Problem 1
An after-school club prepared 26 pencils. Four boxes held five pencils each. How many pencils were left outside the boxes?
3 points
Grade 2 math olympiad mock test
Twelve original problems progress from easier to harder. Complete the set within the suggested time, then review the worked solutions.
This is an independent original MozgoQuest set, not official material from any competition organizer.
How to take the test
- Set aside 35 minutes and work without hints.
- Write an answer for every problem and mark any problem you want to revisit.
- When time is up, open the answer key and award the points shown.
Name: ____________________ Date: ____________________
Select the button or use Ctrl+P. You can also save the worksheet as a PDF from the print dialog.
Problem 2
A rectangular postcard has sides of 5 cm and 8 cm. How many centimeters is its perimeter?
3 points
Problem 3
In the calendar, Friday falls on the 4th. What date will it be on Friday in two weeks?
3 points
Problem 4
Ira, Oleg, and Maxim are standing in a line. Ira is ahead of Oleg, and Oleg is ahead of Maxim. What is Oleg’s position?
3 points
Problem 5
There are three different paths from the house to the park, and two from the park to the library. How many routes are there from home to the library through the park?
4 points
Problem 6
Lena had 100 tenge. She bought three pencils for 18 tenge each. How many tenge does Lena have left?
4 points
Problem 7
Forty-seven badges are arranged in packages of 6 badges. How many complete packages will there be?
4 points
Problem 8
A rectangular flower bed is 8 meters long and 5 meters wide. How many meters of edging are needed around it?
4 points
Problem 9
Continue the sequence: 3, 7, 12, 18. The added number increases by 1 each time. What comes next?
4 points
Problem 10
Continue the sequence 5, 9, 17, 33. Each number is obtained from the preceding number by the same rule. What number comes next?
5 points
Problem 11
Two identical cubes are glued together along one face. How many faces of the resulting solid remain on the outside?
5 points
Problem 12
Sasha had 200 rubles. He bought 2 albums for 47 rubles each and a brush for 35 rubles. How many rubles remained?
5 points
Answer key and solutions
Problem 1. Answer: 6 · 3 points
There are 20 pencils in the boxes, there are 6 left outside.
Problem 2. Answer: 26 · 3 points
A rectangle has two sides of 5 cm and two of 8 cm: 26 cm.
Problem 3. Answer: 18 · 3 points
There are 14 days in two weeks, so the next required date is the 18th.
Problem 4. Answer: 2 · 3 points
The only possible order is Ira, Oleg, Maxim. Oleg is second.
Problem 5. Answer: 6 · 4 points
Each of the first three tracks can be continued in two ways. Total 3 × 2 = 6 routes.
Problem 6. Answer: 46 · 4 points
Three pencils cost 3 × 18 = 54 tenge. After the purchase, 100 − 54 = 46 tenge remained.
Problem 7. Answer: 7 · 4 points
Seven packages hold 7 × 6 = 42 badges, with five badges left over. Therefore, there are 7 complete packages.
Problem 8. Answer: 26 · 4 points
We need the rectangle’s perimeter: 8 + 5 + 8 + 5 = 26 meters.
Problem 9. Answer: 25 · 4 points
The increases are 4, 5, and 6. The next increase is 7, so 18 + 7 = 25.
Problem 10. Answer: 65 · 5 points
Each number is doubled and then 1 is subtracted: 5 → 9 → 17 → 33. The next number is 33 × 2 − 1 = 65.
Problem 11. Answer: 10 · 5 points
Two cubes have 12 faces in total. The two glued faces are inside, leaving 10 faces on the outside.
Problem 12. Answer: 71 · 5 points
The 2 albums cost 2 × 47 = 94 rubles. With the brush, he spent 129 rubles, so 200 − 129 = 71 remained.