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IKMC 2020 - Grades 7-8 - Self-study

Question 1

How many of the numbers 2,20,202,2020 are prime?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 2

In which regular polygon is the marked angle the largest?
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Question 3

Miguel solves six Olympiad problems daily and Lázaro four. How many days does Lázaro need to solve as many problems as Miguel solves in four days?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 4

Which fraction has the largest value?
  1. $\frac{8+5}{3}$
  2. $\frac8{3+5}$
  3. $\frac{3+5}8$
  4. $\frac{8+3}5$
  5. $\frac3{8+5}$

Question 5

A large square is divided into smaller squares, with a diagonal in one of them. What fraction of the large square is shaded?

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  1. 4/5
  2. 3/8
  3. 4/9
  4. 1/3
  5. 1/2

Question 6

Four soccer teams each play every other team once. A win scores 3 points, loss 0, draw 1 for each team. After all matches, which total is impossible for a team?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 7

The shape consists of 36 identical small triangles. What is the smallest number of these triangles that can be added to turn it into a hexagon?

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  1. 10
  2. 12
  3. 15
  4. 18
  5. 24

Question 8

Kanga multiplies three different numbers chosen from −5,−3,−1,2,4,6. What is the smallest product?
  1. −200
  2. −120
  3. −90
  4. −48
  5. −15

Question 9

John takes 3 hours going to school by bus and walking back. By bus both ways he takes 1 hour. How long does walking both ways take?
  1. 3.5 hours
  2. 4 hours
  3. 4.5 hours
  4. 5 hours
  5. 5.5 hours

Question 10

Numbers in a 3 × 3 square are hidden by ink. Row sums and two column sums are shown. What is the third column sum?

Question illustration
  1. 41
  2. 43
  3. 44
  4. 45
  5. 47

Question 11

The shortest path from Atown to Cetown runs through Betown. The two signposts stand along this path. What distance was written on the broken sign?

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  1. 1 km
  2. 3 km
  3. 4 km
  4. 5 km
  5. 9 km

Question 12

Anna aims to walk 5 km per day on average in March. At bedtime on 16 March she has walked 95 km. What average daily distance must she walk on the remaining days?
  1. 5.4 km
  2. 5 km
  3. 4 km
  4. 3.6 km
  5. 3.1 km

Question 13

Which option shows the object viewed from above?

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Question 14

Every pupil either swims or dances or both. Three fifths swim and three fifths dance; five do both. How many pupils are there?
  1. 15
  2. 20
  3. 25
  4. 30
  5. 35

Question 15

Sacha’s garden has the shown shape. All sides are parallel or perpendicular. Some dimensions are marked. What is its perimeter?

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  1. 22
  2. 23
  3. 24
  4. 25
  5. 26

Question 16

Andrew has 27 identical cubes, each with two adjacent faces red. He uses all to build one large cube. At most how many faces of the large cube can be completely red?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 17

A square of area 49 cm² consists of four identical rectangles and a small square. Diagonal AB of a rectangle is 5 cm. What is the small square’s area?

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  1. 1 cm²
  2. 4 cm²
  3. 9 cm²
  4. 16 cm²
  5. 25 cm²

Question 18

Werner earns 20% of his boss’s salary. By what percentage must Werner’s salary increase to equal his boss’s?
  1. 80%
  2. 120%
  3. 180%
  4. 400%
  5. 520%

Question 19

Irene makes a city of identical cubes. One diagram is a top view, the other a side view from an unknown side. What is the greatest possible number of cubes?

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  1. 25
  2. 24
  3. 23
  4. 22
  5. 21

Question 20

Aisha folds the five-cell paper strip numbered 1,2,3,4,5 so all cells overlap in five layers. Which top-to-bottom order is impossible?

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  1. 3,5,4,2,1
  2. 3,4,5,1,2
  3. 3,2,1,4,5
  4. 3,1,2,4,5
  5. 3,4,2,1,5