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In problems 1-2, reduce each fraction to its simplest form. Add both digits of the numerator and the denominator. (For
example, if the fraction is (^) ๎ญ๎ถ๎ต^ , then write
the final answer as ๎ต ๎ ๎ถ ๎ ๎ธ.)
1. (^) ๎ญ๎ผ๎น๎ธ๎น 2. (^) ๎ญ๎ด๎ท๎ถ๎บ๎ป
In problems 3-19, solve the calculation into its simplest form as a proper fraction or a mixed number. Write the numerator of the fraction as your answer. (For example, if the answer is
๎ถ๎ญ๎ด๎ฝ๎น^ , make ๎ท๎ญ๎ถ๎ต^ and write the final
answer as ๎ต.)
3. ๎ต๎ญ๎ป๎ถ ๎ ๎ด๎ญ๎น๎ด 4. ๎ถ๎ญ๎ผ๎ป ๎ ๎ต๎ญ๎ต๎ด๎ป 5. ๎น๎ญ๎ธ๎ต ๎ ๎ด๎ญ๎ด๎ธ๎ด๎ด 6. ๎น๎ญ๎ด๎ต๎ด^ ๎ ๎ท๎ญ๎ด๎น๎ด๎ด
โป You can receive 1.5 points each for problems number 1 to 30.
7. ๎ญ๎ธ๎ถ ๎^ ๎๎ญ๎ต๎ด ๎ ๎ญ๎ถ๎ด^ ๎
8. ๎ท๎ญ๎ท๎ด ๎ ๎ถ๎ญ๎ด๎น๎บ^ ๎ ๎ถ๎ญ๎ป๎ถ 9. ๎ท๎ญ๎ป๎ถ ร ๎ด๎ญ๎บ๎ต 10. ๎ฝ๎๎ธ๎ท ร ๎ท๎ญ๎ผ๎ท 11. ๎ต๎ญ๎ป๎ธ ร ๎ญ๎บ๎ธ^ ร ๎ด๎ญ๎ผ๎ธ 12. ๎ฝ๎๎ถ๎น ร ๎ญ๎ผ๎ท ร ๎ญ๎ป๎บ 13. ๎ถ๎ญ๎ผ๎ด รท ๎ญ๎ด๎ธ๎ป 14. ๎บ๎ญ๎ธ๎ด รท ๎ผ๎๎น
21. (^) ๎น ๎ ๎ถ
ร ๎ต ๎ ๎น
22. (^) ๎ต ๎ ๎บ
ร ๎ฝ ๎ ๎บ ๎ธ
In problems 23-24, calculate the quotient up to the hundredths place and write the remainder. Then, add the quotient and the remainder. Write the decimal part of this number as your answer (For example, if the quotient is ๎ต๎๎ธ๎น and the remainder is ๎ฝ๎๎ฝ๎ฝ๎ท, calculate ๎ต๎๎ธ๎น ๎ ๎ฝ๎๎ฝ๎ฝ๎ท ๎ ๎ต๎๎ธ๎น๎ท, and write the final answer as ๎ธ๎น๎ท.)
23. ๎น ๎ ๎ท ๎ธ ๎ ๎น ๎ท
24.
In problems 25-26, solve each equation as a mixed number in its simplest form. Then add the numerator and the denominator of the mixed number. (For example, if the answer is ๎ท๎ญ๎ถ๎ต^ , write down the final answer as ๎ต ๎ ๎ถ ๎ ๎ธ.)
25. ๎๎ผ รท ๎ญ๎บ๎น^ ๎
ร ๎ญ๎ต๎น๎ผ^ ๎ ๎ด๎ญ๎ด๎ถ๎ด๎ต
26. ๎ต๎๎ป ๎ ๎ผ ๎ ๎ด๎ญ๎ท๎ถ^ ๎ ๎ต๎ญ๎น๎ด
In problems 27-28, solve each question.
27. ๎ ๎ด๎ด ๎ ๎๎ ๎ผ ๎ ๎ ๎ถ ๎ ๎ป๎
๎
๎ ๎ด๎น
28. ๎ต๎ญ๎ป๎ธ ร ๎๎ ๎ต๎ญ๎ผ๎บ^ ๎
รท ๎๎ ๎ธ๎
ร ๎ท๎ญ๎ธ๎ท^ รท ๎๎ ๎ฝ๎๎บ๎
29. What is ten times the perimeter of the shaded area? (๎ฌ ๎ ๎ถ๎๎ด๎ท)
cm
30. (^) Find the height of a cylinder with the given surface area. (๎ฌ ๎ ๎ถ๎๎ด๎ท)
Surface area = ๎ท๎ฝ๎ป๎๎ต cm๎ต
cm
34. Oliver bought ๎ถ ๎ญ๎ต๎ด^ L of disinfectant. He used (^) ๎ญ๎ถ๎ต^ L the first day and
๎ญ๎ธ
๎ต (^) L the next day. How much disinfectant is left? If the answer is
A ๎ญBC^ L, write the sum A ๎ B ๎ C.(Note that (^) ๎ญBC^ is an irreducible fraction and C ๎ B.)
35. Jessica had some crackers. She gave (^) ๎ญ๎บ๎ท^ of the crackers to her
brother after eating (^) ๎ญ๎ผ๎ต^ of them. If Jessica has ๎ต๎ด crackers remaining, how many crackers did Jessica first have?
crackers
36. Marina, Thompson, and Violet were cycling. Marina cycled for (^) ๎ญ๎ธ๎ต
hours, Thompson for ๎ต๎ธ minutes, and Violet for ๎ด๎ถ๎ต๎ฝ seconds. Among the three people, what was the shortest time cycling in minutes?
minutes
37. Tyler saves ๎ถ๎ฝ percent of what he earns. If he earned ๎๎บ๎ป on the first day and ๎๎ผ๎ต on the second day, how much did he save in these two days?
38. Mary has a cylindrical can. When the radius of this can is ๎ธ cm and the height is ๎ธ cm, what is the surface area of the can? ๎๎ฌ ๎ ๎ถ๎๎ด๎ท๎
cm ๎ต
41. In the following figures, circles were arranged according to a certain rule. How many circles should be arranged in the fourth figure? [2.3 points]
Answer : circles
42. The numbers in each row are arranged following the same mathematical rule. Find the sum of A^ and B. [2.3 points]
Answer :
43. How many natural numbers should be placed in the shaded area in the Venn diagram shown below? [3.3 points]
Answer :
44. Which pair of figures is a correct rotation of ๎ด๎ป๎ฝ๎ about the given point of symmetry. [3.3 points]
โ โก โข โฃ
Answer :
A: positive divisors of 42 B: positive divisors of 72
47. You can select three cards from the following five cards ๎ถ , ๎ท ,
๎ธ , ๎น , ๎บ , and complete the multiplication below. A^ is a ๎ถ-digit number. When you do not consider the order of the three numbers, how many unique calculations of A^ are possible? [4.3 points]
ร ร ๎ A
Answer :
48. The example shows that there are ๎น ways to place blocks ( ) in
๎ท empty boxes ( ). Find the number of ways to place blocks
( ) in ๎น empty boxes( ). [4.3 points]
Example
Answer :
49. The following boxes show the division process of the ๎ถ-digit number ABB^ by the ๎ด-digit number C. The letters A, B^ and C^ are all different, and C is not zero. Find the value of A ๎ B ๎ C. [4. points]
Answer :
50. You should fill the following box with all natural numbers from (^) ๎ด to ๎ผ. The product of the numbers in each column is written underneath the table and the sum of the numbers in each row is written on the right, outside the table. What is the ๎ถ-digit number ABC? [4.3 points]
Answer :
