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IKMC 2021 - Grades 9-10 - Self-study

Question 1

Each year, the third Thursday in March is Kangaroo Day. The following dates for the next few years contain one error. Which date is wrong?
  1. 17/3/2022
  2. 16/3/2023
  3. 14/3/2024
  4. 20/3/2025
  5. 19/3/2026

Question 2

Jenny’s weather app predicts the weather and maximum temperatures for the next five days, as shown. Which graph represents the maximum temperatures?

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Question 3

A park is an equilateral triangle. A cat walks from the upper corner to the lower-right corner along one of the three thick paths P, Q, R. Which comparison of their lengths is true?

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  1. P < Q < R
  2. P < R < Q
  3. P < Q = R
  4. P = R < Q
  5. P = Q = R

Question 4

Six rectangles are arranged as shown. The upper-left rectangle has height 6 cm. The numbers inside are areas in cm². What is the height of the bottom-right rectangle?

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  1. 4 cm
  2. 5 cm
  3. 6 cm
  4. 7.5 cm
  5. 10 cm

Question 5

The halftime score of a handball match was 9:14, with the visiting team leading by five goals. In the second half the home team scored twice as many goals as its opponents. The home team won by one goal. What was the final score?
  1. 20:19
  2. 21:20
  3. 22:21
  4. 23:22
  5. 24:23

Question 6

In a jazz band, Giuseppe plays saxophone, Sergio trumpet, and Eliana sings. These three are the same age. The other three members are 19, 20 and 21. The average age of the band is 21. How old is Eliana?
  1. 20
  2. 21
  3. 22
  4. 23
  5. 24

Question 7

Six congruent rhombuses, each of area 5 cm², form a star. Its tips are joined to form the regular hexagon shown. What is the hexagon’s area?

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  1. 36 cm²
  2. 40 cm²
  3. 45 cm²
  4. 48 cm²
  5. 60 cm²

Question 8

A rectangle of perimeter 30 cm is divided into four parts by one vertical and one horizontal line. One part is a square of area 9 cm², as shown. What is the perimeter of rectangle ABCD?

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  1. 14 cm
  2. 16 cm
  3. 18 cm
  4. 21 cm
  5. 24 cm

Question 9

Ally drew three triangles on a grid. Exactly two have equal area, exactly two are isosceles, and exactly two are right-angled. Two are shown. Which could be the third?

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Question 10

A little kangaroo chooses a number. Subtracting 1/10 from it gives the same result as multiplying it by 1/10. What is the number?
  1. $1/100$
  2. $1/11$
  3. $1/10$
  4. $11/100$
  5. $1/9$

Question 11

Tom has ten identical sparklers. He lights the first, then lights each next sparkler when only one tenth of the previous one remains. They burn uniformly along their length, and each lasts 2 minutes. How long until all ten have burned down?
  1. 18 min 20 sec
  2. 18 min 12 sec
  3. 18 min
  4. 17 min
  5. 16 min 40 sec

Question 12

Ahmad climbs eight steps, taking one or two steps at a time. The sixth step has a hole and may not be used. In how many ways can he reach the top?
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10

Question 13

The numbers 1 to 6 are placed in the six circles at the intersections of three rings. The position of 6 is shown. The sums on all three rings are equal. Which number is at the question mark?

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  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 14

2021 leaves remainder 5 when divided by 6, 7, 8 or 9. How many smaller positive integers have this same property?
  1. 4
  2. 3
  3. 2
  4. 1
  5. 0

Question 15

The figure shows a semicircle with centre O. Two angles are given. What is angle α, in degrees?

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  1. 9°
  2. 11°
  3. 16°
  4. 17.5°
  5. 18°

Question 16

Five teams await the start of a competition. Each team consists entirely of boys or entirely of girls, with sizes 9, 15, 17, 19, 21. After one whole team starts, the girls still waiting are three times as numerous as the boys still waiting. How large was the team that started?
  1. 9
  2. 15
  3. 17
  4. 19
  5. 21

Question 17

Five cars start in the order in the first picture and finish in the order in the second. One point is awarded whenever a car overtakes another. What is the smallest possible total number of points?

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  1. 10
  2. 9
  3. 8
  4. 7
  5. 6

Question 18

A 3 × 3 grid starts with zero in each cell. Each operation adds 1 to all four cells of a chosen 2 × 2 subsquare. After several operations, some resulting numbers are hidden as shown. What is the number at the question mark?

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  1. 14
  2. 15
  3. 16
  4. 17
  5. 19

Question 19

What is the sum of the six marked angles in the picture?

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  1. 360°
  2. 900°
  3. 1080°
  4. 1120°
  5. 1440°

Question 20

Eight boxes form a strip. Adjacent pairs have sums a or a+1 as indicated. The first and eighth entries are both 2021. What is a?

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  1. 4041
  2. 4042
  3. 4043
  4. 4044
  5. 4045