Berikut ini adalah soal beserta kunci jawaban Fermat Mathematic Olympiad (FMO) 2021 grade 9 (Sc: Edukultur Indonesia)
A. Warm-up
(4 points per question / No points deducted for wrong answers)
1. The grid below has symbols with its own value. The number at the end of each row or each column is the sums of all figures’ values for that row or column. Can you find the value of the rectangle?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer : B
2. One morning, Tom bought a new clock and set it correctly to 08:30. However, John’s clock moves 4 minutes faster every hour than a normal clock. What time would it show at 13:30 of the next day?
A) 15:26
B) 11:34
C) 13:50
D) 13:10
E) 15:36
Answer : A
3. Jimmy has a square piece of paper. He folds it twice along the dashed lines and cuts the paper as in the picture below. How many pieces will he get after opening it?
A) 13
B) 12
C) 16
D) 10
E) 9
Answer : E
4. A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Carla picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks
A) 13
B) 11
C) 8
D) 6
E) 5
Answer : D
5. Linda draws five squares so that one side of each square coincides with one side of the given pentagon. Find the sum of all grey angles.
A) 360º
B) 180º
C) 300º
D) 320º
E) 540º
Answer : A
B. Speed-up
(6 points per question / No points deducted for wrong answers)
6. Annie wants to fill each cell with a number so that the sum of the numbers in all \(2\times2\) squares are the same. Which number should be filled into the top left corner?
A) 1
B) 9
C) 15
D) 8
E) None of the above
Answer : B
7. Jane spends exactly $190 on three types of cakes. A cupcake costs $2 each. A coconut cake costs $9 each. A chocolate cake costs £12 each. She buys twenty cakes in total, including at least one of each type. How many cupcakes did she buy?
A) 1
B) 2
C) 10
D) 8
E) 18
Answer : B
8. As planned, a factory needs to produce 280 shirts in a given time. However, the
factory makes 1 more shirt each day compared to the plan. Therefore, the factory
finishes 5 day before the schedule. How many days does the factory need to complete the task in reality?
A) 33
B) 37
C) 36
D) 35
E) 34
Answer : D
9. A cow is tied at one corner of a barn by a 14 meter rope as shown below. The barn is 12 meters long and 10 meters wide. How wide in square meters can the cow graze?
A) 147π
B) 152π
C) 288π
D) 196π
E) None of the above
Answer : B
10. Amy needs 3 matches to build a tower with one level, 9 matches to build a tower with 2 levels and 18 matches to build a tower with 3 levels. If she needs exactly 234 matches to build a tower with the given pattern, how many layers does it have?
A) 9
B) 10
C) 11
D) 12
E) 13
Answer : D
C. Challenge
(8 points per question / No points deducted for wrong answers)
11. Each letter is a distinct digit. Find the value of G + A + M + E + S.
A) 23
B) 24
C) 25
D) 26
E) 27
Answer : C
12. Fred wants to put 7 identical cubes into a tank with base 15cm x 10cm and a water level of 4cm. At most how high can the water level reach?
A) 7.8cm
B) 5.8cm
C) 4.8cm
D) 9.8cm
E) 8.8cm
Answer : D
13. Oliver did a road trip and passed through 5 paths A, B, C, D, E with a total time of 2 hours. The time and length of each path is recorded in the diagram with equally-spaced lines below. Find his fastest speed given that his average speed of the whole journey is 37.8km/h.
A) 68km/h
B) 64km/h
C) 60km/h
D) 72km/h
E) 54km/h
Answer : C
14. Isabella uses one of 4 colors: red, green, blue and yellow to paint each of the unit square below. Given that any two squares touching each other cannot have the same color. In how many different ways can Isabella do that?
A) 1056
B) 864
C) 1536
D) 1728
E) None of the above
Answer : A
15. The square below is composed of 4 equilateral triangles, 4 isosceles triangle and 1 small square. What is the ratio of the area of the big square to the small square?
A) \( 2 + \sqrt 3\)
B) \(\sqrt 2 + \sqrt 3 \)
C) \( 1 + \sqrt 3\)
D) \( 2 + \sqrt 2\)
E) \( 3 + \sqrt 2\)
Answer : A
D. Star of hope
(10 points per question/ 10 points deducted for wrong answer)
In this part, you must write your answer on the answer sheet.
16. A rectangular paper ABCD with dimension 5cm x 50cm is red on one side and yellow on the other. Henry folds the paper so that vertex B coincides with the midpoint of the side CD and vertex C coincides with the midpoint of the side AB. What is the area (in cm2) of the visible yellow part of the paper after folding?
Answer : 125
