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IKMC 2010 - Grades 7-8 - Self-study

Question 1

How much is 12 + 23 + 34 + 45 + 56 + 67 + 78 + 89?
  1. 396
  2. 404
  3. 405
  4. other answer

Question 2

How many axes of symmetry does the figure have?

Question illustration
  1. 1
  2. 2
  3. 4
  4. infinitely many

Question 3

Toy kangaroos are packed for shipment. Each of them is packed in a box which is a cube. Exactly eight boxes are packed tightly in a bigger cubic cardboard box. How many kangaroo boxes are on the bottom floor of this big cube?
  1. 1
  2. 2
  3. 3
  4. 4

Question 4

The perimeter of the figure is equal to

Question illustration
  1. $3a+4b$
  2. $3a+8b$
  3. $6a+6b$
  4. $6a+8b$

Question 5

Ehsan draws the six vertices of a regular hexagon and then connects some of the 6 points with lines to obtain a geometric figure. Then this figure is surely not a

Question illustration
  1. trapezium
  2. right angled triangle
  3. square
  4. obtuse angled triangle

Question 6

If we type seven consecutive integer numbers and the sum of the smallest three numbers is 33, which is the sum of the largest three numbers?
  1. 39
  2. 42
  3. 48
  4. 45

Question 7

After stocking up firewood, the worker summed up that from the certain number of logs he made 72 logs besides 53 cuts were made. He saws only one log at a time. How many logs were at the beginning?
  1. 18
  2. 19
  3. 20
  4. 21

Question 8

There are seven bars in the box. They are 3 cm × 1 cm in size. The box is of size 5 cm × 5 cm. Is it possible to slide the bars in the box so there will be room for one more bar? At least how many bars must be moved in that case?

Question illustration
  1. 2
  2. 3
  3. 4
  4. It is impossible

Question 9

A square is divided into 4 smaller equal-sized squares. All the smaller squares are coloured either green or blue. How many different ways are there to colour the given square? (Two colourings are considered the same if one can be rotated to give the other.)

Question illustration
  1. 5
  2. 6
  3. 7
  4. 8

Question 10

The sum of the first hundred positive odd integers subtracted from sum of the first hundred positive even integers is
  1. 0
  2. 50
  3. 100
  4. 10100

Question 11

Grandma baked a cake for her grandchildren who will visit in the afternoon. Unfortunately she forgot whether only 3, 5 or all 6 of her grandchildren will come over. She wants to ensure that every child gets the same amount of cake. Then, to be prepared for all three possibilities she better cut the cake into
  1. 12 pieces
  2. 15 pieces
  3. 18 pieces
  4. 30 pieces

Question 12

Which of the following is the smallest two-digit number that is not the sum of three different one-digit numbers?
  1. 10
  2. 15
  3. 23
  4. 25

Question 13

Fatima needs 18 min to make a long chain by connecting three short chains with extra chain links. How long does it take her to make a really long chain by connecting six short chains in the same way?
  1. 27 min
  2. 30 min
  3. 36 min
  4. 45 min

Question 14

In quadrilateral ABCD we have $AD=BC$, $\angle DAC=50^\circ$, $\angle DCA=65^\circ$ (see the figure). Find the value of $\angle ABC$, given $\angle ACB=70^\circ$.

Question illustration
  1. 55°
  2. 60°
  3. 65°
  4. impossible to determine

Question 15

Saima has wound some rope around a piece of wood. She rotates the wood as shown with the arrow. What does she see after the rotation?

Question illustration
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration

Question 16

There are 50 bricks of white, blue and red colour in the box. The number of white bricks is eleven times the number of blue ones. There are fewer red ones than white ones, but more red ones than blue ones. How many fewer red bricks are there than white ones?
  1. 2
  2. 11
  3. 19
  4. 22

Question 17

On the picture ABCD is a rectangle, PQRS is a square. The shaded area is half of the area of rectangle ABCD. What is the length of PX?

Question illustration
  1. 1
  2. 1.5
  3. 2
  4. 4

Question 18

What is the smallest number of straight lines needed to divide the plane into exactly 5 regions?
  1. 3
  2. 4
  3. 5
  4. another answer

Question 19

If $a-1=b+2=c-3=d+4=e-5$, then which of the numbers a,b,c,d,e is the largest?
  1. a
  2. c
  3. d
  4. e

Question 20

The logo shown is made entirely from semicircular arcs of radius 2 cm, 4 cm or 8 cm. What fraction of the logo is shaded?

Question illustration
  1. $\frac13$
  2. $\frac14$
  3. $\frac15$
  4. $\frac34$