Problem 1
Of the 84 tokens, half were distributed to the players. A third of the remaining ones were put in a box. How many tokens are left on the table?
3 points
Grade 3 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 40 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 flower bed is 12 m long and 7 m wide. How many meters of tape are needed to encircle it with one closed contour?
3 points
Problem 3
For the school stage, choose one of three decorations, one of two curtain colors and one of four lanterns. How many different designs are possible?
3 points
Problem 4
The sequence begins with the numbers 2, 5, 11, 23. Each time the previous number is doubled and 1 is added. What number is next?
3 points
Problem 5
Katya had 72 stickers. She gave a quarter of all the stickers to her sister and a sixth of all the stickers to her friend. How many stickers are left?
4 points
Problem 6
Five friends met and each shook hands with each other exactly once. How many handshakes were there in total?
4 points
Problem 7
A series of numbers is given: 3, 7, 15, 31. Each new number is obtained according to one rule. What number should come next?
4 points
Problem 8
A class bought four notebooks at 125 tenge each and three pens at 80 tenge each. How many tenge did the entire purchase cost?
4 points
Problem 9
A school schedule has four 45-minute lessons and three 10-minute breaks. How many minutes do the lessons and breaks take altogether?
4 points
Problem 10
In a two-digit number, the tens digit is 3 more than the units digit, and the sum of the digits is 11. What number is this?
5 points
Problem 11
For a performance, choose one of 4 shirts, one of 3 pairs of trousers, and one of 2 hats. How many outfits are possible?
5 points
Problem 12
A rectangle has an area of 144 square centimeters and a length of 16 centimeters. What is its perimeter?
5 points
Answer key and solutions
Problem 1. Answer: 28 · 3 points
After half are distributed, 42 tokens remain. One third of 42 is 14, so 28 tokens stay on the table.
Problem 2. Answer: 38 · 3 points
We need a perimeter: two lengths and two widths, a total of 38 meters.
Problem 3. Answer: 24 · 3 points
Each choice of decoration can be combined with 2 curtain colors and 4 lanterns: 3 × 2 × 4 = 24 designs.
Problem 4. Answer: 47 · 3 points
After 23, according to the rule, we get 23 × 2 + 1 = 47.
Problem 5. Answer: 42 · 4 points
A quarter of 72 is 18, a sixth is 12. That leaves 72 − 18 − 12 = 42 stickers.
Problem 6. Answer: 10 · 4 points
The first one shook hands with four, the next one shook hands with three new friends, then two and one. Total 4 + 3 + 2 + 1 = 10.
Problem 7. Answer: 63 · 4 points
The previous number is doubled each time and 1 is added. After 31 we get 31 × 2 + 1 = 63.
Problem 8. Answer: 740 · 4 points
Notebooks cost 4 × 125 = 500 tenge, pens - 3 × 80 = 240 tenge. Together 740 tenge.
Problem 9. Answer: 210 · 4 points
The lessons take 4 × 45 = 180 minutes, and the breaks take 3 × 10 = 30 minutes. The total is 210 minutes.
Problem 10. Answer: 74 · 5 points
Suitable digits are 7 and 4: their sum is 11 and their difference is 3. The result is 74.
Problem 11. Answer: 24 · 5 points
For every shirt there are 3 trouser choices and 2 hats. That gives 4 × 3 × 2 = 24 outfits.
Problem 12. Answer: 50 · 5 points
The width is 144 ÷ 16 = 9 centimeters. The perimeter is 2 × (16 + 9) = 50 centimeters.