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IKMC 2014 - Grades 7-8 - Self-study

Question 1

Each year, the Kangaroo competition is on the third Thursday of March. What is its latest possible date in any year?
  1. 14 March
  2. 15 March
  3. 20 March
  4. 21 March
  5. 22 March

Question 2

How many quadrilaterals of any size are shown in the figure?

Question illustration
  1. 0
  2. 1
  3. 2
  4. 4
  5. 5

Question 3

What is $2014\cdot2014:2014-2014$?
  1. 0
  2. 1
  3. 2013
  4. 2014
  5. 4028

Question 4

Rectangle ABCD has area 10. M and N are the midpoints of AD and BC. What is the area of quadrilateral MBND?

Question illustration
  1. 0.5
  2. 5
  3. 2.5
  4. 7.5
  5. 10

Question 5

Two numbers have product 36 and sum 37. What is their difference?
  1. 1
  2. 4
  3. 10
  4. 26
  5. 35

Question 6

Wanda has several square sheets of area 4. She cuts them into squares and right-angled triangles as in the first diagram. She uses some pieces to make the bird in the second diagram. What is its area?

Question illustration
  1. 3
  2. 4
  3. $9/2$
  4. 5
  5. 6

Question 7

A bucket was half full. A cleaner added 2 litres, making it three-quarters full. What is the capacity of the bucket?
  1. 10 L
  2. 8 L
  3. 6 L
  4. 4 L
  5. 2 L

Question 8

Georg built the shown shape using seven unit cubes. How many more cubes must he add to make a cube with edges of length 3?

Question illustration
  1. 12
  2. 14
  3. 16
  4. 18
  5. 20

Question 9

Which calculation gives the largest result?
  1. $44\times777$
  2. $55\times666$
  3. $77\times444$
  4. $88\times333$
  5. $99\times222$

Question 10

The necklace contains grey and white beads. Arno removes one bead at a time, always from one of the ends. He stops as soon as he has taken his fifth grey bead. What is the greatest number of white beads he can take?

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

Question 11

Jack has a piano lesson twice a week and Hannah has one every other week. In a given term Jack has 15 more lessons than Hannah. How many weeks long is their term?
  1. 30
  2. 25
  3. 20
  4. 15
  5. 10

Question 12

Each circle in the diagram has area $1\text{ cm}^2$. The area common to two overlapping circles is $\frac18\text{ cm}^2$. What is the area covered by the five circles?

Question illustration
  1. $4\text{ cm}^2$
  2. $\frac92\text{ cm}^2$
  3. $\frac{35}8\text{ cm}^2$
  4. $\frac{39}8\text{ cm}^2$
  5. $\frac{19}4\text{ cm}^2$

Question 13

A grandmother, her daughter and her granddaughter notice that their ages sum to 100 years. Each age is a power of 2. How old is the granddaughter?
  1. 1
  2. 2
  3. 4
  4. 8
  5. 16

Question 14

Five equal rectangles are placed inside a square of side 24 cm, as shown. What is the area of one rectangle?

Question illustration
  1. $12\text{ cm}^2$
  2. $16\text{ cm}^2$
  3. $18\text{ cm}^2$
  4. $24\text{ cm}^2$
  5. $32\text{ cm}^2$

Question 15

The heart and arrow start in the shown positions. In each routine, the arrow moves three places clockwise and the heart moves four places anticlockwise, then both stop. They repeat this together. After how many routines will they first land in the same triangular region?

Question illustration
  1. 7
  2. 8
  3. 9
  4. 10
  5. It will never happen

Question 16

In triangle ABC, BH is a perpendicular height and AD bisects angle A. The obtuse angle between BH and AD is four times angle DAB, as shown. What is angle CAB?

Question illustration
  1. $30^\circ$
  2. $45^\circ$
  3. $60^\circ$
  4. $75^\circ$
  5. $90^\circ$

Question 17

Six boys share a flat with two bathrooms, using them from 7:00 each morning. Each bathroom holds at most one person at a time. Their uninterrupted bathroom times are 8,10,12,17,21,22 minutes. What is the earliest finishing time?
  1. 7:45
  2. 7:46
  3. 7:47
  4. 7:48
  5. 7:50

Question 18

A rectangle has sides 6 cm and 11 cm. Choose one long side and draw the bisectors of the angles at its two ends. They divide the other long side into three parts. What are their lengths?
  1. 1 cm, 9 cm, 1 cm
  2. 2 cm, 7 cm, 2 cm
  3. 3 cm, 5 cm, 3 cm
  4. 4 cm, 3 cm, 4 cm
  5. 5 cm, 1 cm, 5 cm

Question 19

Captain Sparrow and his pirate crew dig up gold coins and divide them equally among everyone. With four fewer pirates, each person would get 10 more coins. With 50 fewer coins, each person would get 5 fewer coins. How many coins did they dig up?
  1. 80
  2. 100
  3. 120
  4. 150
  5. 250

Question 20

The average of two positive numbers is 30% less than one of them. By what percentage is the average greater than the other number?
  1. 75%
  2. 70%
  3. 30%
  4. 25%
  5. 20%