Intermediate Math Olympics
Practice Material
Team #: ______
Student #: ______
Student #: ______ / Pairs Event
Page 1 of 8
Work in Mixed Grade Pairs /

Calculators are allowed

MULTIPLE CHOICE (10 questions x 1 mark each = 10 marks)

Place the letter of the best answer in the “Final Answer” Column below.

Final Answer
  1. The value of 25 + 33 is
A) 15B) 19C) 43D) 59E)91
  1. The numbers 1 , , , 1.25from least to greatest are
A) , 1 , 1.25, B) , , 1 , 1.25
C) 1.25, 1 , , D) 1 , 1.25, ,
E) 1.25,1 , ,
  1. Find the most probable total when two numbered cubes (dice) are rolled.
(sides are 1,2,3,4,5,6)
A) 5B) 6C) 7D) 8E) 9
  1. How many axes of symmetry does a regular hexagon have?
A) 10B) 8C) 6D) 4E) 2
  1. A rectangular field has a perimeter of 400 m. Its length is 125 m. Its width is
A) 250 mB) 137.5 mC) 75 mD) 150 mE) 275 m
  1. How much warmer is a temperature of 42°C than a temperature of -6°C ?
A) 7°CB) 48°CC) 34°CD) 36°CE) 47°C
  1. Expressed as a percent, 3 : 8 is equivalent to
A) 3.75 %B) 30 %C) 33%D) 37.5 %E) 266 %
  1. A cube has one corner cut and painted as shown in the diagram. Which of the following shows the top of the cube viewed from directly above?

A)B)C)D)E)

  1. The price of an item is reduced by 20%. Find what percent the discounted price must be increased to bring it back to the original price.
A) 20% B)40%C) 80%D) 100%E) 125%
  1. On a certain store shelf, carton A is older than carton D, carton E is older than carton C, carton B is older than carton A, and Carton C is older than carton B. Find the newest carton of the five.
A) AB) BC) CD) DE) E

SHORT ANSWER (10questions x 2 marks each = 20 marks)

Write the answers to questions 11- 20 in the space provided under each question. Please show your work clearly and explain your reasoning.

11.What is the difference between the sum of the first 20 positive even integers and the sum of the first 20 positive odd integers? That is, what is the value of (2+ 4 + 6 + … +40) – (1 + 3 + 5 + … + 39)?

12.There are two different ways to put the digits 1, 2, 3, 4, and 5 into the blanks between the parentheses, one digit per blank, so that

( ) x ( ) = ( ) + ( )

( )

is a true statement. What are these two ways?

NOTE: Changes in order only are not considered different.

13.Suppose the numbers 1,2,3,… are written in a pyramid as shown. In what row does the number 100 first appear?

1

2 3

4 5 6

7 8 9 10

………….

14.The sum of the squares of the lengths of all the sides of a rectangle is 100m2. What is the length of a diagonal of the rectangle?

15. Two 5m x 5m squares overlap to form a 5m x 7m rectangle. What is the area of the region in which the two squares overlap?

16.Sam opened his piggy-bank to find only some dimes and quarters in the ratio of 2 dimes to 5 quarters. The total value of the money is between $3 and $10. How many possibilities are there for the total amount of money in his bank? What are they?

17.A rectangle is divided into two squares by a line segment joining two of its opposite sides. If the area of one square is 36 m2, what is the perimeter of the rectangle?

18.List the three pairs of positive integers (a,b) which satisfy

24 +ab = 25

19.How can you cut the board into two equal pieces to fill the hole completely?

20. Peter’s dad tells him to give 15 of his 30 candy bars to his brother.

Peter has 15 Mars and 15 Caramilk bars.

He must set the pieces around a large circle, count them, and hand his brother every thirteenth piece until his brother has 15 pieces.

Peter loves Mars bars.

How can he arrange the chocolate bars so that he gets all the Mars bars?

Record your answer using M and C.