FMO – Grade 9

A. Warm-up
(4 points per question / No points deducted for wrong answers)
1. Jack 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) 5 B) 12 C) 7 D) 6 E) 9

2. The librarian found that for every 12 minutes, there is another student entering the
library. The students must leave after reading for 90 minutes. At most how many
students are still in the library when it is about to closed?

A) 4 B) 5 C) 6 D) 7 E) 8

3. There are 4 friends including Jane, Josh, Jack and Jill. They bought 9 different
shirts listed in the table below. Jane bought 2 shirts with the same price. Josh
bought the top three cheapest items. Jack had to pay 50 USD for all of his
shirts. Find the color and the size of Jill’s shirt.

A) White - L B) Grey - M C) Black - S D) Black - M E) Grey - L

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FERMAT Mathematical Olympiad Summer 2021
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4. What is the weight of the heaviest object?

A) 0.4 kg B) 0.8 kg C) 1.6 kg D) 1.2 kg E) 2 kg

5. The diagram shows a quadrilateral PQRS in which PQ and QR have the same length.
Also, PR bisects SPQ and the ratio of SPR to PRS is 2 : 3 . Given that PSR  110o .
How large is PQR ?

A) 124o B) 120o C) 114o D) 126o E) 110o

B. Speed-up
(6 points per question / No points deducted for wrong answers)
6. Given a table in which three squares have been filled with numbers. The remaining
squares need to be filled with numbers so that the sum of each row, each column and
each of the two diagonals are the same. Find the number in the cell with question mark.

20 22

28 ?
A) 6 B) 12 C) 8 D) 10 E) 14

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7. Given 3 circles externally tangent to each other with center A, B and C. If AB  7cm ;
AC  8cm and BC  9cm , what is the total area of these three circles?

A) 29 B) 48 C) 24 D) 50 E) 194

8. Each letter is a distinct digit. Find the value of A + P + P + L + E.

A) 11 B) 12 C) 13 D) 14 E) 15

9. Two friends start riding bike at the same time from A but they follow 2 different
paths as the figure below. Since their speed ratio is 3 : 4, they finally meet each other
at D which is 2km from C. Find the length of the shorter path from A to D.

A) 28km B) 16km C) 8km D) 6km E) 12km

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FERMAT Mathematical Olympiad Summer 2021
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10. While reading a book, Wendy reads one page more each day than the preceding day.
After 4 days, she has read 150 pages. In exactly 10 days, she finishes the book. How
many pages are there in this book?
A) 395 B) 405 C) 375 D) 410 E) 385

C. Challenge
(8 points per question / No points deducted for wrong answers)
11. Peter is putting 99 apples into boxes of two different sizes. A large box can hold 12
apples while a small box can hold 5 apples. All boxes must be full. How many boxes
will he need if this number must be greater than 10?

A) 15 B) 17 C) 12 D) 16 E) 14

12. 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 speed on path B given that the whole journey is 75.6km long.

A) 68km/h B) 64km/h C) 60km/h D) 72km/h E) 54km/h

13. A number is called “lucky” if it is divisible by 2 and all of the digits are different. When
swapping the first and the last digit, we get a new number which is still divisible by 2.
How many 4-digit “lucky” numbers are there?
A) 1600 B) 1120 C) 672 D) 1080 E) 864

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FERMAT Mathematical Olympiad Summer 2021
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14. 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) 10.8cm C) 4.8cm D) 9.8cm E) 8.8cm

15. Given a square paper with side length 20cm. Andy folded it as the figure below to get
a trapezium whose perimeter is 10cm less than the original square. Find the area (in
cm2) of the trapezium.

A) 150cm2 B) 250cm2 C) 350cm2 D) 280cm2 E) None of the above

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 hospital ward has 18 nurses working on three eight-hour shifts a day. During the
pandemic, these nurses work on the following conditions:
a. 13 nurses will report on the first shift
b. 8 nurses will report on the second shift
c. 6 nurses will report on the third shift
If each of the nurses must report at least one shift in a day, what is the greatest
possible number of nurses that must report in all three shifts?
_____________________________________________________________________
Congratulations!
This is the end of the test. Please review the answers carefully before submission.

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FERMAT Mathematical Olympiad Summer 2021
All materials on the test are copyrighted and owned by Fermat Education