Skip to content / Đến nội dung
ThichHocToan.com

IKMC 2017 - Grades 9-10 - Self-study

Question 1

Each number is the sum of the two numbers immediately below it. What goes in the ? cell?

Question illustration
  1. 15
  2. 16
  3. 17
  4. 18
  5. 19

Question 2

Peter writes KANGAROO on transparent glass as shown. He turns the glass over around its right side, then rotates it one half-turn. What does he see?

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

Question 3

Angela layers grey and white asteroids as shown. Their areas are 1, 4, 9 and 16 cm². What is the total visible grey area?

Question illustration
  1. 9 cm²
  2. 10 cm²
  3. 11 cm²
  4. 12 cm²
  5. 13 cm²

Question 4

Maria has 24 euros; each of her three siblings has 12 euros. How much must Maria give EACH sibling so all four have equal amounts?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 6

Question 5

Which picture shows the path of the wheel’s centre as the wheel rolls along the depicted zigzag surface?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 6

Girls dance in a circle. Antonia is fifth to Bianca’s left and eighth to her right. How many girls are there?
  1. 11
  2. 12
  3. 13
  4. 14
  5. 15

Question 7

A circle of radius 1 rolls without slipping along a straight line from K to L, where $KL=11\pi$. Which is its final appearance at L?

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

Question 8

Martin has won 9 of 15 chess games. Five games remain. What is his season success rate if he wins all five?
  1. 60%
  2. 65%
  3. 70%
  4. 75%
  5. 80%

Question 9

One eighth of wedding guests are children. Three sevenths of adult guests are men. What fraction of all guests are women?
  1. $1/2$
  2. $1/3$
  3. $1/5$
  4. $1/7$
  5. $3/7$

Question 10

A box has 203 red, 117 white and 28 blue buttons. Students each take one without looking. How many students must take a button to guarantee at least three of the same colour?
  1. 3
  2. 6
  3. 7
  4. 28
  5. 203

Question 11

In trapezoid ABCD, $AB\parallel CD$, $AB=50$, $CD=20$. E is on AB and DE divides the trapezoid into two equal areas as shown. Find AE.

Question illustration
  1. 25
  2. 30
  3. 35
  4. 40
  5. 45

Question 12

How many natural numbers A have exactly one of A and A+20 being a four-digit number?
  1. 19
  2. 20
  3. 38
  4. 39
  5. 40

Question 13

From the side midpoints of an equilateral triangle, six perpendiculars to its sides are drawn as shown. What fraction of the original triangle is covered by the resulting shaded hexagon?

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

Question 14

The squares of three consecutive positive integers sum to 770. What is the largest integer?
  1. 15
  2. 16
  3. 17
  4. 18
  5. 19

Question 15

A belt drive has wheels A, B, C rotating without slippage. B turns 4 full rounds when A turns 5; B turns 6 rounds when C turns 7. If C has perimeter 30 cm, find A’s perimeter.

Question illustration
  1. 27 cm
  2. 28 cm
  3. 29 cm
  4. 30 cm
  5. 31 cm

Question 16

Tycho jogs on the same three days of the week every week for the coming months, never on consecutive days. How many weekly schedules can he choose?
  1. 6
  2. 7
  3. 9
  4. 10
  5. 35

Question 17

Four brothers have distinct heights. Tobias is shorter than Victor by the same amount that he is taller than Peter; Oscar is shorter than Peter by that amount too. Tobias is 184 cm and their mean is 178 cm. How tall is Oscar?
  1. 160 cm
  2. 166 cm
  3. 172 cm
  4. 184 cm
  5. 190 cm

Question 18

It rained 7 times during a holiday. A rainy morning had a sunny afternoon; a rainy afternoon had a sunny morning. There were 5 sunny mornings and 6 sunny afternoons. How many days did the holiday last?
  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 19

Jenny fills a 3×3 table so all four 2×2 squares have equal sums. Three corner entries are given. What must be in the fourth corner ?

Question illustration
  1. 5
  2. 4
  3. 1
  4. 0
  5. impossible to determine

Question 20

Seven natural numbers a,b,c,d,e,f,g are in a row. Their sum is 2017 and every adjacent pair differs by 1. Which positions can equal 286?
  1. only a or g
  2. only b or f
  3. only c or e
  4. only d
  5. any of them