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IKMC 2005 - Grades 7-8 - Self-study

Question 1

Eight kangaroos occupy the table shown. Each may jump into any free cell. What is the least number that must move so that every row and every column contains exactly two kangaroos?

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  1. 1
  2. 2
  3. 3
  4. 4

Question 2

How many hours are there in half of a third of a quarter of a day?
  1. $\frac13$
  2. $\frac12$
  3. 1
  4. 2

Question 3

A cube has edge 12 cm. An ant moves on its surface from A to B along the path shown. Find the path length.

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  1. 48 cm
  2. 54 cm
  3. 60 cm
  4. It is impossible to determine

Question 4

At National School, 50% of students have bicycles. Of those students, 30% have black bicycles. What percentage of all students have black bicycles?
  1. 15%
  2. 20%
  3. 25%
  4. 40%

Question 5

In triangle ABC, angle A is three times angle B and half angle C. What is angle A?
  1. 30°
  2. 36°
  3. 54°
  4. 60°

Question 6

The diagram shows a room whose adjacent walls are perpendicular. Letters a and b are lengths. What is its area?

Question illustration
  1. $2ab+a(b-a)$
  2. $3a(a+b)-a^2$
  3. $3a(b-a)+a^2$
  4. $3ab$

Question 7

Nida cuts a sheet into 10 pieces, then cuts one piece into 10 pieces. She repeats this same operation three more times. How many pieces are there after the last cut?
  1. 36
  2. 40
  3. 46
  4. 50

Question 8

Crows sit one per pole, leaving one crow without a pole. Later the same crows sit two per pole, leaving one pole empty. How many poles are there?
  1. 2
  2. 3
  3. 4
  4. 5

Question 9

A cube of side 5 consists of black and white unit cubes. Any two sharing a face have different colours, and all corner cubes are black. How many white cubes are used?

Question illustration
  1. 62
  2. 63
  3. 64
  4. 65

Question 10

Concrete is made from 4 shovels of stone, 2 of sand and 1 of cement. How many shovels of stone are needed for 350 shovels of concrete?
  1. 200
  2. 150
  3. 100
  4. 50

Question 11

Edward has 2004 marbles: half blue, a quarter red and a sixth green. How many have some other colour?
  1. 167
  2. 334
  3. 501
  4. 1002

Question 12

For a trip, contributions of Rs.14 each would leave a group Rs.4 short; Rs.16 each would give Rs.6 too much. How much should each person contribute to pay the exact cost?
  1. Rs.14.40
  2. Rs.14.60
  3. Rs.14.80
  4. Rs.15.20

Question 13

Five circles have equal radii and touch as shown. The square joins the centres of the four outer circles. Find the ratio of shaded to unshaded area in all five circles.

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  1. 1 : 1
  2. 2 : 5
  3. 2 : 3
  4. 5 : 4

Question 14

The diagram gives some angles of quadrilateral ABCD. If BC=AD, what is angle ADC?

Question illustration
  1. 75°
  2. 50°
  3. 55°
  4. 65°

Question 15

The watchman works 4 days a week and has a rest on the fifth day. He had been resting on Sunday and began working on Monday. After how many days will his rest fall on Sunday?
  1. 31
  2. 12
  3. 34
  4. 7

Question 16

Which cube can be folded from the net shown?

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Question 17

The figure shows an equilateral triangle and a regular pentagon. What is the marked angle x?

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  1. 108°
  2. 120°
  3. 132°
  4. 136°

Question 18

This is a multiplication table. Which two letters represent the same number?

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  1. L and M
  2. O and N
  3. R and P
  4. M and S

Question 19

Mike chose a three-digit number and a two-digit number. Their difference is 989. Find their sum.
  1. 1000
  2. 1001
  3. 1009
  4. 1010

Question 20

A lies on a circle with centre O. What fraction of the circle consists of points closer to O than to A?
  1. $\frac34$
  2. $\frac23$
  3. $\frac12$
  4. $\frac56$