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IKMC 2010 - Grades 9-10 - Self-study

Question 1

What is 20102010 divided by 2010?
  1. 11
  2. 101
  3. 1001
  4. 10001
  5. Not an integer

Question 2

Ivan scored 85% of all test points; Tibor scored 90%, only one point more. What was the maximum score?
  1. 5
  2. 17
  3. 18
  4. 20
  5. 25

Question 3

The two rows have equal sums. What is *?

Question illustration
  1. 1010
  2. 1020
  3. 1910
  4. 1990
  5. 2020

Question 4

Four identical cubes form the solid shown. Each cube has surface area 24 cm². Find the solid’s surface area.

Question illustration
  1. 80 cm²
  2. 64 cm²
  3. 40 cm²
  4. 32 cm²
  5. 24 cm²

Question 5

Each birthday Roza receives as many flowers as her age. She dries and keeps them all, and now has 120 flowers. How old is she?
  1. 10
  2. 12
  3. 14
  4. 15
  5. 20

Question 6

A strip of paper was folded in half three times and fully unfolded, leaving seven upward or downward creases. Which side view cannot occur?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 7

Six points are marked on a square lattice. Which figure cannot have all vertices among them?

Question illustration
  1. Square
  2. Parallelogram but not rhombus
  3. Trapezoid
  4. Obtuse triangle
  5. All A–D can

Question 8

The picture shows 1+3+5+7=4 × 4. Find 1+3+5+7+9+11+13+15+17.

Question illustration
  1. 14 × 14
  2. 9 × 9
  3. 4 × 4 × 4
  4. 16 × 16
  5. 4 × 9

Question 9

Brigitte visits Verona and crosses each of five famous old bridges over the Adige at least once, no other bridges, starting and ending at the train station. Which number n of river crossings is possible?
  1. 3
  2. 4
  3. 5
  4. 6
  5. 7

Question 10

ABCE is a square; BCF and CDE are equilateral triangles. AB=1. Find FD.

Question illustration
  1. $\sqrt2$
  2. $\sqrt3/2$
  3. $\sqrt3$
  4. $\sqrt5-1$
  5. $\sqrt6-1$

Question 11

My teacher says his age multiplied by his father’s age is 2010. In what year was the teacher born?
  1. 1943
  2. 1953
  3. 1980
  4. 1995
  5. 2005

Question 12

Find the angle marked with a question mark.

Question illustration
  1. $10^\circ$
  2. $20^\circ$
  3. $30^\circ$
  4. $40^\circ$
  5. $50^\circ$

Question 13

How many integers have digit sum 2010 and digit product 2?
  1. 2010
  2. 2009
  3. 2008
  4. 1005
  5. 1004

Question 14

Follow arrows from circle A to circle B and add all numbers passed. How many different sums are possible?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4
  5. 6

Question 15

Three Tuesdays in one month fell on even dates. What weekday was the 21st?
  1. Wednesday
  2. Thursday
  3. Friday
  4. Saturday
  5. Sunday

Question 16

A circle of radius 4 cm is split into four congruent parts by radius 2 cm arcs as shown. Find one part’s perimeter.

Question illustration
  1. $2\pi$
  2. $4\pi$
  3. $6\pi$
  4. $8\pi$
  5. $12\pi$

Question 17

The graph gives distances and times for five students’ runs. Who is fastest?

Question illustration
  1. Alicia
  2. Bea
  3. Carlos
  4. Dani
  5. Ernesto

Question 18

The triangle is folded along the dotted line. Its original area is 1.5 times the resulting figure’s area. The three shaded regions total 1. Find the original area.

Question illustration
  1. 2
  2. 3
  3. 4
  4. 5
  5. Impossible to determine

Question 19

Ten tightly nested shopping trolleys are 2.9 m long, twenty are 4.9 m long. How long is one trolley?

Question illustration
  1. 0.8 m
  2. 1 m
  3. 1.1 m
  4. 1.2
  5. 1.4

Question 20

The large equilateral triangle consists of 36 small equilateral triangles, each area 1 cm². Find area ABC.

Question illustration
  1. 11 cm²
  2. 12 cm²
  3. 13 cm²
  4. 14 cm²
  5. 15 cm²