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IKMC 2016 - Grades 7-8 - Self-study

Question 1

How many whole numbers are there between 20.16 and 3.17?
  1. 15
  2. 16
  3. 17
  4. 18
  5. 19

Question 2

Which traffic sign has the greatest number of axes of symmetry?
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Question 3

What is the sum of the two marked angles?

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  1. $150^\circ$
  2. $180^\circ$
  3. $270^\circ$
  4. $320^\circ$
  5. $360^\circ$

Question 4

Jenny should have added 26 to a number, but instead subtracted 26 and obtained−14. What should she have obtained?
  1. 28
  2. 32
  3. 36
  4. 38
  5. 42

Question 5

Joanna turns the card over about its lower edge, then about its right-hand edge, as shown. What does she see?

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Question 6

Kanga combines 555 groups of 9 stones, then splits the pile into groups of 5 stones. How many groups does she get?
  1. 999
  2. 900
  3. 555
  4. 111
  5. 45

Question 7

The school newspaper says 60% of the teachers travel to school by bike; these are 45 teachers. Only 12% of all teachers use a car. How many use a car?
  1. 4 teachers
  2. 6 teachers
  3. 9 teachers
  4. 10 teachers
  5. 12 teachers

Question 8

ABCD is a rectangle; M, N are midpoints of AB, CD respectively. The circles touch the rectangle sides and each other. If AB=10 cm, what is the area of the grey region?

Question illustration
  1. $\frac{25\pi}4\text{ cm}^2$
  2. $20\text{ cm}^2$
  3. $50-\frac{25\pi}4\text{ cm}^2$
  4. $25\text{ cm}^2$
  5. $5\text{ cm}^2$

Question 9

Two ropes are 1 m and 2 m long. Alex cuts both into parts all of the same length. Which cannot be the total number of parts?
  1. 6
  2. 8
  3. 9
  4. 12
  5. 15

Question 10

Towns P, Q, R, S are connected by the shown roads. A race starts at S, ends at Q and uses every road exactly once. How many routes are possible?

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  1. 10
  2. 8
  3. 6
  4. 4
  5. 2

Question 11

Four identical rectangles are arranged inside a square as shown. Each rectangle has perimeter 16 cm. What is the perimeter of the square?

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  1. 16 cm
  2. 20 cm
  3. 24 cm
  4. 28 cm
  5. 32 cm

Question 12

Petra has 49 blue beads and 1 red bead. How many must she remove so that 90% of the remaining beads are blue?
  1. 4
  2. 10
  3. 29
  4. 39
  5. 40

Question 13

Which fraction is closest to 1/2?
  1. $\frac{25}{79}$
  2. $\frac{27}{59}$
  3. $\frac{29}{57}$
  4. $\frac{52}{79}$
  5. $\frac{57}{92}$

Question 14

Ivor records a knockout tournament’s quarter-finals, semi-finals and final, in no particular order: Bart beat Antony, Carl beat Damien, Glen beat Henry, Glen beat Carl, Carl beat Bart, Ed beat Fred, Glen beat Ed. Who played the final?
  1. Glen and Henry
  2. Glen and Carl
  3. Carl and Bart
  4. Glen and Ed
  5. Carl and Damien

Question 15

Three equilateral triangles are cut from the corners of a larger equilateral triangle of perimeter 60 cm. The remaining figure F has perimeter 40 cm. What is the sum of the perimeters of the three removed triangles?

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  1. 80 cm
  2. 75 cm
  3. 66 cm
  4. 54 cm
  5. 60 cm

Question 16

Tim, Tom, Jim are triplets, born on the same day. Their twin brothers John and James are 3 years younger. Which number could be the sum of the ages of all five?
  1. 36
  2. 53
  3. 76
  4. 89
  5. 92

Question 17

A 3 cm-wide rectangular paper strip is green on one side and yellow on the other. Maria folds it as shown; the green trapeziums are identical. The folded strip spans 27 cm, and the first-fold detail marks a 6 cm vertical part. What is the original strip length?

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  1. 36 cm
  2. 48 cm
  3. 54 cm
  4. 57 cm
  5. 81 cm

Question 18

Kangaroos Jum and Per start jumping simultaneously from the same point in the same direction, one jump per second. Every Jum jump is 6 m. Per’s jumps are 1 m,2 m,3 m, and so on. After how many jumps does Per catch Jum?
  1. 10
  2. 11
  3. 12
  4. 13
  5. 14

Question 19

Seven standard dice are glued into the shown solid. Faces glued together have equal dot counts. How many dots lie on the surface of the solid?

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  1. 24
  2. 90
  3. 95
  4. 105
  5. 126

Question 20

Twenty students sit in pairs. Exactly one third of the boys sit with a girl, and exactly one half of the girls sit with a boy. How many boys are there?
  1. 9
  2. 12
  3. 15
  4. 16
  5. 18