Skip to content / Đến nội dung
ThichHocToan.com

IKMC 2027 - Grades 9-10 - Self-study SET 5 - Thematic Batch 3

Question 1

Sophie is 12 this year, and her mother is four times her age. How old was Sophie when her age was one tenth of her mother’s?

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

Question 2

Julia rolls three standard dice at random. What is the probability that one of the three top-face numbers equals the sum of the other two?

Question illustration
  1. 1/6
  2. 13/72
  3. 7/36
  4. 5/24
  5. 2/9

Question 3

Peter cycles daily. The number of minutes needed to travel 10 km at his average speed equals the numerical value of that speed in km/h. How long does he need to travel 50 km at that speed?

Question illustration
  1. 2 h 2 min 28 s
  2. 2 h 3 min 6 s
  3. 38 min 43 s
  4. 2 h 4 min 12 s
  5. 5 h

Question 4

Using the digits 1,3,5, Tom writes the six three-digit numbers with distinct digits. How many are prime?

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

Question 5

Seven people sit in a row. Each is either a fairy or a witch, and no three witches are consecutive. How many different type patterns are possible?

Question illustration
  1. 44
  2. 55
  3. 64
  4. 81
  5. 128

Question 6

The numbers A, B, C are 2,3,4 in some order. What is the smallest possible value of $A^{B^C}$?

Question illustration
  1. $2^{3^4}$
  2. $2^{4^3}$
  3. $3^{2^4}$
  4. $4^{2^3}$
  5. $4^{3^2}$

Question 7

The eight-digit positive integer $n=\overline{abcdefgh}$ is divisible by 11. Consider $k=\overline{hgfedcba}$, $l=\overline{efghabcd}$ and $m=\overline{adebcfgh}$. How many of k, l, m are divisible by 11?

Question illustration
  1. 0
  2. 1
  3. 2
  4. 3
  5. Depends on n

Question 8

How many reduced fractions lie strictly between 0 and 1 and have numerator plus denominator equal to 2021?

Question illustration
  1. 920
  2. 966
  3. 987
  4. 989
  5. 1931

Question 9

Alex says, “Most guests at this party are under 30.” Julia finds that this is false. Which statement must be true?

Question illustration
  1. Most guests are over 30.
  2. Most guests are at least 30.
  3. At least half the guests are at least 30.
  4. No guest is under 30.
  5. All guests are under 30.

Question 10

Points A, B, C lie on the square grid shown. Given AB=1 cm, find AC in centimetres.

Question illustration
  1. 1
  2. $\sqrt{29}/5$
  3. 7/5
  4. $2\sqrt5$
  5. $5\sqrt5/2$

Question 11

Maria visits Bolobala for 18 days. The park opens only on Tuesday, Saturday and Sunday. On which weekday should she begin her visit to have the most possible park visits?

Question illustration
  1. Monday
  2. Tuesday
  3. Friday
  4. Saturday
  5. Sunday

Question 12

The five rectangles in the diagram have identical dimensions. What is the slope of line AB?

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

Question 13

The diagram shows a cube of edge 1 m and a tetrahedron whose edges are face diagonals of the cube. By how many cubic metres does the cube’s volume exceed the tetrahedron’s?

Question illustration
  1. $\frac{1}{3}$
  2. $\frac{2}{5}$
  3. $\frac{1}{2}$
  4. $\frac{3}{5}$
  5. $\frac{2}{3}$

Question 14

A semicircle has centre O and the two marked angles shown. Find the angle marked with a question mark.

Question illustration
  1. 9°
  2. 11°
  3. 16°
  4. 35°
  5. 18°

Question 15

Tom and Sam run at constant speeds around a closed track, taking 4 and 5 minutes per lap respectively. They start together at the same point in opposite directions. How many times do they meet before first meeting again at their starting point?

Question illustration
  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 16

Alex fills the blank grid cells so that every row and every column has the same sum. What number belongs in the shaded cell?

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

Question 17

On one August day, people observe 100 meteors per hour. On average, how many seconds correspond to one meteor?

Question illustration
  1. 28 seconds
  2. 36 seconds
  3. 40 seconds
  4. 42 seconds
  5. 45 seconds

Question 18

Which listed number is closest to 17×0.3×20.16÷9999?

Question illustration
  1. 0.001
  2. 0.01
  3. 0.1
  4. 1
  5. 10

Question 19

Dividing 2021 by each of 6,7,8,9 leaves remainder 5. How many positive integers below 2021 have this same property?

Question illustration
  1. 0
  2. 2
  3. 4
  4. 6
  5. More than 6

Question 20

After fishing, Alex says: “I caught 22 fish; I caught 2 fewer than Bob; Tom caught 1 fewer than me.” Bob says: “Nobody caught more than me; Tom caught 25; the difference between my catch and Tom’s is 3.” Tom says: “I caught fewer than Alex; Alex caught 23; Bob caught 3 more than Alex.” Each person made exactly two true statements and one false statement. What were Alex’s, Bob’s and Tom’s catches, respectively?

Question illustration
  1. 22,23,24
  2. 22,21,25
  3. 23,25,22
  4. 23,22,26
  5. 24,23,22