10,11) E 513, F 513 $14.00
Euclid Contests (Grade 12) E 613, F 613 $10.00 Descartes Contests (Grade 13/OAC) E 713, F 713 $10.00
PROBLEMS PROBLEMS PROBLEMS BOOKS
Each volume is a collection of problems (multiple choice and full solution), grouped into 9 or more topics. Questions are selected from
previous Canadian Mathematics Competition contests, and full solutions are provided for all questions. The price is $15.00 per volume.
Available in English only. Problems Problems Problems - Volume 1 only is currently available in French.
Volume 1 - 300 problems (Grades 9, 10, and 11) Volume 2 - 325 problems (Grades 9, 10, and 11)
Volume 3 - 235 problems (Senior high school students) Volume 4 - 325 problems (Grades 7, 8, and 9)
Volume 5 - 200 problems (Senior high school students) Volume 6 - 300 problems (Grades 7, 8, and 9)
PROBLEMS AND HOW TO SOLVE THEM - VOLUME 3
This new book continues the collection of problems available for enrichment of students in grades 7 and 8. Included for each of the eight
chapters is a discussion on solving problems, with suggested approaches. There are more than 179 new problems, almost all from Canadian
Mathematics Competitions, with complete solutions. The price is $20. (Available in English only.)
Orders should be addressed to: Canadian Mathematics Competition, Faculty of Mathematics, University of Waterloo, Waterloo,
Ontario, N2L 3G1. Cheques or money orders in Canadian funds should be made payable to "Centre for Education in Mathematics
and Computing". In Canada, add $3.00 for the first item ordered for shipping and handling, plus $1.00 for each subsequent item. No
Provincial Sales Tax is required, but 7% GST must be added, and 15% HST must be added in New Brunswick, Newfoundland and
Nova Scotia. Orders outside of Canada ONLY, add $10.00 for the first item ordered for shipping and handling, plus $2.00 for each
subsequent item. Prices for these publications will remain in effect until September 1, 2001.
NOTE: All publications are protected by copyright. It is unlawful to make copies without written permission.
Canadian
Mathematics
Competition

The Great-West
Life Assurance
Company
IBM
Canada Ltd.
Northern Telecom
(Nortel)
Manulife
Financial
Canadian Institute
of Actuaries
Equitable Life
Chartered Accountants of Canada
Sybase
Inc. (Waterloo)

Instructions
5. Scoring:
Grade 7

Each unanswered question is worth 2 credits, to a maximum of 20 credits.
Part A (5 credits each)
1. The value of 987 + 113 – 1000 is

(A) 90 (B) 10 (C) 110 (D) 2000 (E) 100
9 8
2. As a decimal, + is
10 100
(A) 1.098 (B) 0.98 (C) 0.098 (D) 0.0908 (E) 9.8
3
3. What integer is closest in value to 7 × ?
4
(A) 21 (B) 9 (C) 6 (D) 5 (E) 1
4. The value of the expression 52 – 4 2 + 32 is

(A) 20 (B) 18 (C) 21 (D) 10 (E) 16
5. When a number is divided by 7, it gives a quotient of 4 with a remainder of 6. What is the number?
(A) 17 (B) 168 (C) 34 (D) 31 (E) 46
6. In the addition shown, a digit, either the same or different, 863

can be placed in each of the two boxes. What is the sum of
91
the two missing digits?
(A) 9 (B) 11 (C) 13 7 8
(D) 3 (E) 7 21 8 2
7. The graph shows the complete scoring summary Gaussian Guardians Scoring Summary
for the last game played by the eight players on
Gaussian Guardians intramural basketball team.
The total number of points scored by the
Gaussian Guardians was 10
Number of Points
(A) 54 (B) 8 (C) 12

(D) 58 (E) 46
5
Hyojeong
Winston
Daniel
Curtis
Emily
Kalyn
Sid
Ty
Players
1
8. If of the number represented by x is 32, what is 2x?
2
(A) 128 (B) 64 (C) 32 (D) 256 (E) 16
9. In the given diagram, all 12 of the small rectangles are the

same size. Your task is to completely shade some of the
rectangles until 2 of 3 of the diagram is shaded. The number
3 4
of rectangles you need to shade is
(A) 9 (B) 3 (C) 4
(D) 6 (E) 8
Grade 7
10. The sum of three consecutive integers is 90. What is the largest of the three integers?
(A) 28 (B) 29 (C) 31 (D) 32 (E) 21
Part B (6 credits each)
11. A rectangular building block has a square base ABCD as

shown. Its height is 8 units. If the block has a volume of
288 cubic units, what is the side length of the base? 8
(A) 6 (B) 8 (C) 36
(D) 10 (E) 12 D C
A B
12. A recipe requires 25 mL of butter to be used along with 125 mL of sugar. If 1000 mL of sugar is used,
how much butter would be required?
(A) 100 mL (B) 500 mL (C) 200 mL (D) 3 litres (E) 400 mL
13. Karl had his salary reduced by 10%. He was later promoted and his salary was increased by 10%. If
his original salary was $ 20 000 , what is his present salary?
(A) $16 200 (B) $19 800 (C) $20 000 (D) $20 500 (E) $24 000
14. The area of a rectangle is 12 square metres. The lengths of the sides, in metres, are whole numbers.
The greatest possible perimeter (in metres) is
(A) 14 (B) 16 (C) 12 (D) 24 (E) 26
15. In the diagram, all rows, columns and diagonals have the sum
12. What is the sum of the four corner numbers? 4
(A) 14 (B) 15 (C) 16 4
(D) 17 (E) 12
3
16. Paul, Quincy, Rochelle, Surinder, and Tony are sitting around a table. Quincy sits in the chair between
Paul and Surinder. Tony is not beside Surinder. Who is sitting on either side of Tony?
(A) Paul and Rochelle (B) Quincy and Rochelle (C) Paul and Quincy
(D) Surinder and Quincy (E) Not possible to tell
17. ABCD is a square that is made up of two identical rectangles and two squares of area 4 cm 2 and 16
cm 2 . What is the area, in cm 2 , of the square ABCD?
(A) 64 (B) 49 (C) 25 (D) 36 (E) 20
18. The month of April, 2000, had five Sundays. Three of them fall on even numbered days. The eighth
day of this month is a
(A) Saturday (B) Sunday (C) Monday (D) Tuesday (E) Friday
19. The diagram shows two isosceles right-triangles with sides

as marked. What is the area of the shaded region?
5 cm
(A) 4.5 cm 2 (B) 8 cm 2 (C) 12.5 cm 2
(D) 16 cm 2 (E) 17 cm 2 3 cm
20. A dishonest butcher priced his meat so that meat advertised at $3.79 per kg was actually sold for
$4.00 per kg. He sold 1 800 kg of meat before being caught and fined $500. By how much was he
ahead or behind where he would have been had he not cheated?
(A) $478 loss (B) $122 loss (C) Breaks even (D) $122 gain (E) $478 gain
Grade 7
Part C (8 credits each)

21. In a basketball shooting competition, each competitor shoots ten balls which are numbered from 1 to
10. The number of points earned for each successful shot is equal to the number on the ball. If a
competitor misses exactly two shots, which one of the following scores is not possible?
(A) 52 (B) 44 (C) 41 (D) 38 (E) 35
22. Sam is walking in a straight line towards a lamp post which is 8 m high. When he is 12 m away from
the lamp post, his shadow is 4 m in length. When he is 8 m from the lamp post, what is the length of
his shadow?
1 1 2
(A) 1 m (B) 2 m (C) 2 m (D) 2 m (E) 3 m
2 2 3
23. The total area of a set of different squares, arranged from smallest to largest, is 35 km 2 . The smallest
square has a side length of 500 m. The next larger square has a side length of 1000 m. In the same
way, each successive square has its side length increased by 500 m. What is the total number of
squares?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
24. Twelve points are marked on a rectangular grid, as shown.
How many squares can be formed by joining four of these
points?
(A) 6 (B) 7 (C) 9
(D) 11 (E) 13
25. A square floor is tiled, as partially shown, with a large number

of regular hexagonal tiles. The tiles are coloured blue or white.
Each blue tile is surrounded by 6 white tiles and each white
tile is surrounded by 3 white and 3 blue tiles. Ignoring part
tiles, the ratio of the number of blue tiles to the number of
white tiles is closest to
(A) 1:6 (B) 2:3 (C) 3:10
(D) 1:4 (E) 1:2
Canadian
Mathematics
Competition

The Great-West
Life Assurance
Company
IBM
Canada Ltd.
Northern Telecom
(Nortel)
Manulife
Financial
Canadian Institute
of Actuaries
Equitable Life
of Canada
Sybase
Inc. (Waterloo)

Instructions
5. Scoring:
Grade 7

1. 1999 – 999 + 99 equals

(A) 901 (B) 1099 (C) 1000 (D) 199 (E) 99
2. The integer 287 is exactly divisible by

(A) 3 (B) 4 (C) 5 (D) 7 (E) 6
3. Susan wants to place 35.5 kg of sugar in small bags. If each bag holds 0.5 kg, how many bags are
needed?
(A) 36 (B) 18 (C) 53 (D) 70 (E) 71
1 1 1
4. 1+ + + is equal to
2 4 8
15 3 11 7
(A) (B) 1 (C) (D) 13 (E)
8 14 8 4 8
5. Which one of the following gives an odd integer?

(A) 62 (B) 23 – 17 (C) 9 × 24 (D) 96 ÷ 8 (E) 9 × 41
6. In ∆ ABC , ∠ B = 72° . What is the sum, in degrees, of the A

other two angles?
(A) 144 (B) 72 (C) 108
(D) 110 (E) 288 72°
B C
4
7. If the numbers , 81% and 0.801 are arranged from smallest to largest, the correct order is
5
4 4 4
(A) , 81%, 0.801 (B) 81%, 0.801, (C) 0.801, , 81%
5 5 5
4 4
(D) 81%, , 0.801 (E) , 0.801, 81%
5 5
8. The average of 10, 4, 8, 7, and 6 is

(A) 33 (B)13 (C) 35 (D) 10 (E) 7
9. André is hiking on the paths shown in the map. He is

planning to visit sites A to M in alphabetical order. He can £ B I
never retrace his steps and he must proceed directly from A
one site to the next. What is the largest number of labelled C H J
points he can visit before going out of alphabetical order? D
(A) 6 (B) 7 (C) 8 E G
(D) 10 (E) 13 F K
L
M
10. In the diagram, line segments meet at 90° as shown. If the

short line segments are each 3 cm long, what is the area of
the shape?
(A) 30 (B) 36 (C) 40
(D) 45 (E) 54 3 cm
Grade 7

11. The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles
wide. The number of tiles that touch the walls of the room is
(A) 26 (B) 30 (C) 34 (D) 46 (E) 50
12. Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order.
To decide who goes first in a game, they play “countdown”. Henry starts by saying ‘34’, with Iggy
saying ‘33’. If they continue to count down in their circular order, who will eventually say ‘1’?
(A) Fred (B) Gail (C) Henry (D) Iggy (E) Joan
13. In the diagram, the percentage of small squares that are
shaded is
(A) 9 (B) 33 (C) 36
(D) 56.25 (E) 64
14. Which of the following numbers is an odd integer, contains the digit 5, is divisible by 3, and lies
between 12 2 and 132 ?
(A) 105 (B) 147 (C) 156 (D) 165 (E) 175
15. A box contains 36 pink, 18 blue, 9 green, 6 red, and 3 purple cubes that are identical in size. If a cube
is selected at random, what is the probability that it is green?
1 1 1 1 9
(A) (B) (C) (D) (E)
9 8 5 4 70
16. The graph shown at the right indicates the time taken by
Bina Daniel
five people to travel various distances. On average, which
Time (minutes)
50
person travelled the fastest? 40
(A) Alison (B) Bina (C) Curtis Curtis
30
(D) Daniel (E) Emily 20
Alison Emily
10
1 2 3 4 5
Distance (kilometres)
17. 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?
(A) 34 (B) 36 (C) 107 (D) 152 (E) 245
18. The results of a survey of the hair colour of 600 people are
shown in this circle graph. How many people have blonde black
brown
hair? 22%
32%
(A) 30 (B) 160 (C) 180 red
16%
(D) 200 (E) 420 blonde
Hair Colour
19. What is the area, in m 2 , of the shaded part of the rectangle?

(A) 14 (B) 28 (C) 33.6 4m
(D) 56 (E) 42
14 m
20. The first 9 positive odd integers are placed in the magic
square so that the sum of the numbers in each row, column A 1 B
and diagonal are equal. Find the value of A + E .
(A) 32 (B) 28 (C) 26
5 C 13
(D) 24 (E) 16 D E 3
Grade 7

21. A game is played on the board shown. In this game, a player P
can move three places in any direction (up, down, right or
left) and then can move two places in a direction perpendicular Q R
to the first move. If a player starts at S, which position on the T
board (P, Q, R, T, or W) cannot be reached through any S W
sequence of moves?
(A) P (B) Q (C) R (D) T (E) W
22. Forty-two cubes with 1 cm edges are glued together to form a solid rectangular block. If the perimeter
of the base of the block is 18 cm, then the height, in cm, is
7
(A) 1 (B) 2 (C) (D) 3 (E) 4
3
23. JKLM is a square. Points P and Q are outside the square P
such that triangles JMP and MLQ are both equilateral.
The size, in degrees, of angle PQM is
(A) 10 (B) 15 (C) 25 J
(D) 30 (E) 150 M
Q
K L
24. Five holes of increasing size are cut along the edge of one
face of a box as shown. The number of points scored when a
marble is rolled through that hole is the number above the
hole. There are three sizes of marbles: small, medium and 5
3 4
large. The small marbles fit through any of the holes, the 1 2
medium fit only through holes 3, 4 and 5 and the large fit
only through hole 5. You may choose up to 10 marbles of each size to roll and every rolled marble
goes through a hole. For a score of 23, what is the maximum number of marbles that could have been
rolled?
(A) 12 (B) 13 (C) 14 (D) 15 (E) 16
25. In a softball league, after each team has played every other team 4 times, the total accumulated points
are: Lions 22, Tigers 19, Mounties 14, and Royals 12. If each team received 3 points for a win, 1
point for a tie and no points for a loss, how many games ended in a tie?
(A) 3 (B) 4 (C) 5 (D) 7 (E) 10
Canadian
35 th
th Mathematics
Competition
Anniversary in Mathematics and Computing,
1963 – 1998 University of Waterloo, Waterloo, Ontario

The Great-West
Life Assurance
IBM Company
Canada Ltd.
Northern Telecom
(Nortel)
Manulife
Financial
Canadian Institute
of Actuaries
Equitable Life
of Canada
Sybase
Inc. (Waterloo)
Chartered Accountants Comptables agréés

Instructions
5. Scoring:
Each correct answer is worth 5 credits in Part A, 6 credits in Part B, and 8 credits in Part C.
7. When your supervisor instructs you to begin, you will have sixty minutes of working time.
Grade 7

1998 – 998
1. The value of is
1000
(A) 1 (B) 1000 (C) 0.1 (D) 10 (E) 0.001
2. The number 4567 is tripled. The ones digit (units digit) in the resulting number is
(A) 5 (B) 6 (C) 7 (D) 3 (E) 1
3. If S = 6 × 10 000 + 5 × 1000 + 4 × 10 + 3 × 1, what is S?

(A) 6543 (B) 65 043 (C) 65 431 (D) 65 403 (E) 60 541
4. Jean writes five tests and achieves the marks shown on the 100
graph. What is her average mark on these five tests? 90
(A) 74 (B) 76 (C) 70 80
Marks out of 100

(D) 64 (E) 79 70
60
50
40
30
20
10
0
Test Marks
5. If a machine produces 150 items in one minute, how many would it produce in 10 seconds?
(A) 10 (B) 15 (C) 20 (D) 25 (E) 30
6. In the multiplication question, the sum of the digits in the 879

four boxes is 492
(A) 13 (B) 12 (C) 27 758
(D) 9 (E) 22 7 110
35 600
43 468
7. A rectangular field is 80 m long and 60 m wide. If fence posts are placed at the corners and are 10 m
apart along the 4 sides of the field, how many posts are needed to completely fence the field?
(A) 24 (B) 26 (C) 28 (D) 30 (E) 32
8. Tuesday’s high temperature was 4° C warmer than that of Monday’s. Wednesday’s high temperature
was 6°C cooler than that of Monday’s. If Tuesday’s high temperature was 22° C, what was
Wednesday’s high temperature?
(A) 20°C (B) 24° C (C) 12° C (D) 32°C (E) 16°C
9. Two numbers have a sum of 32. If one of the numbers is – 36 , what is the other number?
(A) 68 (B) – 4 (C) 4 (D) 72 (E) – 68
10. At the waterpark, Bonnie and Wendy decided to race each other down a waterslide. Wendy won by
0.25 seconds. If Bonnie’s time was exactly 7.80 seconds, how long did it take for Wendy to go down
the slide?
(A) 7.80 seconds (B) 8.05 seconds (C) 7.55 seconds (D) 7.15 seconds (E) 7.50 seconds
Grade 7
11. rectangle RR from

Kalyn cut rectangle fromaasheet
sheetofofpaper.
paper A
and then cut
smaller figure is
rectangle S from R. from
then cut All the
thecuts
largewere made
rectangle
parallel to thefigure
R to produce sides S.
of the original rectangle.
In comparing R to S In comparing R to S
8 cm 4 cm
6 cm R 6 cm S 5 cm
8 cm 8 cm
(A) the area and perimeter both decrease
(B) the area decreases and the perimeter increases
(C) the area and perimeter both increase
(D) the area increases and the perimeter decreases
(E) the area decreases and the perimeter stays the same
12. Steve plants ten trees every three minutes. If he continues planting at the same rate, how long will it
take him to plant 2500 trees?
(A) 1 1 h (B) 3 h (C) 5 h (D) 10 h (E) 12 1 h
4 2
13. The pattern of figures is repeated in the sequence

, , , , , , , , , , ... .
The 214th figure in the sequence is
(A) (B) (C) (D) (E)
14. A cube has a volume of 125 cm 3 . What is the area of one face of the cube?
2
(A) 20 cm 2 (B) 25 cm 2 (C) 41 cm 2 (D) 5 cm 2 (E) 75 cm 2
3
15. The diagram shows a magic square in which the sums of

the numbers in any row, column or diagonal are equal. What 8
is the value of n? 9 5
(A) 3 (B) 6 (C) 7
(D) 10 (E) 11 4 n
16. Each of the digits 3, 5, 6, 7, and 8 is placed one to a box in

the diagram. If the two digit number is subtracted from the
three digit number, what is the smallest difference?
(A) 269 (B) 278 (C) 484
(D) 271 (E) 261
17. Claire takes a square piece of paper and folds it in half four times without unfolding, making an
isosceles right triangle each time. After unfolding the paper to form a square again, the creases on the
paper would look like
(A) (B) (C)
(D) (E)
Grade 7
18. The letters of the word ‘GAUSS’ and the digits in the number ‘1998’ are each cycled separately and
then numbered as shown.
1. AUSSG 9981
2. USSGA 9819
3. SSGAU 8199
etc.
If the pattern continues in this way, what number will appear in front of GAUSS 1998?
(A) 4 (B) 5 (C) 9 (D) 16 (E) 20
19. Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point.
If Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?
(A) 7 (B) 8 (C) 4 (D) 5 (E) 11
20. Each of the 12 edges of a cube is coloured either red or green. Every face of the cube has at least one
red edge. What is the smallest number of red edges?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
21. 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.)
(A) 9 (B) 45 (C) 17 (D) 66 (E) 55
22. Each time a bar of soap is used, its volume decreases by 10%. What is the minimum number of times
a new bar would have to be used so that less than one-half its volume remains?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
23. A cube measures 10 cm × 10 cm × 10 cm . Three cuts are

made parallel to the faces of the cube as shown creating
eight separate solids which are then separated. What is the
increase in the total surface area?
(A) 300 cm 2 (B) 800 cm 2 (C) 1200 cm 2
(D) 600 cm 2 (E) 0 cm 2
24. On a large piece of paper, Dana creates a “rectangular spiral”

by drawing line segments of lengths, in cm, of 3
1, 1, 2, 2, 3, 3, 4, 4, ... as shown. Dana’s pen runs out of ink
4 1
after the total of all the lengths he has drawn is 3000 cm. 2
What is the length of the longest line segment that Dana 1 3
draws? 2
(A) 38 (B) 39 (C) 54
(D) 55 (E) 30 4
25. Two natural numbers, p and q, do not end in zero. The product of any pair, p and q, is a power of 10
(that is, 10, 100, 1000, 10 000 , ...). If p > q , the last digit of p – q cannot be
(A) 1 (B) 3 (C) 5 (D) 7 (E) 9

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The CENTRE for EDUCATION

in MATHEMATICS and COMPUTING

Time: 1 hour ©2013 University of Waterloo

Part A: Each correct answer is worth 5.

7. How many positive two-digit whole numbers are divisible by 7?

8. If 9210 − 9124 = 210 − , the value represented by the is

Part B: Each correct answer is worth 6.

14. In the diagram shown, the number of rectangles of all

15. The diagram shows Lori’s house located at (6, 3). If

16. The graph shows points scored by Riley-Ann in her first

18. In the figure shown, the outer square has an area of

Part C: Each correct answer is worth 8.

24. In the diagram shown,

• Q and P are the midpoints of ST and U V ,

What is the ratio of the shaded area to the unshaded

(A) 2 : 3 (B) 3 : 5 (C) 1 : 1

25. On a coordinate grid, Paul draws a line segment of

Time: 1 hour ©2012 University of Waterloo

Part A: Each correct answer is worth 5.

3. Thirty-six hundredths is equal to

5. If P Q is a straight line segment, then the value of x is

8. Ahmed is going to the store. One quarter of the way to

Part B: Each correct answer is worth 6.

14. If x = 4 and 3x + 2y = 30, what is the value of y?

18. JKLM is a square and P QRS is a rectangle. If JK is

20. Toothpicks are used to make rectangular grids, as shown.

Part C: Each correct answer is worth 8.

22. An arithmetic sequence is a sequence in which each term

Time: 1 hour ©2011 Centre for Education in Mathematics and Computing

Part A: Each correct answer is worth 5.

1. The value of 202 − 101 + 9 is equal to

2. Which of the following numbers is equal to 33 million?

5. Two straight lines intersect as shown.

7. Which of the following statements is true?

9. Ben recorded the number of visits to his website from

Part B: Each correct answer is worth 6.

13. On the spinner shown, P Q passes through centre O. If P

18. All four scales shown are balanced.

Part C: Each correct answer is worth 8.

24. P QRS is a parallelogram with area 40. If T and V are

Time: 1 hour ©2010 Centre for Education in Mathematics and Computing

Part A: Each correct answer is worth 5.

3. Students were surveyed about their favourite season. The

9. If the point (3, 4) is reflected in the x-axis, what are the y

Part B: Each correct answer is worth 6.

11. In the diagram, the value of x is

20. A triangular prism is placed on a rectangular prism, as

(A) 76 (B) 78 (C) 72 5 cm 2 cm

Part C: Each correct answer is worth 8.

Gauss Contest (Grade 7)

Time: 1 hour ©2009 Centre for Education in Mathematics and Computing

Part A: Each correct answer is worth 5.

4. In the diagram, the point with coordinates (−2, −3) is

6. If 10.0003 × = 10000.3, the number that should replace the is

7. In the diagram, the value of x is

8. How many 1 cm × 1 cm × 1 cm blocks are needed to

Part B: Each correct answer is worth 6. 2

16. In a magic square, all rows, columns, and diagonals have

Part C: Each correct answer is worth 8.