# GRADE 7 – SAMPEL PAPER FINAL FMO 2021

Berikut ini adalah soal beserta kunci jawaban Fermat Mathematic Olympiad (FMO) 2021 grade 7 (Sc: Edukultur Indonesia)

A. Warm-up
(4 points per question / No points deducted for wrong answers)

1. Andrew starts working on his project at 7:50 in the morning. By 10:20, he has done $$\frac{2}{3}$$ of his project. Then he rests for 45 minutes and continues to work at the same rate. At what time will he finish his project?
A) 11:20
B) 12:20
C) 12:25
D) 11:45
E) 12:45

2. Jack has a square piece of paper. He folds it in half twice and cuts out some shapes as instructed below. How many pieces will he get after cutting?

A) 3
B) 4
C) 5
D) 8
E) 12

3. Jane has a math lesson twice a week and John has a math lesson once every two weeks. In a term, John has 21 fewer lessons than Jane. How many weeks long is their term?
A) 17
B) 21
C) 18
D) 12
E) 14

4. Grade 6A went on a school trip to a water park. The bus went 2km straight, then turned right and kept going for 4km. Then they turn left and went 3km straight. Finally, they went 8km forward until they reached the destination. Find the short distance between the school and the water park.

A) 13km
B) 17km
C) 14km
D) 15km
E) 16km

5. Each letter is a non-zero digit. Find the value of $$F+M+O$$.

A) 6
B) 11
C) 7
D) 8
E) 9

B. Speed-up
(6 points per question / No points deducted for wrong answers)

6. In my street there are 50 houses. On the even side, the houses are numbered 2, 4, 6, and so on. On the odd side, the houses are numbered 1, 3, 5, and so on. I live in the last house on the even side, which is number 48. My friend lives in the last house on the odd side. What is the number of my friend’s house?
A) 45
B) 47
C) 49
D) 51
E) 53

7. Given the rectangle ABFG with ABC = 10º, BCD = 21º, DEF = 23º, EFG = 16º. Find the size of CDE.

A) 17º
B) 18º
C) 19º
D) 20º
E) 21º

8. Jane needs 3 matches to build one layer, 9 matches to build 2 layers and 18 matches to build 3 layers. How many matches are needed to build a shape with 8 layers?

A) 102
B) 100
C) 108
D) 105
E) 111

9. Given three balances below. Find the weight of one plant.

A) 400g
B) 200g
C) 180g
D) 360g
E) 150g

10. Candace stacked 5 boxes of side length 4cm to build the shape below. She painted all surfaces of the shape (except the bottom). Find the total unpainted area in cm².

A) 224
B) 160
C) 256
D) 96
E) 80

C. Challenge
(8 points per question / No points deducted for wrong answers)

11. Given the square ABCD with side length 30cm and 2 circles with center B and C intersecting at M. Find the area of the white region in cm². (Take$$\pi$$ = 3.14)

A) 456
B) 417
C) 492
D) 471
E) 429

12. Lucy and Linda joined a math test. Each of them is given the same list of 40
questions. For each question, the first of them to solve it gets 4 points and the
second to solve it gets 1 point. Lucy solved 20 questions and Linda solved 30
questions. Linda found that they got 146 points altogether. How many questions
were solved by both of them?
A) 18
B) 22
C) 20
D) 16
E) 12

13. A snail can move up or move right to the adjacent cell. Given that it cannot pass through the red walls, in how many different ways can it reach the leaf?
A) 26
B) 27
C) 28
D) 29
E) 30

14.The graph below shows Clover’s distance from home. She first goes to a grocery store to buy some food. Then she goes to the park. But it starts raining so she rushes back to her grandparent’s house. Finally, she rides bicycle to the bookstore and rides back home. Given the average speed of Clover during the whole trip is 8km/hour. How long does she stay at her grandparent’s house?
A) 9 min
B) 10 min
C) 18 min
D) 20 min
E) None of the above

15. Andrea folds 4 identical nets as below to get 4 cubes. She then combines them to form one block such that only faces with the same number can touch each other. What is the largest sum of all numbers on the surface of the block?

A) 76
B) 74
C) 72
D) 66
E) 68

16. How many pairs of unit squares in a $$3\times6$$ table are such that they have no common points? The diagram below shows one such pair.